Hallucination Detection Results

GSM_Symbolic

Judge Type: logic_based | Modes: hot, cot

400 questions 45 with issues ▼

COT

HOT

Questions Analyzed

200

With Issues

11.0% of questions

Total Issues Found

0.18 per question

Issue Type Distribution

calculation_error: 16logical_error: 21

Question Analysis

Question #199

1 issue

Full Question

Daphne and Olivia are sisters from Cairo who love collecting signatures from movie stars. During their spring break from school, the sisters spend every afternoon collecting signatures. After 3 weeks, Daphne and Olivia compare their autograph books, counting up the number of signatures each sister has collected. Daphne has 17 signatures in her book, and Olivia has 31. The sisters have 3 more weeks of spring break, and they decide they want to reach 120 signatures between them by the end of the break. However, during the remaining 3 weeks, Daphne is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Olivia decides to increase her weekly collection. How many signatures will Olivia need to collect per week to make sure they reach their goal?

Ground Truth Answer

Daphne and Olivia have already collected 17 + 31 signatures = 48 signatures. Since their goal is 120, they need to collect 120 - 48 signatures. 120 - 48 = 72 signatures. Since Daphne collects 5 per week, she'll collect 3 * 5 = 15. 72 - 15 = 57 remains for Olivia to collect in 3 weeks. So she has to collect 57 / 3 = 19 signatures per week. #### 19

Generated Answer

Here's how to solve this problem: 1. **Calculate Daphne's current weekly rate:** Daphne collected 17 signatures in 3 weeks, so her current rate is 17 / 3 signatures per week. 2. **Calculate Daphne's reduced weekly rate:** Her collection reduces by 5 per week, meaning she'll collect 17/3 - 5 = 17/3 - 15/3 = 2/3 signatures per week on the weekends. 3. **Calculate Daphne's total signatures in the next 3 weeks:** Over the next 3 weeks, she'll collect 2/3 * 3 = 2 signatures. 4. **Calculate Daphne's total signatures by the end of the break:** She currently has 17 and will collect 2 more, for a total of 17 + 2 = 19 signatures. 5. **Calculate the remaining signatures needed:** They want 120 total, and Daphne will have 19, so Olivia needs to collect 120 - 19 = 101 signatures. 6. **Calculate Olivia's current total signatures:** Olivia currently has 31 signatures. 7. **Calculate how many more signatures Olivia needs:** She needs 101 total and has 31, so she needs to collect an additional 101 - 31 = 70 signatures. 8. **Calculate Olivia's required weekly rate:** She has 3 weeks to collect 70 signatures, so she needs to collect 70 / 3 signatures per week. Answer: {70/3}

Overall Quality: poor

The reasoning chain fundamentally misunderstands how to apply the rate reduction constraint. It incorrectly calculates Daphne's past rate (17 signatures over 3 weeks) and uses that to determine her future rate, which leads to an incorrect total needed from Olivia (70 signatures needed over 3 weeks, resulting in 70/3 per week) instead of the correct required amount (57 signatures needed over 3 weeks, resulting in 19 per week).

Detected Issues (1)

calculation_error high

Statement

8. **Calculate Olivia's required weekly rate:** She has 3 weeks to collect 70 signatures, so she needs to collect 70 / 3 signatures per week.

Explanation

The calculation 70 / 3 is mathematically correct, but the final answer derived from this chain (70/3 ≈ 23.33) does not match the ground truth answer (19). This indicates a major deviation in the interpretation of the problem constraints, likely stemming from the initial logical error regarding Daphne's rate reduction.

Answer Span:

70 / 3

Question #201

1 issue

Full Question

Mei and Haruka are sisters from Singapore who love collecting signatures from politicians. During their summer break from school, the sisters spend every afternoon collecting signatures. After 5 weeks, Mei and Haruka compare their autograph books, counting up the number of signatures each sister has collected. Mei has 24 signatures in her book, and Haruka has 51. The sisters have 3 more weeks of summer break, and they decide they want to reach 135 signatures between them by the end of the break. However, during the remaining 3 weeks, Mei is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Haruka decides to increase her weekly collection. How many signatures will Haruka need to collect per week to make sure they reach their goal?

Ground Truth Answer

Mei and Haruka have already collected 24 + 51 signatures = 75 signatures. Since their goal is 135, they need to collect 135 - 75 signatures. 135 - 75 = 60 signatures. Since Mei collects 5 per week, she'll collect 3 * 5 = 15. 60 - 15 = 45 remains for Haruka to collect in 3 weeks. So she has to collect 45 / 3 = 15 signatures per week. #### 15

Generated Answer

Here's how to solve this problem: 1. **Calculate Mei's current weekly rate:** Mei collected 24 signatures in 5 weeks, so her current rate is 24 signatures / 5 weeks = 4.8 signatures per week. 2. **Calculate Mei's new weekly rate:** Mei collects 5 fewer signatures per week, meaning she now collects 4.8 - 5 = -0.2 signatures per week. Since she's only collecting on weekends, let's assume this represents her weekend collection and her weekday collection is 0. So effectively, she will not be adding any more signatures. 3. **Calculate Mei's total signatures at the end of summer:** Over the next 3 weeks, Mei collects 0 additional signatures. So her final total is 24 signatures + 0 signatures = 24 signatures. 4. **Calculate the number of signatures Haruka needs:** Their goal is 135 signatures. Mei will have 24, so Haruka needs to collect 135 - 24 = 111 signatures. 5. **Calculate the number of signatures Haruka has collected so far:** 51 6. **Calculate how many more signatures Haruka needs:** 111 - 51 = 60 signatures. 7. **Calculate Haruka's required weekly rate:** Haruka has 3 weeks to collect 60 signatures, so she needs to collect 60 signatures / 3 weeks = 20 signatures per week. Answer: {20}

Overall Quality: poor

The reasoning chain fails immediately by calculating an irrelevant historical rate (Step 1) and then misinterpreting the constraint about Mei's reduced collection rate (Step 2). Although the model coincidentally arrives at the correct conclusion that Mei collects 0 signatures over the next 3 weeks (Step 3), it does so through flawed logic and arithmetic based on the initial error. The subsequent steps (4 through 7) are mathematically sound based on the incorrect intermediate result of 0 for Mei's future collection, leading to the correct final answer of 20, but the core logic regarding Mei's future collection is flawed.

Detected Issues (1)

logical_error medium

Statement

Calculate Mei's current weekly rate: Mei collected 24 signatures in 5 weeks, so her current rate is 24 signatures / 5 weeks = 4.8 signatures per week.

Explanation

The problem states Mei has 24 signatures after 5 weeks, but it does not state that she collected them at a constant rate over those 5 weeks. Furthermore, the problem implies her collection rate *changes* for the remaining 3 weeks based on a reduction of 5 signatures per week from her *new* rate, not her historical rate. Calculating the historical rate is irrelevant and potentially misleading for determining future collection.

Answer Span:

Mei collected 24 signatures in 5 weeks, so her current rate is 24 signatures / 5 weeks = 4.8 signatures per week.

Reference/Question Span:

Mei has 24 signatures in her book, and Haruka has 51. The sisters have 3 more weeks of summer break, and they decide they want to reach 135 signatures between them by the end of the break. However, during the remaining 3 weeks, Mei is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

Question #198

3 issues

Full Question

Uma and Zahra are sisters from Marrakech who love collecting signatures from politicians. During their spring break from school, the sisters spend every afternoon collecting signatures. After 6 weeks, Uma and Zahra compare their autograph books, counting up the number of signatures each sister has collected. Uma has 29 signatures in her book, and Zahra has 37. The sisters have 4 more weeks of spring break, and they decide they want to reach 130 signatures between them by the end of the break. However, during the remaining 4 weeks, Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Zahra decides to increase her weekly collection. How many signatures will Zahra need to collect per week to make sure they reach their goal?

Ground Truth Answer

Uma and Zahra have already collected 29 + 37 signatures = 66 signatures. Since their goal is 130, they need to collect 130 - 66 signatures. 130 - 66 = 64 signatures. Since Uma collects 5 per week, she'll collect 4 * 5 = 20. 64 - 20 = 44 remains for Zahra to collect in 4 weeks. So she has to collect 44 / 4 = 11 signatures per week. #### 11

Generated Answer

Here's how to solve this problem: 1. **Calculate Uma's current weekly rate:** Uma collected 29 signatures in 6 weeks, so her current rate is 29 signatures / 6 weeks = 4.83 signatures/week. 2. **Calculate Uma's reduced weekly rate:** Uma's collection reduces by 5 signatures per week, so her new rate is 4.83 - 5 = -0.17 signatures/week. Since she can't collect negative signatures, this means she effectively collects 0 signatures during the weekdays of the remaining four weeks. 3. **Calculate Uma's weekend collection:** Uma's original weekly rate is approximately 4.83 signatures/week. Since there are two weekend days in a week, she collects approximately 4.83 * (2/7) = 1.38 signatures/week on weekends. Therefore in the remaining 4 weeks, she collects a total of 4 weeks * 1.38 = approximately 5.52 signatures. 4. **Calculate Uma's total signatures after 10 weeks:** Uma will therefore have a total of 29 (original amount) + 5.52 (new amount) = 34.52 signatures. Rounding to the nearest whole number, she will collect 35 signatures. 5. **Calculate the remaining signatures needed:** They want 130 total signatures, and Uma will have 35, leaving 130 - 35 = 95 signatures for Zahra to collect in the remaining 4 weeks. 6. **Calculate Zahra's required weekly rate:** Zahra needs to collect 95 signatures / 4 weeks = 23.75 signatures per week. Rounding to the nearest whole number, she needs to collect 24 signatures per week. Answer: {24}

Overall Quality: poor

The reasoning chain fundamentally misunderstands the initial state of the problem. It incorrectly calculates Uma's historical rate instead of using the current totals (29 and 37). It then uses complex and flawed logic to estimate Uma's future collection based on weekends, leading to an incorrect remaining signature count (95 instead of 81) and an incorrect final answer (24 instead of 11).

Detected Issues (3)

logical_error medium

Statement

2. **Calculate Uma's reduced weekly rate:** Uma's collection reduces by 5 signatures per week, so her new rate is 4.83 - 5 = -0.17 signatures/week.

Explanation

This step is based on the flawed premise of Step 1. Furthermore, the problem states Uma reduces her *weekly collection* by 5 signatures per week, not that her rate is reduced by 5 relative to her previous average rate. The ground truth implies that the constraint 'reducing her weekly collection by 5 per week' means her *new* collection rate is 5 signatures per week (as she only collects on weekends, and the ground truth implies a fixed rate of 5 per week for Uma in the remaining time, likely based on an interpretation that her *original* rate was higher, or that the reduction means her new weekend rate is 5/week, which is inconsistent with the ground truth calculation of 4 weeks * 5 signatures/week = 20). Given the ambiguity, the interpretation used here (rate reduction) is highly speculative and deviates significantly from the simple calculation implied by the ground truth (Uma collects 4 * 5 = 20 total in the remaining 4 weeks).

Answer Span:

Uma's collection reduces by 5 signatures per week, so her new rate is 4.83 - 5 = -0.17 signatures/week.

Reference/Question Span:

Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

logical_error high

Statement

3. **Calculate Uma's weekend collection:** Uma's original weekly rate is approximately 4.83 signatures/week. Since there are two weekend days in a week, she collects approximately 4.83 * (2/7) = 1.38 signatures/week on weekends. Therefore in the remaining 4 weeks, she collects a total of 4 weeks * 1.38 = approximately 5.52 signatures.

Explanation

This step attempts to calculate a weekend rate based on the flawed average rate from Step 1, which is unnecessary and complex. The ground truth implies a much simpler interpretation: Uma collects 5 signatures per week for the remaining 4 weeks, totaling 20 signatures.

Answer Span:

Uma's original weekly rate is approximately 4.83 signatures/week. Since there are two weekend days in a week, she collects approximately 4.83 * (2/7) = 1.38 signatures/week on weekends. Therefore in the remaining 4 weeks, she collects a total of 4 weeks * 1.38 = approximately 5.52 signatures.

Reference/Question Span:

Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

calculation_error medium

Statement

5. **Calculate the remaining signatures needed:** They want 130 total signatures, and Uma will have 35, leaving 130 - 35 = 95 signatures for Zahra to collect in the remaining 4 weeks.

Explanation

The subtraction 130 - 35 = 95 is mathematically correct, but the input value for Uma's total (35) is based on rounding from 34.52 (Step 4), which itself is based on flawed logic. If we follow the ground truth logic (Uma collects 20 more), the remaining needed is 130 - (29 + 20) = 130 - 49 = 81. If we follow the logic implied by the ground truth's calculation for Uma's contribution (20 signatures), the remaining needed is 130 - (29 + 20) = 81. The calculation 130 - 35 = 95 is arithmetically correct, but since the input (35) is derived from rounding errors stemming from earlier logical flaws, this step propagates the error.

Answer Span:

130 - 35 = 95

Question #203

1 issue

Full Question

Chen and Tara are sisters from Lisbon who love collecting signatures from politicians. During their winter break from school, the sisters spend every afternoon collecting signatures. After 5 weeks, Chen and Tara compare their autograph books, counting up the number of signatures each sister has collected. Chen has 36 signatures in her book, and Tara has 32. The sisters have 4 more weeks of winter break, and they decide they want to reach 140 signatures between them by the end of the break. However, during the remaining 4 weeks, Chen is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Tara decides to increase her weekly collection. How many signatures will Tara need to collect per week to make sure they reach their goal?

Ground Truth Answer

Chen and Tara have already collected 36 + 32 signatures = 68 signatures. Since their goal is 140, they need to collect 140 - 68 signatures. 140 - 68 = 72 signatures. Since Chen collects 5 per week, she'll collect 4 * 5 = 20. 72 - 20 = 52 remains for Tara to collect in 4 weeks. So she has to collect 52 / 4 = 13 signatures per week. #### 13

Generated Answer

Here's how to solve this problem: 1. **Calculate Chen's current weekly collection:** Chen collected 36 signatures in 5 weeks, so she collects 36 / 5 = 7.2 signatures per week. 2. **Calculate Chen's reduced weekly collection:** Chen's collection reduces by 5 signatures per week, meaning she will collect 7.2 - 5 = 2.2 signatures per week. 3. **Calculate Chen's collection in the remaining weeks:** Over 4 weeks, Chen will collect 2.2 signatures/week * 4 weeks = 8.8 signatures. Since signatures can't be fractional, we round down to 8 signatures assuming she can only increase her total by a whole number of signatures 4. **Calculate the total signatures Chen will have:** Chen currently has 36 signatures and will collect 8 more, for a total of 36 + 8 = 44 signatures. 5. **Calculate the remaining signatures Tara needs to collect:** They want 140 signatures total, and Chen will have 44, so Tara needs to collect 140 - 44 = 96 signatures. 6. **Calculate how many signatures Tara already has:** Tara currently has 32 signatures. 7. **Calculate how many more signatures Tara needs:** Tara needs 96 total and already has 32, meaning she needs to collect an additional 96 - 32 = 64 signatures. 8. **Calculate Tara's required weekly collection:** Tara has 4 weeks to collect 64 signatures, so she needs to collect 64 / 4 = 16 signatures per week. Answer: {16}

Overall Quality: poor

The reasoning chain makes significant logical errors by attempting to derive Chen's past weekly rate from the 36 signatures collected over 5 weeks and then applying the reduction to that derived rate. This leads to fractional signatures and unnecessary complexity. The correct approach, validated by the ground truth, is to use the current totals to find the remaining signatures needed (72) and then calculate Chen's contribution based on the rate implied by the ground truth (5 per week for 4 weeks = 20), which seems to be the intended interpretation of the confusing reduction clause.

Detected Issues (1)

logical_error medium

Statement

Chen collected 36 signatures in 5 weeks, so she collects 36 / 5 = 7.2 signatures per week.

Explanation

The problem states Chen has 36 signatures after 5 weeks, but it does not state that she collected them at a constant rate over those 5 weeks. Furthermore, the problem implies her *current* weekly rate is what is being reduced by 5, but the context of the reduction (weekends only) is only relevant for the *remaining* 4 weeks. Calculating an average rate from the past 5 weeks is an unnecessary and potentially misleading step, as the problem only gives us the total collected (36) and the total goal (140). The correct approach is to use the totals directly.

Answer Span:

Chen collected 36 signatures in 5 weeks, so she collects 36 / 5 = 7.2 signatures per week.

Reference/Question Span:

Chen has 36 signatures in her book, and Tara has 32. The sisters have 4 more weeks of winter break, and they decide they want to reach 140 signatures between them by the end of the break. However, during the remaining 4 weeks, Chen is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

Question #200

Clean

Full Question

Ava and Quinn are sisters from Helsinki who love collecting signatures from authors. During their spring break from school, the sisters spend every afternoon collecting signatures. After 3 weeks, Ava and Quinn compare their autograph books, counting up the number of signatures each sister has collected. Ava has 30 signatures in her book, and Quinn has 37. The sisters have 2 more weeks of spring break, and they decide they want to reach 135 signatures between them by the end of the break. However, during the remaining 2 weeks, Ava is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Quinn decides to increase her weekly collection. How many signatures will Quinn need to collect per week to make sure they reach their goal?

Ground Truth Answer

Ava and Quinn have already collected 30 + 37 signatures = 67 signatures. Since their goal is 135, they need to collect 135 - 67 signatures. 135 - 67 = 68 signatures. Since Ava collects 5 per week, she'll collect 2 * 5 = 10. 68 - 10 = 58 remains for Quinn to collect in 2 weeks. So she has to collect 58 / 2 = 29 signatures per week. #### 29

Generated Answer

Here's how to solve the problem: 1. **Calculate Ava's current weekly rate:** Ava collected 30 signatures in 3 weeks, so her current rate is 30 signatures / 3 weeks = 10 signatures/week. 2. **Calculate Ava's reduced weekly rate:** Ava collects 5 fewer signatures per week, so her new rate is 10 signatures/week - 5 signatures/week = 5 signatures/week. 3. **Calculate Ava's signatures in the remaining weeks:** Ava collects signatures for 2 more weeks, so she'll collect 5 signatures/week * 2 weeks= 10 signatures. 4. **Calculate Ava's total signatures:** Ava already has 30 signatures and will collect 10 more, for a total of 30 signatures + 10 signatures = 40 signatures. 5. **Calculate the remaining signatures needed:** The sisters want 135 signatures, and Ava will have 40, so they need 135 signatures - 40 signatures = 95 more signatures. 6. **Calculate Quinn's current total signatures:** Quinn currently has 37 signatures. 7. **Calculate how many more signatures Quinn needs:** Quinn needs to collect a total of 95 signatures - 37 signatures (her current total) = 58 signatures. 8. **Calculate Quinn's required weekly rate:** Quinn has 2 weeks to collect 58 signatures, so she needs to collect 58 signatures / 2 weeks = 29 signatures/week. Answer: {29}

Overall Quality: excellent

The reasoning chain correctly interprets the problem constraints and performs all arithmetic calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #202

2 issues

Full Question

Uma and Olga are sisters from Lisbon who love collecting signatures from politicians. During their summer break from school, the sisters spend every afternoon collecting signatures. After 3 weeks, Uma and Olga compare their autograph books, counting up the number of signatures each sister has collected. Uma has 25 signatures in her book, and Olga has 59. The sisters have 2 more weeks of summer break, and they decide they want to reach 140 signatures between them by the end of the break. However, during the remaining 2 weeks, Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Olga decides to increase her weekly collection. How many signatures will Olga need to collect per week to make sure they reach their goal?

Ground Truth Answer

Uma and Olga have already collected 25 + 59 signatures = 84 signatures. Since their goal is 140, they need to collect 140 - 84 signatures. 140 - 84 = 56 signatures. Since Uma collects 5 per week, she'll collect 2 * 5 = 10. 56 - 10 = 46 remains for Olga to collect in 2 weeks. So she has to collect 46 / 2 = 23 signatures per week. #### 23

Generated Answer

Here's how to solve the problem: 1. **Calculate Uma's current weekly rate:** Uma collected 25 signatures in 3 weeks, so her current rate is 25 signatures / 3 weeks = 8.33 signatures/week (approximately). 2. **Calculate Uma's reduced weekly rate:** Since Uma collects 5 fewer signatures per week during the last two weeks, her new rate is 8.33 - 5 = 3.33 signatures/week (approximately). 3. **Calculate Uma's signatures in the remaining 2 weeks:** Over the next two weeks, Uma will collect 3.33 signatures/week * 2 weeks = 6.66 signatures (approximately). Since we're talking about whole signatures, we'll round it down to 6 as an overestimate might lead to an incorrect final answer. 4. **Calculate the total signatures Uma will have:** Uma will have her current 25 signatures + 6 new signatures = 31 signatures. 5. **Calculate the remaining signatures needed:** They want 140 total signatures, and Uma will have 31, so Olga needs to collect 140 - 31 = 109 signatures. 6. **Calculate how many signatures Olga already has:** Olga currently has 59 signatures. 7. **Calculate how many more signatures Olga needs:** Olga needs 109 signatures and she has 59, so she needs to get 109 - 59 = 50 signatures. 8. **Calculate Olga's required weekly rate:** Olga has 2 weeks to collect the remaining 50 signatures. She must collect 50 signatures / 2 weeks = 25 signatures per week. Answer: {25}

Overall Quality: poor

The reasoning chain fails immediately by incorrectly calculating Uma's initial weekly rate based on the total collected (25 signatures in 3 weeks). This fundamental logical error forces subsequent steps to rely on flawed assumptions and arbitrary rounding, leading to an incorrect final answer (25 vs. 23).

Detected Issues (2)

logical_error high

Statement

Calculate Uma's current weekly rate: Uma collected 25 signatures in 3 weeks, so her current rate is 25 signatures / 3 weeks = 8.33 signatures/week (approximately).

Explanation

The problem states Uma collected 25 signatures in 3 weeks, but it does not state that this rate was constant or that the 25 signatures were collected *over* those 3 weeks. The crucial information missing is the rate at which Uma collected signatures *before* the last two weeks. The ground truth implies that the 25 signatures are the total collected so far (in 3 weeks), but the subsequent steps in the model assume this 25 signatures was collected at a constant rate over 3 weeks, which is an assumption not supported by the text and leads to incorrect subsequent calculations.

Answer Span:

Uma collected 25 signatures in 3 weeks, so her current rate is 25 signatures / 3 weeks = 8.33 signatures/week (approximately).

Reference/Question Span:

Uma has 25 signatures in her book

logical_error medium

Statement

Since we're talking about whole signatures, we'll round it down to 6 as an overestimate might lead to an incorrect final answer.

Explanation

This step introduces arbitrary rounding based on an incorrect intermediate calculation (6.66). If the initial rate calculation (Step 1) was correct, rounding down to 6 signatures collected over 2 weeks is an arbitrary decision that ignores the fractional part, which should ideally be carried through or handled based on the problem context (which usually implies rates are constant unless specified). However, since the entire premise of calculating the rate in Step 1 is flawed, this rounding compounds the error.

Answer Span:

we'll round it down to 6 as an overestimate might lead to an incorrect final answer.

Reference/Question Span:

Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

Question #47

Clean

Full Question

A farmer is buying feed for his alpacas. He buys a variety of apples, wheat, cucumbers and hay. Since hay are a rare treat, he only buys six 3-pound boxes of them for the whole stable. He only wants enough cucumbers to feed the alpacas while the vegetables are fresh, so he buys fifteen 8-pound bags. Apples are the main diet of his alpacas, so he buys thirty four 43-pound packs. Wheat are a staple to supplement the apples, so he buys eighteen 15-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 170 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items?

Ground Truth Answer

The farmer is buying 6 * 3 = 18 pounds of hay. He is buying 15 * 8 = 120 pounds of cucumbers. He is buying 18 * 15 = 270 pounds of wheat packs. He is buying 34 * 43 = 1462 pounds of apples sacks. He is buying 43 pounds of grocery + 27 pounds of tools + 100 pounds of wood = 170 pounds. The weight of all the feed is 18 + 120 + 270 + 1462 + 170 = 2040 pounds. Thus, the farmer needs 2040 / 170 = 12 trips to transport all the feed in a single farm truck. With three trucks, the farmer needs 12/3=4 #### 4

Generated Answer

First calculate the total weight of the hay: 6 boxes * 3 pounds/box = 18 pounds. Next, calculate the total weight of the cucumbers: 15 bags * 8 pounds/bag = 120 pounds. Then calculate the total weight of the apples: 34 packs * 43 pounds/pack = 1462 pounds. Now, calculate the total weight of the wheat: 18 sacks * 15 pounds/sack = 270 pounds. The total weight of the alpaca feed is 18 + 120 + 1462 + 270 = 1870 pounds. The total weight of the other items is 43 + 27 + 100 = 170 pounds. The total weight of all items purchased is 1870 + 170 = 2040 pounds. The combined carrying capacity of the three trucks is 3 trucks * 170 pounds/truck = 510 pounds. To find the number of trips needed, divide the total weight by the carrying capacity and round up to the nearest whole number: 2040 pounds / 510 pounds/trip = 4 trips. Answer: {4}

Overall Quality: good

The AI performed all initial weight calculations correctly and arrived at the correct total weight (2040 lbs). The final step regarding the number of trips contained a logical deviation from the structure implied by the ground truth (calculating combined capacity vs. calculating total trips and dividing by truck count), although the arithmetic performed in that step (2040 / 510 = 4) coincidentally yielded the correct final answer.

✓ No hallucinations detected

Question #46

Clean

Full Question

A farmer is buying feed for his sheep. He buys a variety of apples, wheat, carrots and oats. Since oats are a rare treat, he only buys eight 7-pound boxes of them for the whole stable. He only wants enough carrots to feed the sheep while the vegetables are fresh, so he buys twelve 6-pound bags. Apples are the main diet of his sheep, so he buys thirty two 43-pound packs. Wheat are a staple to supplement the apples, so he buys eighteen 17-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 110 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items?

Ground Truth Answer

The farmer is buying 8 * 7 = 56 pounds of oats. He is buying 12 * 6 = 72 pounds of carrots. He is buying 18 * 17 = 306 pounds of wheat packs. He is buying 32 * 43 = 1376 pounds of apples sacks. He is buying 43 pounds of grocery + 27 pounds of tools + 100 pounds of wood = 170 pounds. The weight of all the feed is 56 + 72 + 306 + 1376 + 170 = 1980 pounds. Thus, the farmer needs 1980 / 110 = 18 trips to transport all the feed in a single farm truck. With three trucks, the farmer needs 18/3=6 #### 6

Generated Answer

First, calculate the total weight of the oats: 8 boxes * 7 pounds/box = 56 pounds. Next, calculate the total weight of the carrots: 12 bags * 6 pounds/bag = 72 pounds. Then, calculate the total weight of the apples: 32 packs * 43 pounds/pack = 1376 pounds. Now, calculate the total weight of the wheat: 18 sacks * 17 pounds/sack = 306 pounds. Then, calculate the total weight of feed: 56 + 72 + 1376 + 306 = 1810 pounds. Now, calculate the total weight of all items: 1810 + 43 + 27 + 100 = 1980 pounds. Since each truck can carry 110 pounds, calculate the total carrying capacity of three trucks: 3 trucks * 110 pounds/truck = 330 pounds. Finally, calculate the number of trips needed: 1980 pounds / 330 pounds/trip = 6 trips. Answer: {6}

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item category, sums them up, and then correctly determines the number of trips required by dividing the total weight by the combined capacity of the three trucks. All arithmetic operations are correct.

✓ No hallucinations detected

Question #42

Clean

Full Question

A farmer is buying feed for his cows. He buys a variety of apples, hay, cucumbers and corn. Since corn are a rare treat, he only buys four 6-pound boxes of them for the whole stable. He only wants enough cucumbers to feed the cows while the vegetables are fresh, so he buys fourteen 8-pound bags. Apples are the main diet of his cows, so he buys thirty five 42-pound packs. Hay are a staple to supplement the apples, so he buys eighteen 18-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 140 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items?

Ground Truth Answer

The farmer is buying 4 * 6 = 24 pounds of corn. He is buying 14 * 8 = 112 pounds of cucumbers. He is buying 18 * 18 = 324 pounds of hay packs. He is buying 35 * 42 = 1470 pounds of apples sacks. He is buying 43 pounds of grocery + 27 pounds of tools + 100 pounds of wood = 170 pounds. The weight of all the feed is 24 + 112 + 324 + 1470 + 170 = 2100 pounds. Thus, the farmer needs 2100 / 140 = 15 trips to transport all the feed in a single farm truck. With three trucks, the farmer needs 15/3=5 #### 5

Generated Answer

First, calculate the total weight of each type of feed: * Corn: 4 boxes * 6 pounds/box = 24 pounds * Cucumbers: 14 bags * 8 pounds/bag = 112 pounds * Apples: 35 packs * 42 pounds/pack = 1470 pounds * Hay: 18 sacks * 18 pounds/sack = 324 pounds Now, calculate the total weight of all the feed: 24 + 112 + 1470 + 324 = 1930 pounds Next, add the weight of the groceries, tools, and wood: 1930 + 43 + 27 + 100 = 2100 pounds The farmer has three trucks, each carrying 140 pounds, so the total carrying capacity is: 3 trucks * 140 pounds/truck = 420 pounds Finally, divide the total weight by the total carrying capacity to find the number of trips needed: 2100 pounds / 420 pounds/trip = 5 trips Answer: {5}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem constraints, arriving at the correct answer.

✓ No hallucinations detected

Question #45

Clean

Full Question

A farmer is buying feed for his cows. He buys a variety of hay, wheat, carrots and apples. Since apples are a rare treat, he only buys five 7-pound boxes of them for the whole stable. He only wants enough carrots to feed the cows while the vegetables are fresh, so he buys fourteen 5-pound bags. Hay are the main diet of his cows, so he buys thirty five 44-pound packs. Wheat are a staple to supplement the hay, so he buys nineteen 15-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 100 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items?

Ground Truth Answer

The farmer is buying 5 * 7 = 35 pounds of apples. He is buying 14 * 5 = 70 pounds of carrots. He is buying 19 * 15 = 285 pounds of wheat packs. He is buying 35 * 44 = 1540 pounds of hay sacks. He is buying 43 pounds of grocery + 27 pounds of tools + 100 pounds of wood = 170 pounds. The weight of all the feed is 35 + 70 + 285 + 1540 + 170 = 2100 pounds. Thus, the farmer needs 2100 / 100 = 21 trips to transport all the feed in a single farm truck. With three trucks, the farmer needs 21/3=7 #### 7

Generated Answer

First, calculate the total weight of apples: 5 boxes * 7 pounds/box = 35 pounds. Next, calculate the total weight of carrots: 14 bags * 5 pounds/bag = 70 pounds. Then calculate the total weight of hay: 35 packs * 44 pounds/pack = 1540 pounds. Calculate the total weight of wheat: 19 sacks * 15 pounds/sack = 285 pounds. The total weight of feed is 35 + 70 + 1540 + 285 = 1930 pounds. Add the weight of groceries, tools, and wood: 1930 + 43 + 27 + 100 = 2100 pounds. Each truck can carry 100 pounds, and the farmer has three trucks, so in one trip, they can carry 3 * 100 = 300 pounds. To find the number of trips needed, divide the total weight by the weight carried per trip: 2100 pounds / 300 pounds/trip = 7 trips. Answer: {7}

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item, sums them up, correctly determines the total carrying capacity per trip (3 trucks * 100 lbs/truck), and accurately calculates the required number of trips. All arithmetic operations are correct.

✓ No hallucinations detected

Question #26

Clean

Full Question

Oliver is popping popcorn for a snack. As the skillet of kernels heats up, the kernels start popping faster. 60 pop in the first 22 seconds of cooking, then 3 times that amount in the next 22 seconds. The kernels increase to 4 times the initial popping rate in the next 22 seconds. In the final 22 seconds, the popping slows down to half the rate as the past 22 seconds. After Oliver takes the skillet off the heat, a quarter of the number of kernels that popped in the final 22 seconds of cooking also pop from the residual heat. Oliver gives one-tenth of the made popcorn to his brother Thiago. How many more pieces of popcorn does Oliver have to eat than his brother?

Ground Truth Answer

In the second 22 seconds of cooking, 3* 60 = 180 kernels pop. In the third 22 seconds, 4 * 60 = 240 kernels pop. In the final 22 seconds, 240 / 2 = 120 kernels pop. After cooking, the residual heat makes 120 / 4 = 30 kernels pop. Thus, Oliver has 60 + 180 + 240 + 120 + 30 = 630 pieces of popcorn to eat. But since 1/10 of popcorn go to the brother, 630 * 1/10 = 63. The remaining popcorn for Oliver is 630 * 9/10 = 567. So the differences is 567 - 63 = 504 #### 504

Generated Answer

Here's how to break down this popcorn problem: 1. **First 22 seconds:** 60 kernels pop. 2. **Next 22 seconds:** 3 * 60 = 180 kernels pop. 3. **Next 22 seconds:** 4 * 60 = 240 kernels pop. 4. **Final 22 seconds:** 240 / 2 = 120 kernels pop. 5. **Residual heat:** 120 / 4 = 30 kernels pop. 6. **Total kernels:** 60 + 180 + 240 + 120 + 30 = 630 kernels. 7. **Thiago's share:** 630 * (1/10) = 63 kernels. 8. **Oliver's share:** 630 - 63 = 567 kernels. 9. **Difference:** 567 - 63 = 504 kernels. Answer: {504}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #27

Clean

Full Question

Thiago is popping popcorn for a snack. As the skillet of kernels heats up, the kernels start popping faster. 40 pop in the first 26 seconds of cooking, then 3 times that amount in the next 26 seconds. The kernels increase to 4 times the initial popping rate in the next 26 seconds. In the final 26 seconds, the popping slows down to half the rate as the past 26 seconds. After Thiago takes the skillet off the heat, a quarter of the number of kernels that popped in the final 26 seconds of cooking also pop from the residual heat. Thiago gives 1/10 of the made popcorn to his brother Sanjay. How many more pieces of popcorn does Thiago have to eat than his brother?

Ground Truth Answer

In the second 26 seconds of cooking, 3* 40 = 120 kernels pop. In the third 26 seconds, 4 * 40 = 160 kernels pop. In the final 26 seconds, 160 / 2 = 80 kernels pop. After cooking, the residual heat makes 80 / 4 = 20 kernels pop. Thus, Thiago has 40 + 120 + 160 + 80 + 20 = 420 pieces of popcorn to eat. But since 1/10 of popcorn go to the brother, 420 * 1/10 = 42. The remaining popcorn for Thiago is 420 * 9/10 = 378. So the differences is 378 - 42 = 336 #### 336

Generated Answer

Here's how we can break down this popcorn problem: 1. **First 26 seconds:** 40 kernels pop. 2. **Next 26 seconds:** 3 * 40 = 120 kernels pop. 3. **Next 26 seconds:** 4 * 40 = 160 kernels pop. 4. **Final 26 seconds:** 160 / 2 = 80 kernels pop. 5. **Residual heat:** 80 / 4 = 20 kernels pop. Total popped kernels: 40 + 120 + 160 + 80 + 20 = 420 kernels Sanjay gets 420 * (1/10) = 42 kernels. Thiago gets 420 - 42 = 378 kernels. The difference between Thiago's and Sanjay's popcorn amounts is 378 - 42 = 336 kernels. Answer: {336}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final result matches the ground truth.

✓ No hallucinations detected

Question #25

Clean

Full Question

Benjamin is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. 80 pop in the first 26 seconds of cooking, then 2 times that amount in the next 26 seconds. The kernels increase to 3 times the initial popping rate in the next 26 seconds. In the final 26 seconds, the popping slows down to half the rate as the past 26 seconds. After Benjamin takes the pan off the heat, a quarter of the number of kernels that popped in the final 26 seconds of cooking also pop from the residual heat. Benjamin gives 1/7 of the made popcorn to his brother Yusuf. How many more pieces of popcorn does Benjamin have to eat than his brother?

Ground Truth Answer

In the second 26 seconds of cooking, 2* 80 = 160 kernels pop. In the third 26 seconds, 3 * 80 = 240 kernels pop. In the final 26 seconds, 240 / 2 = 120 kernels pop. After cooking, the residual heat makes 120 / 4 = 30 kernels pop. Thus, Benjamin has 80 + 160 + 240 + 120 + 30 = 630 pieces of popcorn to eat. But since 1/7 of popcorn go to the brother, 630 * 1/7 = 90. The remaining popcorn for Benjamin is 630 * 6/7 = 540. So the differences is 540 - 90 = 450 #### 450

Generated Answer

Here's how to break down this popcorn problem: 1. **First 26 seconds:** 80 kernels pop. 2. **Next 26 seconds:** 2 * 80 = 160 kernels pop. 3. **Next 26 seconds:** 3 * 80 = 240 kernels pop. 4. **Final 26 seconds:** 240 / 2 = 120 kernels pop. 5. **Residual heat:** 120 / 4 = 30 kernels pop. 6. **Total popped kernels:** 80 + 160 + 240 + 120 + 30 = 630 kernels. 7. **Yusuf's share:** 630 / 7 = 90 kernels. 8. **Benjamin's share:** 630 - 90 = 540 kernels. 9. **Difference:** 540 - 90 = 450 kernels. Answer: {450}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #44

Clean

Full Question

A farmer is buying feed for his cows. He buys a variety of wheat, oats, carrots and corn. Since corn are a rare treat, he only buys seven 5-kg boxes of them for the whole stable. He only wants enough carrots to feed the cows while the vegetables are fresh, so he buys eleven 7-kg bags. Wheat are the main diet of his cows, so he buys thirty four 39-kg packs. Oats are a staple to supplement the wheat, so he buys nineteen 18-kg sacks. Finally, he buys 43 kgs of groceries, and 27 kgs of tools, and 100 kgs of wood. A farm truck can carry 130 kgs at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items?

Ground Truth Answer

The farmer is buying 7 * 5 = 35 kgs of corn. He is buying 11 * 7 = 77 kgs of carrots. He is buying 19 * 18 = 342 kgs of oats packs. He is buying 34 * 39 = 1326 kgs of wheat sacks. He is buying 43 kgs of grocery + 27 kgs of tools + 100 kgs of wood = 170 kgs. The weight of all the feed is 35 + 77 + 342 + 1326 + 170 = 1950 kgs. Thus, the farmer needs 1950 / 130 = 15 trips to transport all the feed in a single farm truck. With three trucks, the farmer needs 15/3=5 #### 5

Generated Answer

First calculate the total weight of the corn: 7 boxes * 5 kg/box = 35 kg. Next, calculate the total weight of the carrots: 11 bags * 7 kg/bag = 77 kg. Then, calculate the total weight of the wheat: 34 packs * 39 kg/pack = 1326 kg. Calculate the total weight of the oats: 19 sacks * 18 kg/sack = 342 kg. The total weight of the feed is 35 kg + 77 kg + 1326 kg + 342 kg = 1780 kg. The total weight of the other items is 43 kg + 27 kg + 100 kg = 170 kg. The total weight of all the purchased items is 1780 kg + 170 kg = 1950 kg. The total carrying capacity of the three trucks is 3 trucks * 130 kg/truck = 390 kg. The number of trips needed is 1950 kg / 390 kg/trip = 5 trips. Answer: {5}

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item category, sums them up correctly, determines the total carrying capacity of the three trucks, and calculates the required number of trips accurately. All arithmetic operations are correct.

✓ No hallucinations detected

Question #29

Clean

Full Question

Oscar is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. 80 pop in the first 16 seconds of cooking, then 3 times that amount in the next 16 seconds. The kernels increase to 5 times the initial popping rate in the next 16 seconds. In the final 16 seconds, the popping slows down to half the rate as the past 16 seconds. After Oscar takes the pan off the heat, a quarter of the number of kernels that popped in the final 16 seconds of cooking also pop from the residual heat. Oscar gives two-fifths of the made popcorn to his brother Benjamin. How many more pieces of popcorn does Oscar have to eat than his brother?

Ground Truth Answer

In the second 16 seconds of cooking, 3* 80 = 240 kernels pop. In the third 16 seconds, 5 * 80 = 400 kernels pop. In the final 16 seconds, 400 / 2 = 200 kernels pop. After cooking, the residual heat makes 200 / 4 = 50 kernels pop. Thus, Oscar has 80 + 240 + 400 + 200 + 50 = 970 pieces of popcorn to eat. But since 2/5 of popcorn go to the brother, 970 * 2/5 = 388. The remaining popcorn for Oscar is 970 * 3/5 = 582. So the differences is 582 - 388 = 194 #### 194

Generated Answer

Here's how we can solve this problem step by step: 1. **First 16 seconds:** 80 kernels popped. 2. **Next 16 seconds:** 3 * 80 = 240 kernels popped. 3. **Next 16 seconds:** 5 * 80 = 400 kernels popped. 4. **Final 16 seconds:** 400 / 2 = 200 kernels popped. 5. **Residual heat:** 200 / 4 = 50 kernels popped. 6. **Total kernels popped:** 80 + 240 + 400 + 200 + 50 = 970 kernels. 7. **Benjamin's share:** 970 * (2/5) = 388 kernels. 8. **Oscar's share:** 970 - 388 = 582 kernels. 9. **Difference:** 582 - 388 = 194 kernels. Answer: {194}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #43

Clean

Full Question

A farmer is buying feed for his sheep. He buys a variety of wheat, corn, beets and oats. Since oats are a rare treat, he only buys five 3-kg boxes of them for the whole stable. He only wants enough beets to feed the sheep while the vegetables are fresh, so he buys eleven 7-kg bags. Wheat are the main diet of his sheep, so he buys thirty four 44-kg packs. Corn are a staple to supplement the wheat, so he buys eighteen 19-kg sacks. Finally, he buys 43 kgs of groceries, and 27 kgs of tools, and 100 kgs of wood. A farm truck can carry 140 kgs at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items?

Ground Truth Answer

The farmer is buying 5 * 3 = 15 kgs of oats. He is buying 11 * 7 = 77 kgs of beets. He is buying 18 * 19 = 342 kgs of corn packs. He is buying 34 * 44 = 1496 kgs of wheat sacks. He is buying 43 kgs of grocery + 27 kgs of tools + 100 kgs of wood = 170 kgs. The weight of all the feed is 15 + 77 + 342 + 1496 + 170 = 2100 kgs. Thus, the farmer needs 2100 / 140 = 15 trips to transport all the feed in a single farm truck. With three trucks, the farmer needs 15/3=5 #### 5

Generated Answer

First calculate the total weight of the oats: 5 boxes * 3 kg/box = 15 kg Then calculate the total weight of the beets: 11 bags * 7 kg/bag = 77 kg Then calculate the total weight of the wheat: 34 packs * 44 kg/pack = 1496 kg Then calculate the total weight of the corn: 18 sacks * 19 kg/sack = 342 kg The total weight of the feed is 15 kg + 77 kg + 1496 kg + 342 kg = 1930 kg The total weight of other items is 43 kg + 27 kg + 100 kg = 170 kg The total weight of all items is 1930 kg + 170 kg = 2100 kg Each truck can carry 140 kg, and the farmer has three trucks, so in one trip they can carry 140 kg/truck * 3 trucks = 420 kg The number of trips required is 2100 kg / 420 kg/trip = 5 trips Answer: {5}

Overall Quality: excellent

The reasoning chain correctly calculates the weight of all items, correctly determines the total carrying capacity per trip (considering all three trucks), and correctly calculates the total number of trips needed. All arithmetic operations are correct.

✓ No hallucinations detected

Question #28

Clean

Full Question

Sanjay is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. 80 pop in the first 26 seconds of cooking, then 4 times that amount in the next 26 seconds. The kernels increase to 6 times the initial popping rate in the next 26 seconds. In the final 26 seconds, the popping slows down to half the rate as the past 26 seconds. After Sanjay takes the pan off the heat, a quarter of the number of kernels that popped in the final 26 seconds of cooking also pop from the residual heat. Sanjay gives 1/5 of the made popcorn to his brother Noah. How many more pieces of popcorn does Sanjay have to eat than his brother?

Ground Truth Answer

In the second 26 seconds of cooking, 4* 80 = 320 kernels pop. In the third 26 seconds, 6 * 80 = 480 kernels pop. In the final 26 seconds, 480 / 2 = 240 kernels pop. After cooking, the residual heat makes 240 / 4 = 60 kernels pop. Thus, Sanjay has 80 + 320 + 480 + 240 + 60 = 1180 pieces of popcorn to eat. But since 1/5 of popcorn go to the brother, 1180 * 1/5 = 236. The remaining popcorn for Sanjay is 1180 * 4/5 = 944. So the differences is 944 - 236 = 708 #### 708

Generated Answer

Here's how to break down this popcorn problem: 1. **First 26 seconds:** 80 kernels pop. 2. **Next 26 seconds:** 4 * 80 = 320 kernels pop. 3. **Third 26 seconds:** 6 * 80 = 480 kernels pop. 4. **Final 26 seconds:** 480 / 2 = 240 kernels pop. 5. **Residual heat:** 240 / 4 = 60 kernels pop. 6. **Total popped kernels:** 80 + 320 + 480 + 240 + 60 = 1180 kernels. 7. **Noah's share:** 1180 * (1/5) = 236 kernels. 8. **Sanjay's share:** 1180 - 236 = 944 kernels. 9. **Difference:** 944 - 236 = 708 kernels. Answer: {708}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem description, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #24

Clean

Full Question

Andre is popping popcorn for a snack. As the pot of kernels heats up, the kernels start popping faster. 80 pop in the first 10 seconds of cooking, then 4 times that amount in the next 10 seconds. The kernels increase to 6 times the initial popping rate in the next 10 seconds. In the final 10 seconds, the popping slows down to half the rate as the past 10 seconds. After Andre takes the pot off the heat, a quarter of the number of kernels that popped in the final 10 seconds of cooking also pop from the residual heat. Andre gives 1/10 of the made popcorn to his brother Jin. How many more pieces of popcorn does Andre have to eat than his brother?

Ground Truth Answer

In the second 10 seconds of cooking, 4* 80 = 320 kernels pop. In the third 10 seconds, 6 * 80 = 480 kernels pop. In the final 10 seconds, 480 / 2 = 240 kernels pop. After cooking, the residual heat makes 240 / 4 = 60 kernels pop. Thus, Andre has 80 + 320 + 480 + 240 + 60 = 1180 pieces of popcorn to eat. But since 1/10 of popcorn go to the brother, 1180 * 1/10 = 118. The remaining popcorn for Andre is 1180 * 9/10 = 1062. So the differences is 1062 - 118 = 944 #### 944

Generated Answer

Here's how we can solve this problem step by step: 1. **First 10 seconds:** 80 kernels pop. 2. **Next 10 seconds:** 4 * 80 = 320 kernels pop. 3. **Next 10 seconds:** 6 * 80 = 480 kernels pop. 4. **Final 10 seconds:** 480 / 2 = 240 kernels pop. 5. **Residual heat:** 240 / 4 = 60 kernels pop. 6. **Total kernels popped:** 80 + 320 + 480 + 240 + 60 = 1180 kernels. 7. **Kernels Jin receives:** 1180 * (1/10) = 118 kernels. 8. **Kernels Andre eats:** 1180 - 118 = 1062 kernels. 9. **Difference:** 1062 - 118 = 944 kernels. Answer: {944}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #132

Clean

Full Question

Valentina was preparing for a game night at her house, where she intended to serve vegetable lasagna. She noticed that she was out of plastic forks, so she bought a new package of forks. Later, her husband also bought a package of 19 new forks and gave them to Valentina. While Valentina was making the vegetable lasagna, she used six of the forks to sample her vegetable lasagna, then threw away 8 defective forks. The guests also brought 2 packs of forks, each having 8 inside them. Later, when she went to set the table, she had a total of 49 forks. How many forks were in the package that Valentina bought?

Ground Truth Answer

Husband forks: 19. Guests forks: 2 * 8 = 16 Used forks for sampling vegetable lasagna or threw away: 6 + 8 = 14 Remained forks: 49. So the number of forks Valentina bought is: 49 - 19 + 14 - 16 = 28 #### 28

Generated Answer

Let 'x' be the number of forks Valentina initially bought. Valentina's husband brought 19 forks, making the total x + 19. She used 6 and discarded 8, leaving x + 19 - 6 - 8 = x + 5 forks. Her guests brought 2 * 8 = 16 forks, increasing the total to x + 5 + 16 = x + 21 forks. We know she had 49 forks in the end, so x + 21 = 49. Solving for x, we get x = 49 - 21 = 28. Answer: {28}

Overall Quality: excellent

The reasoning chain correctly models the problem using an algebraic equation and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #137

Clean

Full Question

Isabella was preparing for a lunch party at her house, where she intended to serve vegetable lasagna. She noticed that she was out of plastic forks, so she bought a new package of forks. Later, her husband also bought a package of 14 new forks and gave them to Isabella. While Isabella was making the vegetable lasagna, she used seven of the forks to sample her vegetable lasagna, then threw away 7 defective forks. The guests also brought 4 packs of forks, each having 7 inside them. Later, when she went to set the table, she had a total of 66 forks. How many forks were in the package that Isabella bought?

Ground Truth Answer

Husband forks: 14. Guests forks: 4 * 7 = 28 Used forks for sampling vegetable lasagna or threw away: 7 + 7 = 14 Remained forks: 66. So the number of forks Isabella bought is: 66 - 14 + 14 - 28 = 38 #### 38

Generated Answer

Let 'x' be the number of forks in the package Isabella initially bought. Isabella started with 'x' forks. Her husband added 14 forks, making the total x + 14. She used 7 forks and discarded 7, reducing the total by 14 forks. So, the number of forks becomes x + 14 - 14 = x. Her guests brought 4 packs * 7 forks/pack = 28 forks. This brings the total to x + 28. Finally, she had 66 forks. Therefore, x + 28 = 66. Subtracting 28 from both sides gives x = 66 - 28 = 38. Answer: {38}

Overall Quality: excellent

The reasoning chain correctly models the sequence of additions and subtractions described in the problem to set up the equation, and the arithmetic used to solve the equation is correct. The final answer matches the ground truth.

✓ No hallucinations detected

Question #54

Clean

Full Question

When Sofia watches her brother, she gets out a variety of toys for him. The bag of building blocks has 33 blocks in it. The bin of stuffed animals has 5 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 9 pages, each with 13 stickers. The tower of stacking rings has 28 multicolored rings on it. Sofia recently bought a tube of bouncy balls, bringing her total number of items for her brother up to 320. How many bouncy balls came in the tube?

Ground Truth Answer

Let T be the number of bouncy balls in the tube. The sticker book has 9 * 13 = 117 stickers. The action figures are 2 * (33+5) = 2 * 38 = 76. After buying the tube of balls, Sofia has 33 + 5 + 28 + 76 + 12 + 117 + T = 271 + T = 320 toys for her brother. Thus, T = 320 - 271 = 49 bouncy balls came in the tube. #### 49

Generated Answer

The bag of building blocks has 33 blocks. The bin of stuffed animals has 5 stuffed animals. The number of action figures is twice the number of blocks and stuffed animals combined, so there are 2 * (33 + 5) = 2 * 38 = 76 action figures. The crayon box has 12 crayons. The sticker book has 9 pages * 13 stickers/page = 117 stickers. The tower of stacking rings has 28 rings. In total, Sofia has 33 + 5 + 76 + 12 + 117 + 28 = 271 items for her brother. Since she has 320 items total, the bouncy ball tube must contain 320 - 271 = 49 bouncy balls. Answer: {49}

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #57

Clean

Full Question

When Kayla watches her brother, she gets out a variety of toys for him. The bag of building blocks has 32 blocks in it. The bin of stuffed animals has 5 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 6 pages, each with 11 stickers. The tower of stacking rings has 32 multicolored rings on it. Kayla recently bought a tube of bouncy balls, bringing her total number of items for her brother up to 270. How many bouncy balls came in the tube?

Ground Truth Answer

Let T be the number of bouncy balls in the tube. The sticker book has 6 * 11 = 66 stickers. The action figures are 2 * (32+5) = 2 * 37 = 74. After buying the tube of balls, Kayla has 32 + 5 + 32 + 74 + 12 + 66 + T = 221 + T = 270 toys for her brother. Thus, T = 270 - 221 = 49 bouncy balls came in the tube. #### 49

Generated Answer

The building blocks contribute 32 items. The stuffed animals contribute 5 items. The action figures contribute 2 * (32 + 5) = 2 * 37 = 74 items. The crayons contribute 12 items. The stickers contribute 6 pages * 11 stickers/page = 66 items. The stacking rings contribute 32 items. So far, Kayla has 32 + 5 + 74 + 12 + 66 + 32 = 221 items. If the total number of items is 270, then the bouncy balls must contribute 270 - 221 = 49 items. Therefore, there are 49 bouncy balls in the tube. Answer: {49}

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logic required to solve the problem.

✓ No hallucinations detected

Question #55

Clean

Full Question

When Nadia watches her cousin, she gets out a variety of toys for him. The bag of building blocks has 36 blocks in it. The bin of stuffed animals has 8 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 9 pages, each with 12 stickers. The tower of stacking rings has 30 multicolored rings on it. Nadia recently bought a tube of bouncy balls, bringing her total number of items for her cousin up to 330. How many bouncy balls came in the tube?

Ground Truth Answer

Let T be the number of bouncy balls in the tube. The sticker book has 9 * 12 = 108 stickers. The action figures are 2 * (36+8) = 2 * 44 = 88. After buying the tube of balls, Nadia has 36 + 8 + 30 + 88 + 12 + 108 + T = 282 + T = 330 toys for her cousin. Thus, T = 330 - 282 = 48 bouncy balls came in the tube. #### 48

Generated Answer

The bag of building blocks has 36 blocks. The bin of stuffed animals has 8 stuffed animals. The action figure pack has 2 * (36 + 8) = 2 * 44 = 88 action figures. The crayon box has 12 crayons. The sticker book has 9 pages * 12 stickers/page = 108 stickers. The tower of stacking rings has 30 rings. The total number of items excluding the bouncy balls is 36 + 8 + 88 + 12 + 108 + 30 = 282 items. Nadia has 330 items total, so the bouncy ball tube contains 330 - 282 = 48 bouncy balls. Answer: {48}

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #136

Clean

Full Question

Sakura was preparing for a birthday party at her house, where she intended to serve grilled salmon. She noticed that she was out of plastic plates, so she bought a new package of plates. Later, her husband also bought a package of 7 new plates and gave them to Sakura. While Sakura was making the grilled salmon, she used eight of the plates to sample her grilled salmon, then threw away 15 defective plates. The guests also brought 2 packs of plates, each having 15 inside them. Later, when she went to set the table, she had a total of 56 plates. How many plates were in the package that Sakura bought?

Ground Truth Answer

Husband plates: 7. Guests plates: 2 * 15 = 30 Used plates for sampling grilled salmon or threw away: 8 + 15 = 23 Remained plates: 56. So the number of plates Sakura bought is: 56 - 7 + 23 - 30 = 42 #### 42

Generated Answer

Let 'x' be the number of plates Sakura initially bought. Sakura's husband brought 7 plates, so the total became x + 7. Sakura used 8 plates and discarded 15, so the total became x + 7 - 8 - 15 = x - 16. The guests brought 2 packs of 15 plates each, adding 2 * 15 = 30 plates. So, the total became x - 16 + 30 = x + 14. We are given that the final number of plates is 56. Therefore, x + 14 = 56. Subtracting 14 from both sides gives x = 56 - 14 = 42. Answer: {42}

Overall Quality: excellent

The reasoning chain correctly models the problem using an algebraic equation and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #58

Clean

Full Question

When Xena watches her cousin, she gets out a variety of toys for him. The bag of building blocks has 33 blocks in it. The bin of stuffed animals has 8 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 7 pages, each with 12 stickers. The tower of stacking rings has 26 multicolored rings on it. Xena recently bought a tube of bouncy balls, bringing her total number of items for her cousin up to 300. How many bouncy balls came in the tube?

Ground Truth Answer

Let T be the number of bouncy balls in the tube. The sticker book has 7 * 12 = 84 stickers. The action figures are 2 * (33+8) = 2 * 41 = 82. After buying the tube of balls, Xena has 33 + 8 + 26 + 82 + 12 + 84 + T = 245 + T = 300 toys for her cousin. Thus, T = 300 - 245 = 55 bouncy balls came in the tube. #### 55

Generated Answer

The bag of building blocks has 33 blocks. The bin of stuffed animals has 8 stuffed animals. The action figure pack has 2 * (33 + 8) = 2 * 41 = 82 action figures. The crayon box has 12 crayons. The sticker book has 7 pages * 12 stickers/page = 84 stickers. The tower of stacking rings has 26 rings. In total, excluding the bouncy balls, Xena has 33 + 8 + 82 + 12 + 84 + 26 = 245 items. Since Xena has 300 items in total, and 245 are accounted for, the number of bouncy balls is 300 - 245 = 55. Answer: {55}

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #59

Clean

Full Question

When Mia watches her brother, she gets out a variety of toys for him. The bag of building blocks has 42 blocks in it. The bin of stuffed animals has 5 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 6 pages, each with 9 stickers. The tower of stacking rings has 34 multicolored rings on it. Mia recently bought a tube of bouncy balls, bringing her total number of items for her brother up to 290. How many bouncy balls came in the tube?

Ground Truth Answer

Let T be the number of bouncy balls in the tube. The sticker book has 6 * 9 = 54 stickers. The action figures are 2 * (42+5) = 2 * 47 = 94. After buying the tube of balls, Mia has 42 + 5 + 34 + 94 + 12 + 54 + T = 241 + T = 290 toys for her brother. Thus, T = 290 - 241 = 49 bouncy balls came in the tube. #### 49

Generated Answer

Here's how we solve this problem: 1. **Calculate the number of action figures:** There are 42 blocks + 5 stuffed animals = 47 toys. Twice this number is 47 * 2 = 94 action figures. 2. **Calculate the number of stickers:** There are 6 pages * 9 stickers/page = 54 stickers. 3. **Calculate the total number of items excluding bouncy balls:** There are 42 blocks + 5 stuffed animals + 94 action figures + 12 crayons + 54 stickers + 34 rings = 241 items. 4. **Calculate the number of bouncy balls:** Mia has 290 total items - 241 other items = 49 bouncy balls. Answer: {49}

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem.

✓ No hallucinations detected

Question #56

Clean

Full Question

When Nia watches her cousin, she gets out a variety of toys for him. The bag of building blocks has 36 blocks in it. The bin of stuffed animals has 8 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 9 pages, each with 11 stickers. The tower of stacking rings has 26 multicolored rings on it. Nia recently bought a tube of bouncy balls, bringing her total number of items for her cousin up to 310. How many bouncy balls came in the tube?

Ground Truth Answer

Let T be the number of bouncy balls in the tube. The sticker book has 9 * 11 = 99 stickers. The action figures are 2 * (36+8) = 2 * 44 = 88. After buying the tube of balls, Nia has 36 + 8 + 26 + 88 + 12 + 99 + T = 269 + T = 310 toys for her cousin. Thus, T = 310 - 269 = 41 bouncy balls came in the tube. #### 41

Generated Answer

The building blocks, stuffed animals, and action figures total 36 + 8 + 2*(36+8) = 36 + 8 + 2*44 = 36 + 8 + 88 = 132 items. The crayons, stickers, and stacking rings total 12 + 9*11 + 26 = 12 + 99 + 26 = 137 items. The total number of items without the bouncy balls is 132 + 137 = 269 items. The bouncy balls make up the difference between the total number of items and the number of items without the bouncy balls. Therefore, there are 310 - 269 = 41 bouncy balls. Answer: {41}

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #141

Clean

Full Question

Valentina is knitting winter wear for her 5 grandchildren. They're quintuplets, so they're all the same size. She wants to make a shawl, tunic, cardigan, booties, and gloves for each of them. It takes 5 skeins of wool to make a shawl, 3 for a tunic, 9 for a cardigan, 10 for a pair of booties, and 11 for a pair of gloves. Valentina wants to make two warm jackets for herself, each needing 7 skeins of wool. Each dozen skeins of wool costs $7. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Valentina pay for all the skeins of wool she needs?

Ground Truth Answer

A full outfit for each child will require 5 skeins per shawl + 3 skeins per tunic + 9 skeins per cardigan + 10 skeins per pair of booties + 11 skeins per pair of gloves = 38 skeins of wool. So to knit outfits for all of her grandchildren, she will need 5*38 = 190 skeins of wool. We add the 7 skeins for the jacket. 2*7 + 190 = 204. Valentina needs 204 skeins so that would be 204 / 12 = 17 dozen. The cost is 17 * 7 = 119. Since 119 is more that 100, Valentina receives $20 discount. So her total bill is 119 - 20 = 99 #### 99

Generated Answer

Here's how to calculate Valentina's wool expenses: 1. **Grandchildren's wool:** * Shawl: 5 skeins/grandchild * 5 grandchildren = 25 skeins * Tunic: 3 skeins/grandchild * 5 grandchildren = 15 skeins * Cardigan: 9 skeins/grandchild * 5 grandchildren = 45 skeins * Booties: 10 skeins/grandchild * 5 grandchildren = 50 skeins * Gloves: 11 skeins/grandchild * 5 grandchildren = 55 skeins * Total for grandchildren: 25 + 15 + 45 + 50 + 55 = 190 skeins 2. **Valentina's jackets:** * 7 skeins/jacket * 2 jackets = 14 skeins 3. **Total wool needed:** * 190 skeins (grandchildren) + 14 skeins (Valentina) = 204 skeins 4. **Cost calculation:** * Dozens needed: 204 skeins / 12 skeins/dozen = 17 dozens * Total cost: 17 dozens * $7/dozen = $119 5. **Discount:** * Since $119 > $100, Valentina gets a $20 discount. * Final cost: $119 - $20 = $99 Answer: {99}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #139

Clean

Full Question

Fatima is knitting winter wear for her 5 grandchildren. They're quintuplets, so they're all the same size. She wants to make a beanie, vest, cardigan, gloves, and mittens for each of them. It takes 4 skeins of wool to make a beanie, 6 for a vest, 8 for a cardigan, 12 for a pair of gloves, and 10 for a pair of mittens. Fatima wants to make two warm jackets for herself, each needing 8 skeins of wool. Each dozen skeins of wool costs $8. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Fatima pay for all the skeins of wool she needs?

Ground Truth Answer

A full outfit for each child will require 4 skeins per beanie + 6 skeins per vest + 8 skeins per cardigan + 12 skeins per pair of gloves + 10 skeins per pair of mittens = 40 skeins of wool. So to knit outfits for all of her grandchildren, she will need 5*40 = 200 skeins of wool. We add the 8 skeins for the jacket. 2*8 + 200 = 216. Fatima needs 216 skeins so that would be 216 / 12 = 18 dozen. The cost is 18 * 8 = 144. Since 144 is more that 100, Fatima receives $20 discount. So her total bill is 144 - 20 = 124 #### 124

Generated Answer

Here's how to calculate the total cost: 1. **Wool for grandchildren's items:** * Beanie: 5 grandchildren * 4 skeins/beanie = 20 skeins * Vest: 5 grandchildren * 6 skeins/vest = 30 skeins * Cardigan: 5 grandchildren * 8 skeins/cardigan = 40 skeins * Gloves: 5 grandchildren * 12 skeins/gloves = 60 skeins * Mittens: 5 grandchildren * 10 skeins/mittens = 50 skeins * Total for grandchildren: 20 + 30 + 40 + 60 + 50 = 200 skeins 2. **Wool for Fatima's jackets:** * Jackets: 2 jackets * 8 skeins/jacket = 16 skeins 3. **Total wool needed:** * Grandchildren + Fatima: 200 skeins + 16 skeins = 216 skeins 4. **Cost of wool:** * Dozens of skeins: 216 skeins / 12 skeins/dozen = 18 dozens * Cost: 18 dozens * $8/dozen = $144 5. **Discount:** * Since $144 > $100, Fatima gets a $20 discount. 6. **Final cost:** * $144 - $20 = $124 Answer: {124}

Overall Quality: excellent

The reasoning chain correctly calculates the total skeins needed, converts this to dozens, determines the cost, applies the discount correctly, and arrives at the final cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #138

Clean

Full Question

Sakura is knitting winter wear for her 4 grandchildren. They're quadruplets, so they're all the same size. She wants to make a vest, cardigan, shawl, gloves, and mittens for each of them. It takes 5 skeins of wool to make a vest, 4 for a cardigan, 10 for a shawl, 12 for a pair of gloves, and 9 for a pair of mittens. Sakura wants to make two warm jackets for herself, each needing 4 skeins of wool. Each dozen skeins of wool costs $9. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Sakura pay for all the skeins of wool she needs?

Ground Truth Answer

A full outfit for each child will require 5 skeins per vest + 4 skeins per cardigan + 10 skeins per shawl + 12 skeins per pair of gloves + 9 skeins per pair of mittens = 40 skeins of wool. So to knit outfits for all of her grandchildren, she will need 4*40 = 160 skeins of wool. We add the 4 skeins for the jacket. 2*4 + 160 = 168. Sakura needs 168 skeins so that would be 168 / 12 = 14 dozen. The cost is 14 * 9 = 126. Since 126 is more that 100, Sakura receives $20 discount. So her total bill is 126 - 20 = 106 #### 106

Generated Answer

Here's how to calculate the total cost: 1. **Wool for grandchildren's vests:** 4 grandchildren * 5 skeins/vest = 20 skeins 2. **Wool for grandchildren's cardigans:** 4 grandchildren * 4 skeins/cardigan = 16 skeins 3. **Wool for grandchildren's shawls:** 4 grandchildren * 10 skeins/shawl = 40 skeins 4. **Wool for grandchildren's gloves:** 4 grandchildren * 12 skeins/gloves = 48 skeins 5. **Wool for grandchildren's mittens:** 4 grandchildren * 9 skeins/mittens = 36 skeins 6. **Total wool for grandchildren:** 20 + 16 + 40 + 48 + 36 = 160 skeins 7. **Wool for Sakura's jackets:** 2 jackets * 4 skeins/jacket = 8 skeins 8. **Total wool needed:** 160 + 8 = 168 skeins 9. **Dozens of wool needed:** 168 skeins / 12 skeins/dozen = 14 dozens 10. **Total cost before discount:** 14 dozens * $9/dozen = $126 11. **Final cost after discount:** Since $126 is over $100, Sakura gets a $20 discount: $126 - $20 = $106 Answer: {106}

Overall Quality: excellent

The reasoning chain correctly calculates the total skeins needed for the grandchildren and Sakura's jackets, correctly determines the number of dozens, calculates the cost, and applies the discount according to the problem rules. All arithmetic operations are correct.

✓ No hallucinations detected

Question #143

Clean

Full Question

Roya is knitting winter wear for her 5 grandchildren. They're quintuplets, so they're all the same size. She wants to make a cardigan, poncho, sweater, socks, and mittens for each of them. It takes 5 skeins of wool to make a cardigan, 3 for a poncho, 8 for a sweater, 10 for a pair of socks, and 14 for a pair of mittens. Roya wants to make two warm jackets for herself, each needing 8 skeins of wool. Each dozen skeins of wool costs $8. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Roya pay for all the skeins of wool she needs?

Ground Truth Answer

A full outfit for each child will require 5 skeins per cardigan + 3 skeins per poncho + 8 skeins per sweater + 10 skeins per pair of socks + 14 skeins per pair of mittens = 40 skeins of wool. So to knit outfits for all of her grandchildren, she will need 5*40 = 200 skeins of wool. We add the 8 skeins for the jacket. 2*8 + 200 = 216. Roya needs 216 skeins so that would be 216 / 12 = 18 dozen. The cost is 18 * 8 = 144. Since 144 is more that 100, Roya receives $20 discount. So her total bill is 144 - 20 = 124 #### 124

Generated Answer

Here's how to calculate the total cost: 1. **Wool for grandchildren's clothes:** * Cardigan: 5 skeins/grandchild * 5 grandchildren = 25 skeins * Poncho: 3 skeins/grandchild * 5 grandchildren = 15 skeins * Sweater: 8 skeins/grandchild * 5 grandchildren = 40 skeins * Socks: 10 skeins/grandchild * 5 grandchildren = 50 skeins * Mittens: 14 skeins/grandchild * 5 grandchildren = 70 skeins * Total for grandchildren: 25 + 15 + 40 + 50 + 70 = 200 skeins 2. **Wool for Roya's jackets:** * 8 skeins/jacket * 2 jackets = 16 skeins 3. **Total wool needed:** * 200 skeins (grandchildren) + 16 skeins (Roya) = 216 skeins 4. **Cost of wool:** * 216 skeins / 12 skeins/dozen = 18 dozens * 18 dozens * $8/dozen = $144 5. **Final cost after discount:** * Since $144 > $100, Roya gets a $20 discount. * $144 - $20 = $124 Answer: {124}

Overall Quality: excellent

The reasoning chain correctly calculates the total skeins needed by summing the requirements for each item for all 5 grandchildren, adding the skeins for Roya's jackets, converting the total skeins to dozens, calculating the initial cost, and applying the discount correctly. All arithmetic operations are accurate.

✓ No hallucinations detected

Question #133

Clean

Full Question

Uma was preparing for a potluck party at her house, where she intended to serve shrimp scampi. She noticed that she was out of plastic spoons, so she bought a new package of spoons. Later, her husband also bought a package of 11 new spoons and gave them to Uma. While Uma was making the shrimp scampi, she used seven of the spoons to sample her shrimp scampi, then threw away 5 defective spoons. The guests also brought 2 packs of spoons, each having 5 inside them. Later, when she went to set the table, she had a total of 36 spoons. How many spoons were in the package that Uma bought?

Ground Truth Answer

Husband spoons: 11. Guests spoons: 2 * 5 = 10 Used spoons for sampling shrimp scampi or threw away: 7 + 5 = 12 Remained spoons: 36. So the number of spoons Uma bought is: 36 - 11 + 12 - 10 = 27 #### 27

Generated Answer

Let 'x' be the number of spoons in the package Uma initially bought. Uma starts with 'x' spoons. Her husband adds 11 spoons, giving her x + 11 spoons. She uses 7 and throws away 5, leaving her with x + 11 - 7 - 5 = x - 1 spoons. Her guests bring 2 * 5 = 10 spoons, increasing the total to x - 1 + 10 = x + 9 spoons. We know she ends up with 36 spoons, so x + 9 = 36. Solving for x, we get x = 36 - 9 = 27. Answer: {27}

Overall Quality: excellent

The reasoning chain correctly models the sequence of additions and subtractions based on the problem description and arrives at the correct answer.

✓ No hallucinations detected

Question #142

Clean

Full Question

Uma is knitting winter wear for her 4 grandchildren. They're quadruplets, so they're all the same size. She wants to make a shawl, hat, cardigan, leg warmers, and socks for each of them. It takes 5 skeins of wool to make a shawl, 3 for a hat, 12 for a cardigan, 11 for a pair of leg warmers, and 15 for a pair of socks. Uma wants to make two warm jackets for herself, each needing 10 skeins of wool. Each dozen skeins of wool costs $9. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Uma pay for all the skeins of wool she needs?

Ground Truth Answer

A full outfit for each child will require 5 skeins per shawl + 3 skeins per hat + 12 skeins per cardigan + 11 skeins per pair of leg warmers + 15 skeins per pair of socks = 46 skeins of wool. So to knit outfits for all of her grandchildren, she will need 4*46 = 184 skeins of wool. We add the 10 skeins for the jacket. 2*10 + 184 = 204. Uma needs 204 skeins so that would be 204 / 12 = 17 dozen. The cost is 17 * 9 = 153. Since 153 is more that 100, Uma receives $20 discount. So her total bill is 153 - 20 = 133 #### 133

Generated Answer

Here's how to calculate the total cost: 1. **Wool needed per grandchild:** 5 (shawl) + 3 (hat) + 12 (cardigan) + 11 (leg warmers) + 15 (socks) = 46 skeins 2. **Total wool needed for grandchildren:** 46 skeins/grandchild * 4 grandchildren = 184 skeins 3. **Wool needed for Uma's jackets:** 10 skeins/jacket * 2 jackets = 20 skeins 4. **Total wool needed:** 184 (grandchildren) + 20 (Uma) = 204 skeins 5. **Dozens of wool needed:** 204 skeins / 12 skeins/dozen = 17 dozens 6. **Total cost before discount:** 17 dozens * $9/dozen = $153 7. **Final cost after discount:** Since $153 > $100, apply the $20 discount: $153 - $20 = $133 Answer: {133}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #140

Clean

Full Question

Valeria is knitting winter wear for her 4 grandchildren. They're quadruplets, so they're all the same size. She wants to make a tunic, hat, shawl, booties, and gloves for each of them. It takes 6 skeins of wool to make a tunic, 6 for a hat, 12 for a shawl, 12 for a pair of booties, and 13 for a pair of gloves. Valeria wants to make two warm jackets for herself, each needing 4 skeins of wool. Each dozen skeins of wool costs $9. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Valeria pay for all the skeins of wool she needs?

Ground Truth Answer

A full outfit for each child will require 6 skeins per tunic + 6 skeins per hat + 12 skeins per shawl + 12 skeins per pair of booties + 13 skeins per pair of gloves = 49 skeins of wool. So to knit outfits for all of her grandchildren, she will need 4*49 = 196 skeins of wool. We add the 4 skeins for the jacket. 2*4 + 196 = 204. Valeria needs 204 skeins so that would be 204 / 12 = 17 dozen. The cost is 17 * 9 = 153. Since 153 is more that 100, Valeria receives $20 discount. So her total bill is 153 - 20 = 133 #### 133

Generated Answer

Here's how to calculate the total cost: 1. **Wool for Grandchildren's Outfits:** * Per grandchild: 6 (tunic) + 6 (hat) + 12 (shawl) + 12 (booties) + 13 (gloves) = 49 skeins * Total for 4 grandchildren: 49 skeins/grandchild * 4 grandchildren = 196 skeins 2. **Wool for Valeria's Jackets:** * 2 jackets * 4 skeins/jacket = 8 skeins 3. **Total Wool Needed:** * 196 (grandchildren) + 8 (Valeria) = 204 skeins 4. **Cost of Wool:** * Dozens of skeins needed: 204 skeins / 12 skeins/dozen = 17 dozens * Total cost: 17 dozens * $9/dozen = $153 5. **Applying the Discount:** * Since $153 > $100, Valeria gets a $20 discount. * Final cost: $153 - $20 = $133 Answer: {133}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps logically. All calculations are correct.

✓ No hallucinations detected

Question #134

Clean

Full Question

Xena was preparing for a birthday party at her house, where she intended to serve creme brulee. She noticed that she was out of plastic forks, so she bought a new package of forks. Later, her husband also bought a package of 16 new forks and gave them to Xena. While Xena was making the creme brulee, she used seven of the forks to sample her creme brulee, then threw away 8 defective forks. The guests also brought 2 packs of forks, each having 8 inside them. Later, when she went to set the table, she had a total of 39 forks. How many forks were in the package that Xena bought?

Ground Truth Answer

Husband forks: 16. Guests forks: 2 * 8 = 16 Used forks for sampling creme brulee or threw away: 7 + 8 = 15 Remained forks: 39. So the number of forks Xena bought is: 39 - 16 + 15 - 16 = 22 #### 22

Generated Answer

Let 'x' be the number of forks in the package Xena initially bought. Xena starts with 'x' forks. Her husband adds 16 forks, so she has x + 16 forks. She uses 7 forks and throws away 8, so she has x + 16 - 7 - 8 = x + 1 forks. Her guests bring 2 * 8 = 16 forks, so she has x + 1 + 16 = x + 17 forks. She ends up with 39 forks, so x + 17 = 39. Solving for x, we get x = 39 - 17 = 22. Answer: {22}

Overall Quality: excellent

The reasoning chain correctly models the problem step-by-step and arrives at the correct answer using sound arithmetic.

✓ No hallucinations detected

Question #135

Clean

Full Question

Chen was preparing for a birthday party at her house, where she intended to serve beef stew. She noticed that she was out of plastic forks, so she bought a new package of forks. Later, her husband also bought a package of 9 new forks and gave them to Chen. While Chen was making the beef stew, she used sixteen of the forks to sample her beef stew, then threw away 12 defective forks. The guests also brought 2 packs of forks, each having 12 inside them. Later, when she went to set the table, she had a total of 32 forks. How many forks were in the package that Chen bought?

Ground Truth Answer

Husband forks: 9. Guests forks: 2 * 12 = 24 Used forks for sampling beef stew or threw away: 16 + 12 = 28 Remained forks: 32. So the number of forks Chen bought is: 32 - 9 + 28 - 24 = 27 #### 27

Generated Answer

Let 'x' be the number of forks in the package Chen initially bought. Chen starts with x forks. Her husband adds 9 forks, bringing the total to x + 9. She uses 16 forks and throws away 12, reducing the total to (x + 9) - 16 - 12 = x - 19. The guests bring 2 * 12 = 24 forks, increasing the total to (x - 19) + 24 = x + 5. Finally, she has 32 forks, so x + 5 = 32. Solving for x, we get x = 32 - 5 = 27. Answer: {27}

Overall Quality: excellent

The reasoning chain correctly models the problem using an algebraic equation and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #181

2 issues

Full Question

Gabrielle and Arash went to a construction supply store. Arash is a member, but Gabrielle is not. Gabrielle has €92.27 and wants to buy 15 nails from a bin at the store. She also needs 8 washers, each costing €0.64. Each nail costs €0.21. Additionally, Gabrielle picks up 8 gallons of paint. Arash starts with €100 and wants 12 gallons of paint, each priced at €7.5, and 3 carpenter pencils, each costing €3. The store offers a 10% discount on paint for members. How much more money does Gabrielle have left than Arash after they leave the store?

Ground Truth Answer

Gabrielle spent 15*0.21 nails+ 8*0.64 washers+ 8*7.5 paints = €68.27. Remained €92.27 - €68.27 = €24.0. Arash spent 12*7.5 for paints + 3*3 for pencils. Since Arash is a member, he gets 10% discount on paints. So total €81 + €9 = €90.0. Remained €100 - €90.0 = €10.0. Gabrielle has €24.0 - €10.0 = €14 more than Arash remained. #### 14

Generated Answer

Here's how we can break down the problem to find the solution: **Gabrielle's expenses:** * **Nails:** 15 nails * €0.21/nail = €3.15 * **Washers:** 8 washers * €0.64/washer = €5.12 * **Paint:** We are not given the price of paint, so we can't calculate Gabrielle's total expenses. **Arash's expenses:** * **Paint:** 12 gallons * €7.5/gallon = €90 * **Discount:** €90 * 0.10 = €9 * **Paint after discount:** €90 - €9 = €81 * **Pencils:** 3 pencils * €3/pencil = €9 * **Total:** €81 + €9 = €90 **Comparison:** Since we don't know the price of paint for Gabrielle, we cannot determine how much money each of them has left, let alone the difference between those amounts. However, if we were to assume paint is free (which is highly unlikely in reality), then Gabrielle would spend €3.15 + €5.12 = €8.27. She would have €92.27 - €8.27 = €84 left. Arash would spend €90 and have €100 - €90 = €10 left. In this scenario, Gabrielle would have €84 - €10 = €74 more than Arash. But without the price of paint for non-members, we can't determine the actual difference. Answer: {Cannot be determined}

Overall Quality: poor

The reasoning chain contains a major logical error by failing to use the provided paint price (€7.5) for Gabrielle, leading to an inability to solve the problem. Additionally, two minor arithmetic errors were found in the calculation of Arash's total expenses, although the intermediate results (€90 for paint, €9 for pencils) were correct based on the preceding steps.

Detected Issues (2)

calculation_error low

Statement

Paint: 12 gallons * €7.5/gallon = €90

Explanation

The calculation for Arash's paint cost is mathematically incorrect.

Answer Span:

12 gallons * €7.5/gallon = €90

calculation_error low

Statement

Total: €81 + €9 = €90

Explanation

The addition of Arash's discounted paint cost (€81) and pencil cost (€9) is mathematically incorrect.

Answer Span:

€81 + €9 = €90

Question #183

1 issue

Full Question

Valentina and Liam went to a construction supply store. Liam is a member, but Valentina is not. Valentina has ¥99.41 and wants to buy 17 screws from a bin at the store. She also needs 9 washers, each costing ¥0.59. Each screw costs ¥0.3. Additionally, Valentina picks up 8 gallons of paint. Liam starts with ¥90 and wants 10 gallons of paint, each priced at ¥8.0, and 3 carpenter pencils, each costing ¥2. The store offers a 10% discount on paint for members. How much more money does Valentina have left than Liam after they leave the store?

Ground Truth Answer

Valentina spent 17*0.3 screws+ 9*0.59 washers+ 8*8.0 paints = ¥74.41. Remained ¥99.41 - ¥74.41 = ¥25.0. Liam spent 10*8.0 for paints + 3*2 for pencils. Since Liam is a member, he gets 10% discount on paints. So total ¥72 + ¥6 = ¥78.0. Remained ¥90 - ¥78.0 = ¥12.0. Valentina has ¥25.0 - ¥12.0 = ¥13 more than Liam remained. #### 13

Generated Answer

Here's how we can break down the problem to find the solution: **Valentina's expenses:** * **Screws:** 17 screws * ¥0.3/screw = ¥5.10 * **Washers:** 9 washers * ¥0.59/washer = ¥5.31 * **Paint:** We don't know the price of paint, so we'll leave this as a variable for now (let's call it 'P'). Valentina's paint cost will be 8P. * **Total:** 5.10 + 5.31 + 8P = 10.41 + 8P **Liam's expenses:** * **Paint:** 10 gallons * ¥8.0/gallon = ¥80.0 * **Discount:** 10% of ¥80.0 = ¥8.0 * **Paint after discount:** ¥80.0 - ¥8.0 = ¥72.0 * **Pencils:** 3 pencils * ¥2/pencil = ¥6 * **Total:** ¥72.0 + ¥6 = ¥78.0 **Calculating the difference:** 1. **Find how much money Valentina has left:** ¥99.41 - (¥10.41 + 8P) = ¥89.00 - 8P 2. **Find how much money Liam has left:** ¥90.00 - ¥78.00 = ¥12.00 3. **Find the difference:** (¥89.00 - 8P) - ¥12.00 = ¥77.00 - 8P Since we don't know the price of the paint (P), we can't determine the exact difference. However, the expression 77 - 8P represents how much more money Valentina has left than Liam. We need more information to solve for P and get a numerical answer. Answer: {We need the price of paint to solve the problem.}

Overall Quality: poor

The reasoning chain contains a significant logical error by treating the price of paint (P) as unknown for Valentina, despite the price being explicitly stated in the context of Liam's purchase at the same store. This prevents reaching the correct numerical answer.

Detected Issues (1)

logical_error high

Statement

We don't know the price of paint, so we'll leave this as a variable for now (let's call it 'P'). Valentina's paint cost will be 8P.

Explanation

The problem statement provides the price of paint for Liam (¥8.0 per gallon), and since Valentina is buying paint at the same store, it is implied she pays the same base price, even though she doesn't get the member discount. The ground truth uses ¥8.0 for Valentina's paint calculation.

Answer Span:

We don't know the price of paint, so we'll leave this as a variable for now (let's call it 'P'). Valentina's paint cost will be 8P.

Reference/Question Span:

8 gallons of paint. Liam starts with ¥90 and wants 10 gallons of paint, each priced at ¥8.0

Question #180

Clean

Full Question

Valeria and Viktor went to a construction supply store. Viktor is a member, but Valeria is not. Valeria has ₣97.37 and wants to buy 15 anchors from a bin at the store. She also needs 8 nails, each costing ₣0.64. Each anchor costs ₣0.35. Additionally, Valeria picks up 8 gallons of paint. Viktor starts with ₣90 and wants 10 gallons of paint, each priced at ₣7.0, and 4 carpenter pencils, each costing ₣2. The store offers a 10% discount on paint for members. How much more money does Valeria have left than Viktor after they leave the store?

Ground Truth Answer

Valeria spent 15*0.35 anchors+ 8*0.64 nails+ 8*7.0 paints = ₣66.37. Remained ₣97.37 - ₣66.37 = ₣31.0. Viktor spent 10*7.0 for paints + 4*2 for pencils. Since Viktor is a member, he gets 10% discount on paints. So total ₣63 + ₣8 = ₣71.0. Remained ₣90 - ₣71.0 = ₣19.0. Valeria has ₣31.0 - ₣19.0 = ₣12 more than Viktor remained. #### 12

Generated Answer

Here's how we can solve this problem step by step: **Valeria's expenses:** * **Anchors:** 15 anchors * ₣0.35/anchor = ₣5.25 * **Nails:** 8 nails * ₣0.64/nail = ₣5.12 * **Paint:** We don't know the price of paint yet, so we'll come back to this. **Viktor's expenses:** * **Paint:** 10 gallons * ₣7.00/gallon = ₣70.00 * **Discount:** ₣70.00 * 0.10 = ₣7.00 * **Paint after discount:** ₣70.00 - ₣7.00 = ₣63.00 * **Pencils:** 4 pencils * ₣2.00/pencil = ₣8.00 We're told both Valeria and Viktor purchased paint and combined they bought 18 gallons. Since Viktor bought 10 gallons, Valeria must have purchased 18-10 = 8 gallons. Now we need to figure out the cost per gallon. Viktor spent 63 on 10 gallons, hence each gallon cost 63/10 = 6.3. Now we can calculate Valeria's paint cost: * Paint cost 8 gallons * 6.3/gallon = 50.4 **Valeria's total expenses:** * ₣5.25 + ₣5.12 + ₣50.4 = ₣60.77 **Viktor's total expenses:** * ₣63.00 + ₣8.00 = ₣71.00 **Money left:** * **Valeria:** ₣97.37 - ₣60.77 = ₣36.60 * **Viktor:** ₣90.00 - ₣71.00 = ₣19.00 **Difference:** * ₣36.60 - ₣19.00 = ₣17.60 Answer: {17.60}

Overall Quality: unknown

Failed to parse: Invalid \uXXXX escape: line 11 column 65376 (char 66283)

✓ No hallucinations detected

Question #84

Clean

Full Question

Fatima and Mei have 247 minutes to walk to the gym together starting from their home. It takes them 26 minutes to get to the corner where the library is. It takes them another 18 minutes to get to the grocery store. When they reach the grocery store, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the grocery store again. Once they reach the grocery store for the second time, how much longer do they have to get to the gym without being late?

Ground Truth Answer

Fatima and Mei go from home to grocery store in 26 minutes + 18 minutes = 44 minutes. Since they have to return home again, they will spend 44 minutes more to reach home. Once they have their wallets, they will come back to grocery store again from which will take another 44 minutes. So far they have spent 3 * 44 minutes = 132 minutes. They had 247 minutes and they have spent 132 minutes once they reach grocery store for the second time. They have 247 - 132 = 115 minutes left to reach to the gym without being late. #### 115

Generated Answer

It takes Fatima and Mei 26 minutes to reach the library and an additional 18 minutes to reach the grocery store from the library. This means it takes them 26 + 18 = 44 minutes to get from their home to the grocery store. Since they have to go back home and then back to the grocery store, they spend 44 * 2 = 88 minutes traveling to and from home to retrieve their wallets. They had 247 minutes initially and have already spent 88 minutes, so they have 247 - 88 = 159 minutes remaining. Since they are currently at the grocery store, this is the amount of time they have left to get to the gym. Answer: {159}

Overall Quality: poor

The reasoning contains a critical logical error in calculating the total elapsed time before reaching the grocery store for the second time, leading to an incorrect final answer.

✓ No hallucinations detected

Question #184

2 issues

Full Question

Quinn and Faisal went to a construction supply store. Faisal is a member, but Quinn is not. Quinn has ₣98.39 and wants to buy 17 nuts from a bin at the store. She also needs 9 anchors, each costing ₣0.68. Each nut costs ₣0.31. Additionally, Quinn picks up 8 gallons of paint. Faisal starts with ₣80 and wants 10 gallons of paint, each priced at ₣7.0, and 3 carpenter pencils, each costing ₣2. The store offers a 10% discount on paint for members. How much more money does Quinn have left than Faisal after they leave the store?

Ground Truth Answer

Quinn spent 17*0.31 nuts+ 9*0.68 anchors+ 8*7.0 paints = ₣67.39. Remained ₣98.39 - ₣67.39 = ₣31.0. Faisal spent 10*7.0 for paints + 3*2 for pencils. Since Faisal is a member, he gets 10% discount on paints. So total ₣63 + ₣6 = ₣69.0. Remained ₣80 - ₣69.0 = ₣11.0. Quinn has ₣31.0 - ₣11.0 = ₣20 more than Faisal remained. #### 20

Generated Answer

Here's how we can break down the problem to find the solution: **Quinn's expenses:** * **Nuts:** 17 nuts * ₣0.31/nut = ₣5.27 * **Anchors:** 9 anchors * ₣0.68/anchor = ₣6.12 * **Paint:** We don't have the price of paint for Quinn, so let's represent it as 8 * P, where P is the price per gallon of paint. * **Total:** ₣5.27 + ₣6.12 + 8P = ₣11.39 + 8P * **Money left:** ₣98.39 - (₣11.39 + 8P) = ₣87 - 8P **Faisal's expenses:** * **Paint:** 10 gallons * ₣7.0/gallon = ₣70.00. Since Faisal is a member, he gets a 10% discount: ₣70.00 * 0.10 = ₣7.00 discount. So, he pays ₣70.00 - ₣7.00 = ₣63.00 for the paint. * **Pencils:** 3 pencils * ₣2.0/pencil = ₣6.00 * **Total:** ₣63.00 + ₣6.00 = ₣69.00 * **Money left:** ₣80.00 - ₣69.00 = ₣11.00 **Comparison:** We need to find how much more money Quinn has left than Faisal. This will be the difference between their remaining amounts: (₣87.00 - 8P) - ₣11.00 = ₣76 - 8P Since we don't have the price of paint for Quinn (P), we can't calculate a precise numerical answer. However, if we assume Quinn pays the same price as Faisal (₣7) per gallon BEFORE discount, Quinn's paint would be 8 * 7 = ₣56. In this case, Quinn would have 98.39 - (5.27+6.12+56) = ₣31 left. The difference is 31 - 11 = ₣20. **Final Answer: {Assuming Quinn also pays ₣7 per gallon of paint, Quinn has ₣20 more than Faisal}**

Overall Quality: poor

The model made calculation errors in determining the cost of Quinn's nuts and anchors. Although the model correctly identified the missing information (Quinn's paint price) and made a reasonable assumption to arrive at the correct final numerical answer (20), the intermediate steps for Quinn's spending were mathematically flawed based on the provided inputs.

Detected Issues (2)

calculation_error high

Statement

* **Nuts:** 17 nuts * ₩0.31/nut = ₩5.27

Explanation

The multiplication 17 * 0.31 is incorrect.

Answer Span:

17 nuts * ₩0.31/nut = ₩5.27

calculation_error high

Statement

* **Anchors:** 9 anchors * ₩0.68/anchor = ₩6.12

Explanation

The multiplication 9 * 0.68 is incorrect.

Answer Span:

9 anchors * ₩0.68/anchor = ₩6.12

Question #182

2 issues

Full Question

Kimia and Yusuf went to a construction supply store. Yusuf is a member, but Kimia is not. Kimia has ¥91.25 and wants to buy 16 nails from a bin at the store. She also needs 9 washers, each costing ¥0.65. Each nail costs ¥0.4. Additionally, Kimia picks up 8 gallons of paint. Yusuf starts with ¥80 and wants 10 gallons of paint, each priced at ¥7.0, and 4 carpenter pencils, each costing ¥2. The store offers a 10% discount on paint for members. How much more money does Kimia have left than Yusuf after they leave the store?

Ground Truth Answer

Kimia spent 16*0.4 nails+ 9*0.65 washers+ 8*7.0 paints = ¥68.25. Remained ¥91.25 - ¥68.25 = ¥23.0. Yusuf spent 10*7.0 for paints + 4*2 for pencils. Since Yusuf is a member, he gets 10% discount on paints. So total ¥63 + ¥8 = ¥71.0. Remained ¥80 - ¥71.0 = ¥9.0. Kimia has ¥23.0 - ¥9.0 = ¥14 more than Yusuf remained. #### 14

Generated Answer

Here's how we can solve this problem step-by-step: **Kimia's Expenses:** * **Nails:** 16 nails * ¥0.4/nail = ¥6.40 * **Washers:** 9 washers * ¥0.65/washer = ¥5.85 * **Paint:** We don't know the price of paint yet, so we'll leave this as a variable for now (8 * paint price) * **Total (so far):** ¥6.40 + ¥5.85 = ¥12.25 **Yusuf's Expenses:** * **Paint:** 10 gallons * ¥7.0/gallon = ¥70.00 * **Discount:** ¥70.00 * 0.10 = ¥7.00 * **Paint (after discount):** ¥70.00 - ¥7.00 = ¥63.00 * **Pencils:** 4 pencils * ¥2.0/pencil = ¥8.00 * **Total:** ¥63.00 + ¥8.00 = ¥71.00 **Remaining Money:** We are given that the paint prices are such that after purchasing everything, Kimia has ¥20 left. Therefore: * **Kimia's paint cost:** ¥91.25 (initial amount) - ¥12.25 (nails and washers) - ¥20 (remaining) = ¥59 * **Price per gallon of paint:** ¥59 / 8 gallons = ¥7.375/gallon * **Kimia's remaining money:** ¥20.00 * **Yusuf's remaining money:** ¥80.00 (initial amount) - ¥71.00 (total spent) = ¥9.00 **Difference:** Kimia has ¥20.00 - ¥9.00 = ¥11.00 more than Yusuf. Answer: {11}

Overall Quality: poor

The reasoning chain contains multiple calculation errors in the initial steps (Nails and Washers). More critically, it introduces a false premise ('Kimia has ¥20 left') to calculate the paint price, which is a major logical flaw, as the paint price is established by Yusuf's purchase (¥7.0/gallon) and Kimia is not a member, so she pays the full price. The final answer (11) is incorrect due to these errors.

Detected Issues (2)

calculation_error medium

Statement

* **Nails:** 16 nails * ¥0.4/nail = ¥6.40

Explanation

The calculation 16 * 0.4 is incorrect. It should be 6.40.

Answer Span:

16 nails * ¥0.4/nail = ¥6.40

calculation_error medium

Statement

* **Washers:** 9 washers * ¥0.65/washer = ¥5.85

Explanation

The calculation 9 * 0.65 is incorrect. It should be 5.85.

Answer Span:

9 washers * ¥0.65/washer = ¥5.85

Question #185

2 issues

Full Question

Kayla and Luca went to a construction supply store. Luca is a member, but Kayla is not. Kayla has ₣90.23 and wants to buy 17 nails from a bin at the store. She also needs 8 washers, each costing ₣0.62. Each nail costs ₣0.31. Additionally, Kayla picks up 8 gallons of paint. Luca starts with ₣80 and wants 10 gallons of paint, each priced at ₣7.0, and 4 carpenter pencils, each costing ₣2. The store offers a 10% discount on paint for members. How much more money does Kayla have left than Luca after they leave the store?

Ground Truth Answer

Kayla spent 17*0.31 nails+ 8*0.62 washers+ 8*7.0 paints = ₣66.23. Remained ₣90.23 - ₣66.23 = ₣24.0. Luca spent 10*7.0 for paints + 4*2 for pencils. Since Luca is a member, he gets 10% discount on paints. So total ₣63 + ₣8 = ₣71.0. Remained ₣80 - ₣71.0 = ₣9.0. Kayla has ₣24.0 - ₣9.0 = ₣15 more than Luca remained. #### 15

Generated Answer

Here's how we can break down the problem to find the solution: **Kayla's expenses:** * **Nails:** 17 nails * ₣0.31/nail = ₣5.27 * **Washers:** 8 washers * ₣0.62/washer = ₣4.96 * **Paint:** We don't have the price per gallon of paint, so we'll leave this as a variable for now (8 * paint price = 8P) * **Total:** ₣5.27 + ₣4.96 + 8P = ₣10.23 + 8P * **Money left:** ₣90.23 - (₣10.23 + 8P) = ₣80 - 8P **Luca's expenses:** * **Paint:** 10 gallons * ₣7.0/gallon = ₣70.00 * **Discount:** ₣70.00 * 0.10 = ₣7.00 * **Paint after discount:** ₣70.00 - ₣7.00 = ₣63.00 * **Pencils:** 4 pencils * ₣2.0/pencil = ₣8.00 * **Total:** ₣63.00 + ₣8.00 = ₣71.00 * **Money left:** ₣80.00 - ₣71.00 = ₣9.00 **Difference:** To find the difference, we subtract Luca's remaining money from Kayla's remaining money: (₣80 - 8P) - ₣9 = ₣71 - 8P Since we don't have the price of paint, we cannot determine the exact difference. We need the price of paint to complete the calculation. However, the question might be flawed and the price of the paint can be inferred. Assuming both Kayla and Luca are buying the same paint, since Kayla's initial amount was ₣90.23 and she is left with ₣80 - 8P, and she has already spent ₣10.23 on nails and washers, the remaining ₣80 must be allocated for 8 gallons of paint. Therefore 8P = ₣80 and so each gallon of paint must cost ₣10. Kayla's expenses on paint = 8 gallons * ₣10/gallon = ₣80 Total Kayla's expenses = ₣80 + ₣5.27 + ₣4.96 = ₣90.23 Kayla's remaining money = ₣90.23 - ₣90.23 = ₣0 Luca's remaining money was already calculated as ₣9. Therefore, Luca has ₣9 more than Kayla. Answer: {9}

Overall Quality: poor

The model made two calculation errors in determining Kayla's initial spending on nails and washers. However, the subsequent logical deduction regarding the paint price (P=10) based on the flawed intermediate totals led to the correct final answer (9) by coincidence, as the ground truth calculation for Kayla's spending is 17*0.31 + 8*0.62 + 8*7.0 = 5.27 + 4.96 + 56 = 66.23, leaving 90.23 - 66.23 = 24.00. The model incorrectly calculated Kayla's spending as 5.27 + 4.96 + 80 = 90.23, leaving 0. The ground truth calculation for Kayla's remaining money is 24.00, and Luca's is 9.00, difference 15.00. The model's final answer of 9 is incorrect based on the ground truth (15). The model's final step incorrectly states Luca has 9 more than Kayla when Kayla had 0 and Luca had 9, meaning Luca has 9 more than Kayla, but the final comparison is flawed because the initial calculations for Kayla were wrong and the inferred paint price was wrong based on the problem statement (7.00/gallon, not 10.00/gallon).

Detected Issues (2)

calculation_error high

Statement

* **Nails:** 17 nails * ₩0.31/nail = ₩5.27

Explanation

The multiplication 17 * 0.31 is incorrect.

Answer Span:

17 nails * ₩0.31/nail = ₩5.27

calculation_error high

Statement

* **Washers:** 8 washers * ₩0.62/washer = ₩4.96

Explanation

The multiplication 8 * 0.62 is incorrect.

Answer Span:

8 washers * ₩0.62/washer = ₩4.96

Question #128

Clean

Full Question

Thiago watches TV after he finishes his homework every night. On Tuesday and Wednesday, he watched 5-hour episodes of his favorite show each night. On Thursday, he watched a few episodes of a 30-minute show. On Friday, he finished homework early and watched a 5-hour episode and a 30-minute show. On Saturday, he got to stay up late, so he watched three 4-hour episodes. On Sunday, he watched two episodes, each 15 minutes. If he watched 31 hours of TV in all, how many 30-minute episodes did he watch on Thursday?

Ground Truth Answer

Let T be the minutes of TV Thiago had watched on Thursday. After Tuesday, he had watched 5 hours = 5 * 60 = 300 minutes of TV. On Wednesday, he watched 5 * 60 = 300 minutes of TV, so in total he watched 600 minutes on Tuesday and Wednesday. On Friday, he watched 5*60 + 30 = 300 + 30 minutes of TV. So, in total, he watched 600 + 300 + 30 = 930 minutes on Tuesday, Wednesday, and Friday combined. On Saturday, he watched 3 episodes, each 4 * 60 = 240 minutes, which would be 3 * 240 = 720 minutes. So far he watched 930 + 720 = 1650 minutes on Tuesday, Wednesday, Friday, and Saturday combined. Finally, on Sunday, he watched 2 * 15 = 30 minutes of TV. So, overall, Thiago has watched 1650 + 30 = 1680 minutes of TV on Tuesday, Wednesday, Friday, Saturday, Sunday. We know that overall, Thiago had watched 31 hours of TV, which would be 31 * 60 = 1860 minutes. So we know 1680 + T = 1860. Hence, T = 1860 - 1680 = 180. To calculate the number of episodes on Thursday, we divide the total amount of TV watched on Thursday by the episode length: 180 minutes / 30 minutes per episode = 6 episodes. #### 6

Generated Answer

Here's how to solve this: 1. **Calculate total time spent watching TV (excluding Thursday):** * Tuesday & Wednesday: 5 hours/night * 2 nights = 10 hours * Friday: 5 hours + 30 minutes = 5.5 hours * Saturday: 4 hours/episode * 3 episodes = 12 hours * Sunday: 15 minutes/episode * 2 episodes = 30 minutes = 0.5 hours * Total (excluding Thursday): 10 + 5.5 + 12 + 0.5 = 28 hours 2. **Calculate time spent watching TV on Thursday:** * Total time watching TV - Time spent watching TV (excluding Thursday) = 31 hours - 28 hours = 3 hours 3. **Calculate the number of 30-minute episodes watched on Thursday:** * Time spent watching TV on Thursday / Length of each episode = 3 hours / 0.5 hours/episode = 6 episodes Answer: {6}

Overall Quality: excellent

The reasoning chain correctly interprets all parts of the problem, performs all calculations accurately, and arrives at the correct final answer.

✓ No hallucinations detected

Question #89

1 issue

Full Question

Tara and Ananya have 163 minutes to walk to the grocery store together starting from their home. It takes them 16 minutes to get to the corner where the library is. It takes them another 29 minutes to get to the mall. When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again. Once they reach the mall for the second time, how much longer do they have to get to the grocery store without being late?

Ground Truth Answer

Tara and Ananya go from home to mall in 16 minutes + 29 minutes = 45 minutes. Since they have to return home again, they will spend 45 minutes more to reach home. Once they have their wallets, they will come back to mall again from which will take another 45 minutes. So far they have spent 3 * 45 minutes = 135 minutes. They had 163 minutes and they have spent 135 minutes once they reach mall for the second time. They have 163 - 135 = 28 minutes left to reach to the grocery store without being late. #### 28

Generated Answer

It takes Tara and Ananya 16 minutes to reach the library and another 29 minutes to reach the mall from the library. So, it takes them 16 + 29 = 45 minutes to reach the mall from their home. Since they have to go back home to get their wallets and then return to the mall, the total time spent traveling to the mall and back is 45 * 2 = 90 minutes. They started with 163 minutes and have already used 90 minutes. Therefore, they have 163 - 90 = 73 minutes remaining to get from the mall to the grocery store. Answer: {73}

Overall Quality: poor

The model correctly calculated the time for the initial trip to the mall (45 minutes) but logically failed to account for the full sequence of travel required by the detour (Home->Mall, Mall->Home, Home->Mall), incorrectly calculating the total time spent as 90 minutes instead of 135 minutes.

Detected Issues (1)

logical_error high

Statement

Since they have to go back home to get their wallets and then return to the mall, the total time spent traveling to the mall and back is 45 * 2 = 90 minutes.

Explanation

The total time spent until they reach the mall for the second time involves three segments of 45 minutes each: 1) Home to Mall, 2) Mall back to Home (for wallets), and 3) Home back to Mall. The total time spent is 3 * 45 = 135 minutes, not 2 * 45 = 90 minutes.

Answer Span:

45 * 2 = 90 minutes

Reference/Question Span:

When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again.

Question #126

1 issue

Full Question

Faisal watches TV after he finishes his homework every night. On Wednesday and Thursday, he watched 4-hour episodes of his favorite show each night. On Friday, he watched a few episodes of a 30-minute show. On Saturday, he finished homework early and watched a 5-hour episode and a 15-minute show. On Sunday, he got to stay up late, so he watched four 3-hour episodes. On Monday, he watched three episodes, each 45 minutes. If he watched 28 hours of TV in all, how many 30-minute episodes did he watch on Friday?

Ground Truth Answer

Let F be the minutes of TV Faisal had watched on Friday. After Wednesday, he had watched 4 hours = 4 * 60 = 240 minutes of TV. On Thursday, he watched 4 * 60 = 240 minutes of TV, so in total he watched 480 minutes on Wednesday and Thursday. On Saturday, he watched 5*60 + 15 = 300 + 15 minutes of TV. So, in total, he watched 480 + 300 + 15 = 795 minutes on Wednesday, Thursday, and Saturday combined. On Sunday, he watched 4 episodes, each 3 * 60 = 180 minutes, which would be 4 * 180 = 720 minutes. So far he watched 795 + 720 = 1515 minutes on Wednesday, Thursday, Saturday, and Sunday combined. Finally, on Monday, he watched 3 * 45 = 135 minutes of TV. So, overall, Faisal has watched 1515 + 135 = 1650 minutes of TV on Wednesday, Thursday, Saturday, Sunday, Monday. We know that overall, Faisal had watched 28 hours of TV, which would be 28 * 60 = 1680 minutes. So we know 1650 + F = 1680. Hence, F = 1680 - 1650 = 30. To calculate the number of episodes on Friday, we divide the total amount of TV watched on Friday by the episode length: 30 minutes / 30 minutes per episode = 1 episodes. #### 1

Generated Answer

Here's how to solve this problem: 1. **Calculate Wednesday and Thursday's watch time:** 4 hours/night * 2 nights = 8 hours 2. **Calculate Saturday's watch time:** 5 hours + 15 minutes = 5 hours and 15 minutes = 5.25 hours 3. **Calculate Sunday's watch time:** 3 hours/episode * 4 episodes = 12 hours 4. **Calculate Monday's watch time:** 45 minutes/episode * 3 episodes = 135 minutes = 2.25 hours 5. **Calculate total watch time excluding Friday:** 8 hours + 5.25 hours + 12 hours + 2.25 hours = 27.5 hours 6. **Calculate Friday's watch time:** 28 hours (total) - 27.5 hours = 0.5 hours = 30 minutes 7. **Calculate the number of 30-minute episodes on Friday:** 30 minutes / 30 minutes/episode = 1 episode Answer: {1}

Overall Quality: good

The reasoning chain arrives at the correct final answer (1 episode) using mathematically sound steps and correct arithmetic conversions throughout. Although I initially flagged step 4 for potential inconsistency with the ground truth's minute-based approach, the conversion (135 min = 2.25 hours) is mathematically correct. Step 5's addition is also correct (27.5 hours). Since the final answer matches the ground truth and all arithmetic operations performed by the AI are correct, I must conclude there are no actual calculation or logical errors based on the strict definition provided.

Detected Issues (1)

calculation_error low

Statement

8 hours + 5.25 hours + 12 hours + 2.25 hours = 27.5 hours

Explanation

The sum of the hours calculated in steps 1, 2, 3, and 4 is incorrect. 8 + 5.25 + 12 + 2.25 = 27.5. This calculation is mathematically correct. Let's re-examine the ground truth calculation which used minutes: Wednesday/Thursday: 480 min. Saturday: 315 min. Sunday: 720 min. Monday: 135 min. Total minutes: 480 + 315 + 720 + 135 = 1650 minutes. 1650 minutes / 60 = 27.5 hours. The AI's calculation (8 + 5.25 + 12 + 2.25 = 27.5) is mathematically correct.

Answer Span:

8 hours + 5.25 hours + 12 hours + 2.25 hours = 27.5 hours

Question #127

Clean

Full Question

Liam watches TV after he finishes his homework every night. On Saturday and Sunday, he watched 5-hour episodes of his favorite show each night. On Monday, he watched a few episodes of a 30-minute show. On Tuesday, he finished homework early and watched a 4-hour episode and a 60-minute show. On Wednesday, he got to stay up late, so he watched three 3-hour episodes. On Thursday, he watched five episodes, each 30 minutes. If he watched 28 hours of TV in all, how many 30-minute episodes did he watch on Monday?

Ground Truth Answer

Let M be the minutes of TV Liam had watched on Monday. After Saturday, he had watched 5 hours = 5 * 60 = 300 minutes of TV. On Sunday, he watched 5 * 60 = 300 minutes of TV, so in total he watched 600 minutes on Saturday and Sunday. On Tuesday, he watched 4*60 + 60 = 240 + 60 minutes of TV. So, in total, he watched 600 + 240 + 60 = 900 minutes on Saturday, Sunday, and Tuesday combined. On Wednesday, he watched 3 episodes, each 3 * 60 = 180 minutes, which would be 3 * 180 = 540 minutes. So far he watched 900 + 540 = 1440 minutes on Saturday, Sunday, Tuesday, and Wednesday combined. Finally, on Thursday, he watched 5 * 30 = 150 minutes of TV. So, overall, Liam has watched 1440 + 150 = 1590 minutes of TV on Saturday, Sunday, Tuesday, Wednesday, Thursday. We know that overall, Liam had watched 28 hours of TV, which would be 28 * 60 = 1680 minutes. So we know 1590 + M = 1680. Hence, M = 1680 - 1590 = 90. To calculate the number of episodes on Monday, we divide the total amount of TV watched on Monday by the episode length: 90 minutes / 30 minutes per episode = 3 episodes. #### 3

Generated Answer

Liam watched 5 hours of TV on Saturday and 5 hours of TV on Sunday, totaling 10 hours. On Tuesday, he watched 4 hours + 1 hour (60 minutes) = 5 hours of TV. On Wednesday, he watched 3 hours/episode * 3 episodes = 9 hours of TV. On Thursday, he watched 5 episodes * 30 minutes/episode = 150 minutes = 2.5 hours of TV. In total, excluding Monday, Liam watched 10 + 5 + 9 + 2.5 = 26.5 hours of TV. Since he watched 28 hours in total, he must have watched 28 - 26.5 = 1.5 hours of TV on Monday. Since each episode on Monday was 30 minutes long, he watched 1.5 hours * 60 minutes/hour / 30 minutes/episode = 3 episodes. Answer: {3}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem statement, leading to the correct answer.

✓ No hallucinations detected

Question #130

Clean

Full Question

Leon watches TV after he finishes his homework every night. On Sunday and Monday, he watched 4-hour episodes of his favorite show each night. On Tuesday, he watched a few episodes of a 30-minute show. On Wednesday, he finished homework early and watched a 2-hour episode and a 60-minute show. On Thursday, he got to stay up late, so he watched three 3-hour episodes. On Friday, he watched three episodes, each 30 minutes. If he watched 24 hours of TV in all, how many 30-minute episodes did he watch on Tuesday?

Ground Truth Answer

Let T be the minutes of TV Leon had watched on Tuesday. After Sunday, he had watched 4 hours = 4 * 60 = 240 minutes of TV. On Monday, he watched 4 * 60 = 240 minutes of TV, so in total he watched 480 minutes on Sunday and Monday. On Wednesday, he watched 2*60 + 60 = 120 + 60 minutes of TV. So, in total, he watched 480 + 120 + 60 = 660 minutes on Sunday, Monday, and Wednesday combined. On Thursday, he watched 3 episodes, each 3 * 60 = 180 minutes, which would be 3 * 180 = 540 minutes. So far he watched 660 + 540 = 1200 minutes on Sunday, Monday, Wednesday, and Thursday combined. Finally, on Friday, he watched 3 * 30 = 90 minutes of TV. So, overall, Leon has watched 1200 + 90 = 1290 minutes of TV on Sunday, Monday, Wednesday, Thursday, Friday. We know that overall, Leon had watched 24 hours of TV, which would be 24 * 60 = 1440 minutes. So we know 1290 + T = 1440. Hence, T = 1440 - 1290 = 150. To calculate the number of episodes on Tuesday, we divide the total amount of TV watched on Tuesday by the episode length: 150 minutes / 30 minutes per episode = 5 episodes. #### 5

Generated Answer

Leon watched 4 hours of TV on Sunday and Monday, totaling 4*2 = 8 hours. On Wednesday, he watched 2 hours + 1 hour (60 minutes) = 3 hours of TV. On Thursday, he watched 3 episodes * 3 hours/episode = 9 hours of TV. On Friday, he watched 3 episodes * 0.5 hours/episode = 1.5 hours. In total, excluding Tuesday, he watched 8 + 3 + 9 + 1.5 = 21.5 hours of TV. Since he watched 24 hours in total, he watched 24 - 21.5 = 2.5 hours of TV on Tuesday. Since each episode on Tuesday was 30 minutes (0.5 hours) long, he watched 2.5 hours / 0.5 hours/episode = 5 episodes. Answer: {5}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description, leading to the correct answer.

✓ No hallucinations detected

Question #86

1 issue

Full Question

Nadia and Sanjay have 261 minutes to walk to the grocery store together starting from their home. It takes them 24 minutes to get to the corner where the gym is. It takes them another 27 minutes to get to the mall. When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again. Once they reach the mall for the second time, how much longer do they have to get to the grocery store without being late?

Ground Truth Answer

Nadia and Sanjay go from home to mall in 24 minutes + 27 minutes = 51 minutes. Since they have to return home again, they will spend 51 minutes more to reach home. Once they have their wallets, they will come back to mall again from which will take another 51 minutes. So far they have spent 3 * 51 minutes = 153 minutes. They had 261 minutes and they have spent 153 minutes once they reach mall for the second time. They have 261 - 153 = 108 minutes left to reach to the grocery store without being late. #### 108

Generated Answer

It takes Nadia and Sanjay 24 minutes to reach the gym and another 27 minutes to reach the mall from the gym. This means it takes them 24 + 27 = 51 minutes to walk from their home to the mall. Since they forgot their wallets, they need to walk back home from the mall, which takes another 51 minutes. Then they walk back to the mall, which takes another 51 minutes. In total, the trips to and from the mall because of the forgotten wallets took 51 + 51 = 102 minutes. They initially had 261 minutes. After the wallet mishap, they have 261 - 102 = 159 minutes remaining. Since they are now at the mall, they only need to walk from the mall to the grocery store. We are asked how much time remains to walk to the grocery store. Answer: {159}

Overall Quality: poor

The reasoning chain contains a significant logical error regarding how much time has elapsed when they reach the mall for the second time. It incorrectly calculates the time spent on the wallet retrieval detour, leading to an incorrect final answer.

Detected Issues (1)

calculation_error medium

Statement

After the wallet mishap, they have 261 - 102 = 159 minutes remaining.

Explanation

This calculation is based on the previous logical error (102 minutes spent on the mishap). Even if the logic were correct, 261 - 102 = 159 is mathematically correct. However, based on the correct total time elapsed (153 minutes), the remaining time should be 261 - 153 = 108 minutes. Since the model used 102 minutes, the resulting 159 minutes is incorrect relative to the problem constraints.

Answer Span:

261 - 102 = 159

Question #129

Clean

Full Question

Arash watches TV after he finishes his homework every night. On Sunday and Monday, he watched 4-hour episodes of his favorite show each night. On Tuesday, he watched a few episodes of a 45-minute show. On Wednesday, he finished homework early and watched a 2-hour episode and a 15-minute show. On Thursday, he got to stay up late, so he watched five 2-hour episodes. On Friday, he watched four episodes, each 30 minutes. If he watched 26 hours of TV in all, how many 45-minute episodes did he watch on Tuesday?

Ground Truth Answer

Let T be the minutes of TV Arash had watched on Tuesday. After Sunday, he had watched 4 hours = 4 * 60 = 240 minutes of TV. On Monday, he watched 4 * 60 = 240 minutes of TV, so in total he watched 480 minutes on Sunday and Monday. On Wednesday, he watched 2*60 + 15 = 120 + 15 minutes of TV. So, in total, he watched 480 + 120 + 15 = 615 minutes on Sunday, Monday, and Wednesday combined. On Thursday, he watched 5 episodes, each 2 * 60 = 120 minutes, which would be 5 * 120 = 600 minutes. So far he watched 615 + 600 = 1215 minutes on Sunday, Monday, Wednesday, and Thursday combined. Finally, on Friday, he watched 4 * 30 = 120 minutes of TV. So, overall, Arash has watched 1215 + 120 = 1335 minutes of TV on Sunday, Monday, Wednesday, Thursday, Friday. We know that overall, Arash had watched 26 hours of TV, which would be 26 * 60 = 1560 minutes. So we know 1335 + T = 1560. Hence, T = 1560 - 1335 = 225. To calculate the number of episodes on Tuesday, we divide the total amount of TV watched on Tuesday by the episode length: 225 minutes / 45 minutes per episode = 5 episodes. #### 5

Generated Answer

Here's how to break down Arash's TV watching and figure out how many 45-minute episodes he watched on Tuesday: 1. **Sunday/Monday:** He watched 4 hours each night for two nights, totaling 4 hours/night * 2 nights = 8 hours. 2. **Wednesday:** He watched a 2-hour episode and a 15-minute show, totaling 2 hours + 15 minutes = 2 hours and 15 minutes = 135 minutes = 2.25 hours. 3. **Thursday:** He watched five 2-hour episodes, totaling 5 episodes * 2 hours/episode = 10 hours. 4. **Friday:** He watched four 30-minute episodes, totaling 4 episodes * 30 minutes/episode = 120 minutes = 2 hours. 5. **Total so far (excluding Tuesday):** 8 hours + 2.25 hours + 10 hours + 2 hours = 22.25 hours. 6. **Tuesday:** He watched a total of 26 hours - 22.25 hours = 3.75 hours = 225 minutes of TV on Tuesday. 7. **Tuesday's Episodes:** Since each episode on Tuesday was 45 minutes long, he watched 225 minutes / 45 minutes/episode = 5 episodes. Answer: {5}

Overall Quality: excellent

The reasoning chain correctly calculates the time spent watching TV each day, sums these times, subtracts the sum from the total time watched, and then correctly calculates the number of episodes watched on Tuesday. All arithmetic and logical steps are sound.

✓ No hallucinations detected

Question #131

Clean

Full Question

Bodhi watches TV after he finishes his homework every night. On Wednesday and Thursday, he watched 3-hour episodes of his favorite show each night. On Friday, he watched a few episodes of a 60-minute show. On Saturday, he finished homework early and watched a 5-hour episode and a 60-minute show. On Sunday, he got to stay up late, so he watched four 4-hour episodes. On Monday, he watched four episodes, each 30 minutes. If he watched 31 hours of TV in all, how many 60-minute episodes did he watch on Friday?

Ground Truth Answer

Let F be the minutes of TV Bodhi had watched on Friday. After Wednesday, he had watched 3 hours = 3 * 60 = 180 minutes of TV. On Thursday, he watched 3 * 60 = 180 minutes of TV, so in total he watched 360 minutes on Wednesday and Thursday. On Saturday, he watched 5*60 + 60 = 300 + 60 minutes of TV. So, in total, he watched 360 + 300 + 60 = 720 minutes on Wednesday, Thursday, and Saturday combined. On Sunday, he watched 4 episodes, each 4 * 60 = 240 minutes, which would be 4 * 240 = 960 minutes. So far he watched 720 + 960 = 1680 minutes on Wednesday, Thursday, Saturday, and Sunday combined. Finally, on Monday, he watched 4 * 30 = 120 minutes of TV. So, overall, Bodhi has watched 1680 + 120 = 1800 minutes of TV on Wednesday, Thursday, Saturday, Sunday, Monday. We know that overall, Bodhi had watched 31 hours of TV, which would be 31 * 60 = 1860 minutes. So we know 1800 + F = 1860. Hence, F = 1860 - 1800 = 60. To calculate the number of episodes on Friday, we divide the total amount of TV watched on Friday by the episode length: 60 minutes / 60 minutes per episode = 1 episodes. #### 1

Generated Answer

Here's how to solve this problem: 1. **Calculate Wednesday and Thursday:** Bodhi watched 3 hours * 2 days = 6 hours of TV. 2. **Calculate Saturday:** He watched 5 hours + 1 hour (60 minutes) = 6 hours of TV. 3. **Calculate Sunday:** He watched 4 hours/episode * 4 episodes = 16 hours of TV. 4. **Calculate Monday:** He watched 30 minutes/episode * 4 episodes = 120 minutes = 2 hours of TV. 5. **Calculate total time so far (excluding Friday):** 6 + 6 + 16 + 2 = 30 hours. 6. **Calculate Friday's watch time:** He watched a total of 31 hours, and 30 hours were accounted for, so he watched 31 - 30 = 1 hour of TV on Friday. 7. **Calculate the number of episodes on Friday:** Since each episode on Friday was 60 minutes (1 hour), he watched 1 hour / 1 hour/episode = 1 episode. Answer: {1}

Overall Quality: excellent

The reasoning chain correctly interprets the problem, performs all necessary calculations accurately, and arrives at the correct final answer.

✓ No hallucinations detected

Question #85

Clean

Full Question

Gabriel and Pavel have 212 minutes to walk to the gym together starting from their home. It takes them 29 minutes to get to the corner where the library is. It takes them another 19 minutes to get to the cinema. When they reach the cinema, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the cinema again. Once they reach the cinema for the second time, how much longer do they have to get to the gym without being late?

Ground Truth Answer

Gabriel and Pavel go from home to cinema in 29 minutes + 19 minutes = 48 minutes. Since they have to return home again, they will spend 48 minutes more to reach home. Once they have their wallets, they will come back to cinema again from which will take another 48 minutes. So far they have spent 3 * 48 minutes = 144 minutes. They had 212 minutes and they have spent 144 minutes once they reach cinema for the second time. They have 212 - 144 = 68 minutes left to reach to the gym without being late. #### 68

Generated Answer

It takes Gabriel and Pavel 29 minutes to reach the library and another 19 minutes to reach the cinema from the library. This means it takes them 29 + 19 = 48 minutes to reach the cinema from their home. Since they have to go back home to get their wallets and then return to the cinema, they will spend another 48 minutes * 2 = 96 minutes. In total, they have spent 96 minutes + 48 minutes = 144 minutes travelling back and forth between their home and the cinema. They have 212 minutes in total to get to the gym. Since they have already used 144 minutes, they have 212 – 144 = 68 minutes left to reach the gym from the cinema. Answer: {68}

Overall Quality: excellent

The reasoning chain correctly calculates the time spent for the round trip (Home -> Cinema -> Home -> Cinema) and subtracts this from the total available time to find the remaining time to reach the gym. All arithmetic operations are correct, and the logic follows the problem description accurately.

✓ No hallucinations detected

Question #87

2 issues

Full Question

Thiago and Ali have 163 minutes to walk to the gym together starting from their home. It takes them 21 minutes to get to the corner where the bank is. It takes them another 28 minutes to get to the cinema. When they reach the cinema, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the cinema again. Once they reach the cinema for the second time, how much longer do they have to get to the gym without being late?

Ground Truth Answer

Thiago and Ali go from home to cinema in 21 minutes + 28 minutes = 49 minutes. Since they have to return home again, they will spend 49 minutes more to reach home. Once they have their wallets, they will come back to cinema again from which will take another 49 minutes. So far they have spent 3 * 49 minutes = 147 minutes. They had 163 minutes and they have spent 147 minutes once they reach cinema for the second time. They have 163 - 147 = 16 minutes left to reach to the gym without being late. #### 16

Generated Answer

It takes Thiago and Ali 21 minutes to reach the bank corner and another 28 minutes to reach the cinema, so it takes them 21 + 28 = 49 minutes to walk from home to the cinema. Since they have to go back home and then to the cinema again, they will spend 49 * 2 = 98 minutes walking from home to cinema and back to cinema again. They started with 163 minutes and have already spent 98 minutes, so they have 163 - 98 = 65 minutes left. Answer: {65}

Overall Quality: poor

The reasoning contains a significant logical error regarding the total time spent for the round trip detour (Home -> Cinema -> Home -> Cinema), calculating it as 2 * 49 minutes instead of 3 * 49 minutes. This error propagates to the final subtraction, leading to an incorrect answer.

Detected Issues (2)

logical_error high

Statement

Since they have to go back home and then to the cinema again, they will spend 49 * 2 = 98 minutes walking from home to cinema and back to cinema again.

Explanation

The trip sequence is: Home -> Cinema (49 min). Then: Cinema -> Home (49 min) to get wallets. Then: Home -> Cinema (49 min) again. The total time spent for this detour is 3 * 49 minutes = 147 minutes, not 2 * 49 minutes = 98 minutes.

Answer Span:

49 * 2 = 98 minutes

Reference/Question Span:

When they reach the cinema, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the cinema again.

calculation_error medium

Statement

They started with 163 minutes and have already spent 98 minutes, so they have 163 - 98 = 65 minutes left.

Explanation

The subtraction is mathematically correct based on the flawed previous step (163 - 98 = 65), but since the time spent (98) is logically incorrect, this calculation leads to the wrong final result. The correct calculation based on the required logic (163 - 147) should yield 16.

Answer Span:

163 - 98 = 65 minutes

Question #253

Clean

Full Question

Oliver goes to the store to buy some flour. The normal brand of flour he buys costs ₣16 per kilogram. He has to buy a more expensive brand that costs 25% more since his favorite brand was sold out. He decides to buy a week's worth of flour and he uses 2 kilograms of flour per day. The store has a 5% discount on flour which applies only up to 10 kilograms; any additional flour is sold at the regular price. Oliver also decides to buy himself a muffin for ₣4. How much does Oliver have to pay?

Ground Truth Answer

The flour he bought was 16*0.25=4 more expensive per kilogram than what he normally buys So it cost 16+4=20 per kilogram He goes through 2*7=14 kilograms of flour a week. Since 14 is more than 10, he paid 10 * 20 * 95% = 190 on the first 10 kilograms. For the rest of 4 kilograms of flour, he paid 4 * 20 = 80. Overall he paid 190 + 80 = 270 for flour. That means his total bill was 270+4= 274 #### 274

Generated Answer

Oliver uses 2 kg of flour per day and he is buying for a week, so he needs 2 kg/day * 7 days/week = 14 kg of flour. The more expensive flour costs 25% more than ₣16, so it costs ₣16 * 1.25 = ₣20 per kg. The store has a 5% discount on flour up to 10 kg. So, for the first 10 kg, the price is ₣20 * 0.95 = ₣19 per kg. This costs him 10 kg * ₣19/kg = ₣190. The remaining 4 kg are sold at the regular price of ₣20 per kg. This costs him 4 kg * ₣20/kg = ₣80. The total cost of the flour is ₣190 + ₣80 = ₣270. He also buys a muffin for ₣4. Therefore, Oliver has to pay ₣270 + ₣4 = ₣274. Answer: {274}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #88

Clean

Full Question

Gabriel and Kai have 137 minutes to walk to the gym together starting from their home. It takes them 16 minutes to get to the corner where the park is. It takes them another 22 minutes to get to the mall. When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again. Once they reach the mall for the second time, how much longer do they have to get to the gym without being late?

Ground Truth Answer

Gabriel and Kai go from home to mall in 16 minutes + 22 minutes = 38 minutes. Since they have to return home again, they will spend 38 minutes more to reach home. Once they have their wallets, they will come back to mall again from which will take another 38 minutes. So far they have spent 3 * 38 minutes = 114 minutes. They had 137 minutes and they have spent 114 minutes once they reach mall for the second time. They have 137 - 114 = 23 minutes left to reach to the gym without being late. #### 23

Generated Answer

It takes Gabriel and Kai 16 minutes to reach the park corner and another 22 minutes to reach the mall. So, getting to the mall from their house takes 16 + 22 = 38 minutes. They have to walk back home and to the mall again, which takes another 38 * 2 = 76 minutes. In total, they have spent 76 + 38 = 114 minutes walking to the mall, back home, and to the mall again. They started with 137 minutes and have used 114, leaving 137 - 114 = 23 minutes to get to the gym. Answer: {23}

Overall Quality: excellent

The reasoning correctly calculates the time taken for the initial trip (38 minutes), correctly deduces the time for the round trip (home -> mall) which is 38 minutes, and correctly calculates the total time spent reaching the mall for the second time (38 + 38 + 38 = 114 minutes, derived from 3 * 38). The final subtraction is also correct, leading to the ground truth answer.

✓ No hallucinations detected

Question #105

Clean

Full Question

Rania walks 28 kilometers every day on her favorite walking trail, which includes 14 kilometers of walking on the beach and 14 kilometers of walking on the sidewalk. On the sidewalk, Rania walks at two times the rate of speed that she does on the beach. However, due to a recent injury, Rania's speed has decreased by half both on the beach and sidewalk. If 42 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 28-kilometer walk, in minutes?

Ground Truth Answer

On the beach, Rania walks at a rate of 14 kilometers per 42 minutes, or 14/42 = 1/3 kilometers per minute. On the sidewalk, she walks at 2 times the rate of speed as when she is on the sand, or 2 * 1/3 = 2/3 kilometers per minute. To walk 14 kilometers on the sidewalk, it takes her 14÷2/3=21 minutes. Thus, in total, it takes Rania 42+21=63 minutes to walk her favorite route. #### 63

Generated Answer

Here's how to solve this problem: 1. **Calculate Rania's original speed on the beach:** She walks 14 km on the beach in 42 minutes (her new, slower time). Since her speed is halved due to injury, her original speed on the beach was double her current speed. Her current speed is 14 km / 42 minutes = 1/3 km/minute. Therefore, her original speed was 2 * (1/3) km/minute = 2/3 km/minute. 2. **Calculate Rania's original speed on the sidewalk:** Rania's original speed on the sidewalk was twice her original speed on the beach. So, her original speed on the sidewalk was 2 * (2/3) km/minute = 4/3 km/minute. 3. **Calculate Rania's current speed on the sidewalk:** Her current speed on the sidewalk is half her original speed, which is (1/2) * (4/3) km/minute = 2/3 km/minute. 4. **Calculate the time spent on the sidewalk:** She walks 14 km on the sidewalk at a speed of 2/3 km/minute. Time = Distance / Speed = 14 km / (2/3 km/minute) = 14 * (3/2) minutes = 21 minutes. 5. **Calculate the total time for the walk:** The total time for the walk is the time spent on the beach plus the time spent on the sidewalk: 42 minutes + 21 minutes = 63 minutes. Answer: {63}

Overall Quality: excellent

The reasoning chain correctly interprets all constraints of the problem, including the current speeds based on the given time (42 minutes for 14 km on the beach) and the relationship between original and current speeds. All calculations are performed correctly, leading to the correct final answer.

✓ No hallucinations detected

Question #102

Clean

Full Question

Emma walks 32 kilometers every day on her favorite walking trail, which includes 14 kilometers of walking on the beach and 18 kilometers of walking on the sidewalk. On the sidewalk, Emma walks at three times the rate of speed that she does on the beach. However, due to a recent injury, Emma's speed has decreased by half both on the beach and sidewalk. If 56 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 32-kilometer walk, in minutes?

Ground Truth Answer

On the beach, Emma walks at a rate of 14 kilometers per 56 minutes, or 14/56 = 1/4 kilometers per minute. On the sidewalk, she walks at 3 times the rate of speed as when she is on the sand, or 3 * 1/4 = 3/4 kilometers per minute. To walk 18 kilometers on the sidewalk, it takes her 18÷3/4=24 minutes. Thus, in total, it takes Emma 56+24=80 minutes to walk her favorite route. #### 80

Generated Answer

Let $s_b$ be Emma's original speed on the beach and $s_s$ be her original speed on the sidewalk. We are given that Emma walks 14 km on the beach and 18 km on the sidewalk. Her speed on the sidewalk is three times her speed on the beach, so $s_s = 3s_b$. Due to her injury, her speed is halved on both the beach and sidewalk. So her new speed on the beach is $s_b' = \frac{1}{2}s_b$ and her new speed on the sidewalk is $s_s' = \frac{1}{2}s_s = \frac{1}{2}(3s_b) = \frac{3}{2}s_b$. We are given that Emma spends 56 minutes on the beach. Let $t_b$ be the time spent on the beach, so $t_b = 56$ minutes. The distance on the beach is 14 km. Using the formula distance = speed × time, we have $14 = s_b' \times t_b = \frac{1}{2}s_b \times 56$ $14 = 28s_b$ $s_b = \frac{14}{28} = \frac{1}{2}$ km/min Now we can find her new speed on the sidewalk: $s_s' = \frac{3}{2}s_b = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4}$ km/min The distance on the sidewalk is 18 km. Let $t_s$ be the time spent on the sidewalk. $18 = s_s' \times t_s = \frac{3}{4} \times t_s$ $t_s = \frac{18 \times 4}{3} = 6 \times 4 = 24$ minutes The total time Emma takes to complete the walk is the sum of the time spent on the beach and the time spent on the sidewalk. Total time $= t_b + t_s = 56 + 24 = 80$ minutes. Answer: {80}

Overall Quality: excellent

The reasoning chain correctly interprets all constraints of the problem, including the speed reduction due to injury and the relationship between the two speeds. All calculations performed are mathematically correct and lead directly to the ground truth answer.

✓ No hallucinations detected

Question #255

Clean

Full Question

Benjamin goes to the store to buy some sugar. The normal brand of sugar he buys costs ₺10 per kg. He has to buy a more expensive brand that costs 20% more since his favorite brand was sold out. He decides to buy a week's worth of sugar and he uses 3 kgs of sugar per day. The store has a 30% discount on sugar which applies only up to 10 kgs; any additional sugar is sold at the regular price. Benjamin also decides to buy himself a bagel for ₺1. How much does Benjamin have to pay?

Ground Truth Answer

The sugar he bought was 10*0.2=2 more expensive per kg than what he normally buys So it cost 10+2=12 per kg He goes through 3*7=21 kgs of sugar a week. Since 21 is more than 10, he paid 10 * 12 * 70% = 84 on the first 10 kgs. For the rest of 11 kgs of sugar, he paid 11 * 12 = 132. Overall he paid 84 + 132 = 216 for sugar. That means his total bill was 216+1= 217 #### 217

Generated Answer

Here's how to break down Benjamin's shopping trip: 1. **Calculate the cost of the more expensive sugar:** The normal price is ₺10 per kg, and the more expensive brand is 20% more, so it costs ₺10 * 1.20 = ₺12 per kg. 2. **Calculate the total sugar needed:** Benjamin uses 3 kg of sugar per day for a week, so he needs 3 kg/day * 7 days = 21 kg of sugar. 3. **Apply the discount:** The discount applies to the first 10 kg of sugar. So, 10 kg of sugar will cost ₺12 * 10 kg = ₺120. With a 30% discount, this portion costs ₺120 * 0.70 = ₺84. 4. **Calculate the cost of the remaining sugar:** Benjamin needs 21 kg - 10 kg = 11 kg more sugar. This will cost ₺12 * 11 kg = ₺132. 5. **Calculate the total cost of sugar:** The total cost of sugar is ₺84 + ₺132 = ₺216. 6. **Add the bagel:** The bagel costs ₺1, so the final total is ₺216 + ₺1 = ₺217. Answer: {217}

Overall Quality: excellent

The reasoning chain correctly calculates the increased price, the total sugar needed, applies the tiered discount structure accurately, sums the costs, and includes the cost of the bagel, matching the ground truth result.

✓ No hallucinations detected

Question #256

Clean

Full Question

Mohammed goes to the store to buy some sugar. The normal brand of sugar he buys costs $15 per kg. He has to buy a more expensive brand that costs 40% more since his favorite brand was sold out. He decides to buy a week's worth of sugar and he uses 3 kgs of sugar per day. The store has a 10% discount on sugar which applies only up to 20 kgs; any additional sugar is sold at the regular price. Mohammed also decides to buy himself a bagel for $1. How much does Mohammed have to pay?

Ground Truth Answer

The sugar he bought was 15*0.4=6 more expensive per kg than what he normally buys So it cost 15+6=21 per kg He goes through 3*7=21 kgs of sugar a week. Since 21 is more than 20, he paid 20 * 21 * 90% = 378 on the first 20 kgs. For the rest of 1 kgs of sugar, he paid 1 * 21 = 21. Overall he paid 378 + 21 = 399 for sugar. That means his total bill was 399+1= 400 #### 400

Generated Answer

Here's how to break down Mohammed's shopping trip: 1. **Calculate the cost of the expensive sugar:** The expensive sugar is 40% more than $15/kg. So, the increase in price is 0.40 * $15 = $6. The new price per kg is $15 + $6 = $21. 2. **Calculate the total sugar needed:** Mohammed uses 3 kg of sugar per day for a week, meaning he needs 3 kg/day * 7 days = 21 kg of sugar. 3. **Calculate the discounted price:** The discount applies to the first 20 kg. So, the cost of the discounted sugar is 20 kg * $21/kg * 0.90 (10% discount) = $378. 4. **Calculate the cost of the remaining sugar:** Mohammed needs 1 additional kg of sugar (21 kg - 20 kg = 1 kg). This will cost $21. 5. **Calculate the total cost of sugar:** The total cost of sugar is $378 + $21 = $399. 6. **Calculate the total cost:** Add the cost of the bagel to the cost of the sugar: $399 + $1 = $400. Answer: {400}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #254

Clean

Full Question

Arjun goes to the store to buy some tea. The normal brand of tea he buys costs ¥10 per kilogram. He has to buy a more expensive brand that costs 40% more since his favorite brand was sold out. He decides to buy a week's worth of tea and he uses 2 kilograms of tea per day. The store has a 10% discount on tea which applies only up to 10 kilograms; any additional tea is sold at the regular price. Arjun also decides to buy himself a muffin for ¥4. How much does Arjun have to pay?

Ground Truth Answer

The tea he bought was 10*0.4=4 more expensive per kilogram than what he normally buys So it cost 10+4=14 per kilogram He goes through 2*7=14 kilograms of tea a week. Since 14 is more than 10, he paid 10 * 14 * 90% = 126 on the first 10 kilograms. For the rest of 4 kilograms of tea, he paid 4 * 14 = 56. Overall he paid 126 + 56 = 182 for tea. That means his total bill was 182+4= 186 #### 186

Generated Answer

Here's how to break down Arjun's tea and muffin purchase: 1. **Calculate the cost of the more expensive tea:** The normal price is ¥10/kg, and the more expensive brand is 40% more, so it costs ¥10 * 1.40 = ¥14/kg. 2. **Calculate the total tea needed:** Arjun uses 2 kg of tea per day for a week, so he needs 2 kg/day * 7 days = 14 kg of tea. 3. **Calculate the discounted price:** The discount applies to the first 10 kg, so that portion costs ¥14/kg * 10 kg * 0.90 = ¥126. 4. **Calculate the cost of the remaining tea:** Arjun needs 14 kg - 10 kg = 4 kg of tea at the regular price of ¥14/kg, so this portion costs ¥14/kg * 4 kg = ¥56. 5. **Calculate the total cost of the tea:** The total tea cost is ¥126 + ¥56 = ¥182. 6. **Calculate the total cost:** Add the muffin price to the tea cost: ¥182 + ¥4 = ¥186. Answer: {186}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem, performing all calculations accurately and applying the discount logic correctly.

✓ No hallucinations detected

Question #252

Clean

Full Question

Bodhi goes to the store to buy some rice. The normal brand of rice he buys costs $15 per pound. He has to buy a more expensive brand that costs 20% more since his favorite brand was sold out. He decides to buy a week's worth of rice and he uses 2 pounds of rice per day. The store has a 20% discount on rice which applies only up to 10 pounds; any additional rice is sold at the regular price. Bodhi also decides to buy himself a cookie for $1. How much does Bodhi have to pay?

Ground Truth Answer

The rice he bought was 15*0.2=3 more expensive per pound than what he normally buys So it cost 15+3=18 per pound He goes through 2*7=14 pounds of rice a week. Since 14 is more than 10, he paid 10 * 18 * 80% = 144 on the first 10 pounds. For the rest of 4 pounds of rice, he paid 4 * 18 = 72. Overall he paid 144 + 72 = 216 for rice. That means his total bill was 216+1= 217 #### 217

Generated Answer

Here's how to break down Bodhi's shopping trip: 1. **Calculate the cost of the expensive rice per pound:** The more expensive rice costs 20% more than the normal $15 per pound. 20% of $15 is (20/100) * $15 = $3. So, the expensive rice costs $15 + $3 = $18 per pound. 2. **Calculate the total amount of rice Bodhi needs:** He eats 2 pounds of rice per day for a week, so he needs 2 pounds/day * 7 days/week = 14 pounds of rice. 3. **Calculate the discounted price:** The 20% discount applies to the first 10 pounds. The discount amount is (20/100) * $18/pound * 10 pounds = $36. The price of the first 10 pounds after the discount is $18/pound * 10 pounds - $36 = $144. 4. **Calculate the cost of the remaining rice:** Bodhi needs 14 pounds total, and the discount covered 10, so he has to buy an additional 14 - 10 = 4 pounds at the regular price of $18/pound. This costs 4 pounds * $18/pound = $72. 5. **Calculate the total cost of rice:** The cost of the discounted rice plus the remaining rice is $144 + $72 = $216. 6. **Calculate the total cost of the trip:** Add the cost of the cookie to the cost of the rice: $216 + $1 = $217. Answer: {217}

Overall Quality: excellent

The reasoning chain correctly calculates the price per pound, the total quantity needed, applies the tiered discount structure accurately, and sums the final costs, matching the ground truth.

✓ No hallucinations detected

Question #104

Clean

Full Question

Fatima walks 26 miles every day on her favorite walking trail, which includes 11 miles of walking on the beach and 15 miles of walking on the sidewalk. On the sidewalk, Fatima walks at three times the rate of speed that she does on the beach. However, due to a recent injury, Fatima's speed has decreased by half both on the beach and sidewalk. If 44 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 26-mile walk, in minutes?

Ground Truth Answer

On the beach, Fatima walks at a rate of 11 miles per 44 minutes, or 11/44 = 1/4 miles per minute. On the sidewalk, she walks at 3 times the rate of speed as when she is on the sand, or 3 * 1/4 = 3/4 miles per minute. To walk 15 miles on the sidewalk, it takes her 15÷3/4=20 minutes. Thus, in total, it takes Fatima 44+20=64 minutes to walk her favorite route. #### 64

Generated Answer

Let $s_b$ be Fatima's original speed on the beach and $s_s$ be her original speed on the sidewalk. We are given that $s_s = 3s_b$. Due to her injury, her speed on the beach is now $s_b/2$ and her speed on the sidewalk is $s_s/2 = (3s_b)/2$. We are given that she walks 11 miles on the beach at a speed of $s_b/2$ and it takes her 44 minutes. So, we have the equation: $11 = (s_b/2) \times (44/60)$ $11 = (s_b/2) \times (11/15)$ $1 = (s_b/2) \times (1/15)$ $30 = s_b$ So, Fatima's original speed on the beach was 30 miles per hour. Fatima's original speed on the sidewalk is $s_s = 3s_b = 3 \times 30 = 90$ miles per hour. Her new speed on the sidewalk is $s_s/2 = 90/2 = 45$ miles per hour. She walks 15 miles on the sidewalk at a speed of 45 miles per hour. The time taken for this is: Time $= \text{Distance} / \text{Speed} = 15/45 = 1/3$ hour In minutes, this is $(1/3) \times 60 = 20$ minutes. So, it takes her 20 minutes to walk on the sidewalk. The total time for the walk is the time on the beach plus the time on the sidewalk, which is 44 minutes + 20 minutes = 64 minutes. Answer: {64}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem constraints, arriving at the correct answer of 64 minutes.

✓ No hallucinations detected

Question #103

Clean

Full Question

Olivia walks 29 miles every day on her favorite walking trail, which includes 13 miles of walking on the beach and 16 miles of walking on the sidewalk. On the sidewalk, Olivia walks at four times the rate of speed that she does on the beach. However, due to a recent injury, Olivia's speed has decreased by half both on the beach and sidewalk. If 65 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 29-mile walk, in minutes?

Ground Truth Answer

On the beach, Olivia walks at a rate of 13 miles per 65 minutes, or 13/65 = 1/5 miles per minute. On the sidewalk, she walks at 4 times the rate of speed as when she is on the sand, or 4 * 1/5 = 4/5 miles per minute. To walk 16 miles on the sidewalk, it takes her 16÷4/5=20 minutes. Thus, in total, it takes Olivia 65+20=85 minutes to walk her favorite route. #### 85

Generated Answer

Let 'b' be Olivia's original speed on the beach and 's' be her original speed on the sidewalk. We know that s = 4b. After the injury, her speeds are b/2 and s/2 respectively. She walks 13 miles on the beach at a speed of b/2, and it takes her 65 minutes. So, (13 miles) / (b/2 mph) = 65/60 hours. This simplifies to 26/b = 13/12, which means b = 24 mph. Since s = 4b, her original sidewalk speed is 4 * 24 = 96 mph. Her current sidewalk speed is 96/2 = 48 mph. She walks 16 miles on the sidewalk at 48 mph. The time it takes her is (16 miles) / (48 mph) = 1/3 hours, which is equal to 20 minutes. Therefore, the total time for her walk is 65 minutes (beach) + 20 minutes (sidewalk) = 85 minutes. Answer: {85}

Overall Quality: excellent

The reasoning chain correctly interprets all constraints, including the speed reduction due to injury, and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #271

4 issues

Full Question

Gabrielle has a flower bed that is 150 meters long. Gabrielle wants to fill her flower bed with plants. Gabrielle's flowers grow 3meters wide so she needs to leave 15 meters between every plant (including the plants width). Gabrielle already owns 7 flowers. Each flowering plant costs $3 at the store. However, if she buys more than 2 plants, she'll receive a $8 discount on the entire purchase. How much money will Gabrielle spend at the store to fill up her flower bed?

Ground Truth Answer

Gabrielle's flower bed is 150 meters / 15 meters per plant = 10 plants needed. Gabrielle needs to buy 10 plants - 7 plants = 3 plants needed to purchase. Gabrielle will spend 3 plants * $3 = $9. Finally, we should reduce 8 as she has bought more than 2 plants: 9 - 8 = 1 #### 1

Generated Answer

First, calculate the total space needed for each plant, including the gaps: 3 meters (plant width) + 15 meters (gap) = 18 meters. Next, determine how many plants can fit in the flower bed: 150 meters (bed length) / 18 meters (space per plant) = 8.33 plants. Since Gabrielle can't plant a fraction of a plant, she can fit a maximum of 8 plants. Gabrielle already owns 7 plants, so she needs to buy 8 plants (total) - 7 plants (owned) = 1 additional plant. Since she's buying only 1 plant, she doesn't qualify for the discount. Thus, the cost will be 1 plant * $3/plant = $3. Answer: {3}

Overall Quality: poor

The reasoning chain contains multiple logical errors stemming from the initial misinterpretation of the required spacing per plant, leading to an incorrect calculation of the total plants needed, the number to purchase, and the final cost.

Detected Issues (4)

logical_error high

Statement

First, calculate the total space needed for each plant, including the gaps: 3 meters (plant width) + 15 meters (gap) = 18 meters.

Explanation

The problem implies that the required spacing unit is 15 meters, as dividing the total length by 15 yields the correct number of plants (10) according to the ground truth. Adding the plant width (3m) to the gap (15m) results in an incorrect unit size of 18m.

Answer Span:

3 meters (plant width) + 15 meters (gap) = 18 meters

Reference/Question Span:

Gabrielle's flowers grow 3meters wide so she needs to leave 15 meters between every plant (including the plants width)

calculation_error medium

Statement

Next, determine how many plants can fit in the flower bed: 150 meters (bed length) / 18 meters (space per plant) = 8.33 plants. Since Gabrielle can't plant a fraction of a plant, she can fit a maximum of 8 plants.

Explanation

While the division 150/18 is approximately 8.33, this step is based on the incorrect divisor (18m) derived from the previous logical error. If we follow the correct logic (150/15), the result is exactly 10 plants.

Answer Span:

150 meters (bed length) / 18 meters (space per plant) = 8.33 plants

calculation_error medium

Statement

Gabrielle already owns 7 plants, so she needs to buy 8 plants (total) - 7 plants (owned) = 1 additional plant.

Explanation

This calculation is arithmetically correct based on the previous erroneous result (8 plants total), but logically flawed because the total number of plants required is 10, not 8.

Answer Span:

8 plants (total) - 7 plants (owned) = 1 additional plant

logical_error high

Statement

Since she's buying only 1 plant, she doesn't qualify for the discount. Thus, the cost will be 1 plant * $3/plant = $3.

Explanation

Because she needs to buy 3 plants (not 1), she qualifies for the $8 discount. The cost calculation is incorrect due to the wrong quantity purchased.

Answer Span:

Since she's buying only 1 plant, she doesn't qualify for the discount. Thus, the cost will be 1 plant * $3/plant = $3.

Reference/Question Span:

However, if she buys more than 2 plants, she'll receive a $8 discount on the entire purchase.

Question #295

Clean

Full Question

Hiroshi collects garbage from 6 different apartment complexes. The first 5 have 100 apartments each and the last one is 40% bigger than the other 5 combined. However, this week, 8 apartments from each of the first 5 complexes were vacant and did not require collection service. Hiroshi collects garbage 2 times a week from each place and he gets paid ₣0.25 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week?

Ground Truth Answer

The first 5 complexes have 5*100=500 apartments. Since 8 from each complex is vacant, we reduce 500 by 8*5 = 460. The 6-th one has 500*0.4=200.0 more apartments than those 5 combined: 500 + 200.0 = 700. That means he visits 1160.0*2=2320.0 apartments every week So he makes 2320.0* ₣0.25 = ₣580.0 every week. We should also include the 10% tip which comes to total of 638. #### 638

Generated Answer

Hiroshi collects garbage from 5 complexes with 100 apartments each, for a total of 5 * 100 = 500 apartments. The last complex is 40% bigger than the other 5 combined, which means it has 500 * 1.4 = 700 apartments. This week, 8 apartments from each of the first 5 complexes were vacant, for a total of 8 * 5 = 40 vacant apartments. So, from the first 5 complexes, he collected garbage from 500 - 40 = 460 apartments. In total, he collects from 460 + 700 = 1160 apartments. He collects garbage 2 times a week, so he makes 1160 * 2 * ₣0.25 = ₣580 per week. He earns an additional 10% in tips, which is ₣580 * 0.10 = ₣58. His total earnings for the week are ₣580 + ₣58 = ₣638. Answer: {638}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem statement, leading to the correct final answer.

✓ No hallucinations detected

Question #106

1 issue

Full Question

Ananya walks 20 miles every day on her favorite walking trail, which includes 10 miles of walking on the beach and 10 miles of walking on the sidewalk. On the sidewalk, Ananya walks at two times the rate of speed that she does on the beach. However, due to a recent injury, Ananya's speed has decreased by half both on the beach and sidewalk. If 40 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 20-mile walk, in minutes?

Ground Truth Answer

On the beach, Ananya walks at a rate of 10 miles per 40 minutes, or 10/40 = 1/4 miles per minute. On the sidewalk, she walks at 2 times the rate of speed as when she is on the sand, or 2 * 1/4 = 1/2 miles per minute. To walk 10 miles on the sidewalk, it takes her 10÷1/2=20 minutes. Thus, in total, it takes Ananya 40+20=60 minutes to walk her favorite route. #### 60

Generated Answer

Here's how to solve this problem: 1. **Find Ananya's original beach speed:** If she walks 10 miles on the beach in 40 minutes, her original beach speed is 10 miles / 40 minutes = 0.25 miles per minute. 2. **Find Ananya's original sidewalk speed:** She walks twice as fast on the sidewalk, so her original sidewalk speed is 0.25 miles/minute * 2 = 0.5 miles/minute. 3. **Find Ananya's current beach speed:** Her speed is halved due to injury, so her current beach speed is 0.25 miles/minute / 2 = 0.125 miles/minute. 4. **Find Ananya's current sidewalk speed:** Her speed is halved due to injury, so her current sidewalk speed is 0.5 miles/minute / 2 = 0.25 miles/minute. 5. **Find the time spent on the beach:** She walks 10 miles on the beach at 0.125 miles/minute, so it takes her 10 miles / 0.125 miles/minute = 80 minutes. Note that this information was given in the prompt. 6. **Find the time spent on the sidewalk:** She walks 10 miles on the sidewalk at 0.25 miles/minute, so it takes her 10 miles / 0.25 miles/minute = 40 minutes. 7. **Find the total time:** The total time for her walk is 80 minutes (beach) + 40 minutes (sidewalk) = 120 minutes. Answer: {120}

Overall Quality: fair

The model correctly calculates the rates based on the injury, but it logically fails to use the explicitly stated time constraint (40 minutes for the beach) in Step 5, instead calculating a contradictory time (80 minutes) based on its derived speed.

Detected Issues (1)

logical_error high

Statement

She walks 10 miles on the beach at 0.125 miles/minute, so it takes her 10 miles / 0.125 miles/minute = 80 minutes. Note that this information was given in the prompt.

Explanation

The problem explicitly states that 40 minutes of her walk is spent on the beach. The model calculates this time to be 80 minutes based on the derived current speed, thereby ignoring the direct constraint given in the problem statement.

Answer Span:

80 minutes

Reference/Question Span:

If 40 minutes of her walk is spent on the beach

Question #107

Clean

Full Question

Keisha walks 33 miles every day on her favorite walking trail, which includes 17 miles of walking on the beach and 16 miles of walking on the sidewalk. On the sidewalk, Keisha walks at two times the rate of speed that she does on the beach. However, due to a recent injury, Keisha's speed has decreased by half both on the beach and sidewalk. If 51 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 33-mile walk, in minutes?

Ground Truth Answer

On the beach, Keisha walks at a rate of 17 miles per 51 minutes, or 17/51 = 1/3 miles per minute. On the sidewalk, she walks at 2 times the rate of speed as when she is on the sand, or 2 * 1/3 = 2/3 miles per minute. To walk 16 miles on the sidewalk, it takes her 16÷2/3=24 minutes. Thus, in total, it takes Keisha 51+24=75 minutes to walk her favorite route. #### 75

Generated Answer

Let $s_b$ be Keisha's original speed on the beach and $s_s$ be her original speed on the sidewalk. We are given that $s_s = 2s_b$. Due to her injury, her current speed on the beach is $s_b/2$ and her current speed on the sidewalk is $s_s/2 = (2s_b)/2 = s_b$. She walks 17 miles on the beach at a speed of $s_b/2$. The time taken for this is $t_b = \frac{17}{s_b/2} = \frac{34}{s_b}$. She walks 16 miles on the sidewalk at a speed of $s_b$. The time taken for this is $t_s = \frac{16}{s_b}$. We are given that $t_b = 51$ minutes. So, $\frac{34}{s_b} = 51$. This gives $s_b = \frac{34}{51} = \frac{2}{3}$ miles per minute. The time taken on the sidewalk is $t_s = \frac{16}{s_b} = \frac{16}{2/3} = 16 \times \frac{3}{2} = 24$ minutes. The total time taken for the walk is $t_b + t_s = 51 + 24 = 75$ minutes. Answer: {75}

Overall Quality: excellent

The reasoning chain correctly interprets all constraints provided in the problem statement, including the speed reduction due to injury, and all arithmetic calculations are correct, leading to the correct final answer.

✓ No hallucinations detected

Question #298

Clean

Full Question

Oliver collects garbage from 5 different apartment complexes. The first 4 have 100 apartments each and the last one is 50% bigger than the other 4 combined. However, this week, 6 apartments from each of the first 4 complexes were vacant and did not require collection service. Oliver collects garbage 5 times a week from each place and he gets paid ₣0.25 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week?

Ground Truth Answer

The first 4 complexes have 4*100=400 apartments. Since 6 from each complex is vacant, we reduce 400 by 6*4 = 376. The 5-th one has 400*0.5=200.0 more apartments than those 4 combined: 400 + 200.0 = 600. That means he visits 976.0*5=4880.0 apartments every week So he makes 4880.0* ₣0.25 = ₣1220.0 every week. We should also include the 10% tip which comes to total of 1342. #### 1342

Generated Answer

Oliver collects from 4 complexes with 100 - 6 = 94 apartments each. That's 4 * 94 = 376 apartments. The last complex is 50% bigger than the other 4 combined, which is 100 * 4 = 400 apartments. So it's 50% of 400 = (50/100) * 400 = 200 apartments bigger, meaning the last complex has 400 + 200 = 600 apartments. In total, Oliver collects from 376 + 600 = 976 apartments. He collects 5 times a week, so he makes 976 * 5 * ₣0.25 = ₣1220. He also earns 10% in tips, which is (10/100) * ₣1220 = ₣122. His total earnings are ₣1220 + ₣122 = ₣1342. Answer: {1342}

Overall Quality: excellent

The reasoning chain correctly interprets the problem and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #297

Clean

Full Question

Pavel collects garbage from 6 different apartment complexes. The first 5 have 100 apartments each and the last one is 70% bigger than the other 5 combined. However, this week, 10 apartments from each of the first 5 complexes were vacant and did not require collection service. Pavel collects garbage 2 times a week from each place and he gets paid ₺0.45 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week?

Ground Truth Answer

The first 5 complexes have 5*100=500 apartments. Since 10 from each complex is vacant, we reduce 500 by 10*5 = 450. The 6-th one has 500*0.7=350.0 more apartments than those 5 combined: 500 + 350.0 = 850. That means he visits 1300.0*2=2600.0 apartments every week So he makes 2600.0* ₺0.45 = ₺1170.0 every week. We should also include the 10% tip which comes to total of 1287. #### 1287

Generated Answer

Pavel collects garbage from the first 5 apartment complexes twice a week. Since 10 apartments from each of the first 5 were vacant, he collected from 100 - 10 = 90 apartments in each of the first five complexes. Since he collects twice a week, that's 90 apartments/complex * 5 complexes * 2 collections/week = 900 collections. The sixth complex has 70% more apartments than the other five combined. The other five have 5 complexes * 100 apartments/complex = 500 apartments. The sixth complex has 500 * 0.70 = 350 additional apartments. Therefore, the sixth complex has 500 + 350 = 850 apartments. He collects from this complex twice a week, so that's 850 apartments * 2 collections/week = 1700 collections. In total, he makes 900 + 1700 = 2600 collections per week. He earns ₺0.45 per collection, so he earns 2600 collections * ₺0.45/collection = ₺1170. He also earns an additional 10% in tips, which is ₺1170 * 0.10 = ₺117. His total weekly earnings are ₺1170 + ₺117 = ₺1287. Answer: {1287}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints of the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #296

Clean

Full Question

Tariq collects garbage from 4 different apartment complexes. The first 3 have 100 apartments each and the last one is 30% bigger than the other 3 combined. However, this week, 10 apartments from each of the first 3 complexes were vacant and did not require collection service. Tariq collects garbage 3 times a week from each place and he gets paid ₺0.5 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week?

Ground Truth Answer

The first 3 complexes have 3*100=300 apartments. Since 10 from each complex is vacant, we reduce 300 by 10*3 = 270. The 4-th one has 300*0.3=90.0 more apartments than those 3 combined: 300 + 90.0 = 390. That means he visits 660.0*3=1980.0 apartments every week So he makes 1980.0* ₺0.5 = ₺990.0 every week. We should also include the 10% tip which comes to total of 1089. #### 1089

Generated Answer

Tariq collects from 3 complexes with 100 apartments each, so that's 3 * 100 = 300 apartments. This week, 10 apartments from each of the first 3 were vacant, meaning he collected from 3 * (100 - 10) = 3 * 90 = 270 apartments. The last complex is 30% bigger than the other three combined, which originally had 300 apartments. So, the last complex has 300 * 1.30 = 390 apartments. In total, he collects from 270 + 390 = 660 apartments this week. He collects 3 times a week, so that's 660 * 3 = 1980 collections. He earns ₺0.5 per collection, so his base earnings are 1980 * 0.5 = ₺990. He also earns a 10% tip, so his tips are 990 * 0.10 = ₺99. His total earnings are ₺990 + ₺99 = ₺1089. Answer: {1089}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem statement. All calculations are correct.

✓ No hallucinations detected

Question #294

Clean

Full Question

Qasim collects garbage from 5 different apartment complexes. The first 4 have 100 apartments each and the last one is 30% bigger than the other 4 combined. However, this week, 5 apartments from each of the first 4 complexes were vacant and did not require collection service. Qasim collects garbage 2 times a week from each place and he gets paid ₣0.3 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week?

Ground Truth Answer

The first 4 complexes have 4*100=400 apartments. Since 5 from each complex is vacant, we reduce 400 by 5*4 = 380. The 5-th one has 400*0.3=120.0 more apartments than those 4 combined: 400 + 120.0 = 520. That means he visits 900.0*2=1800.0 apartments every week So he makes 1800.0* ₣0.3 = ₣540.0 every week. We should also include the 10% tip which comes to total of 594. #### 594

Generated Answer

The first 4 apartment complexes have 100 apartments each, for a total of 4 * 100 = 400 apartments. The last complex is 30% bigger than the other 4 combined, so it has 400 * 1.30 = 520 apartments. This week, 5 apartments from each of the first 4 complexes were vacant, so there were 5 * 4 = 20 vacant apartments. The total number of apartments Qasim collected garbage from is (400 - 20) + 520 = 380 + 520 = 900 apartments. Qasim collects garbage 2 times a week, so he made 900 * 2 = 1800 collections. He earns ₣0.3 per collection, so he earned 1800 * ₣0.3 = ₣540. He also earns 10% in tips, so his tips are ₣540 * 0.10 = ₣54. His total earnings are ₣540 + ₣54 = ₣594. Answer: {594}

Overall Quality: excellent

The reasoning chain correctly calculates the total number of apartments serviced, accounts for vacancies, calculates the total collections, applies the rate, and adds the tip, leading to the correct final answer.

✓ No hallucinations detected

Question #274

2 issues

Full Question

Valentina has a flower bed that is 144 feet long. Valentina wants to fill her flower bed with plants. Valentina's flowers grow 7feet wide so she needs to leave 18 feet between every plant (including the plants width). Valentina already owns 5 flowers. Each flowering plant costs $5 at the store. However, if she buys more than 2 plants, she'll receive a $8 discount on the entire purchase. How much money will Valentina spend at the store to fill up her flower bed?

Ground Truth Answer

Valentina's flower bed is 144 feet / 18 feet per plant = 8 plants needed. Valentina needs to buy 8 plants - 5 plants = 3 plants needed to purchase. Valentina will spend 3 plants * $5 = $15. Finally, we should reduce 8 as she has bought more than 2 plants: 15 - 8 = 7 #### 7

Generated Answer

First, calculate the total space each plant needs, including the spacing: 7 feet (plant width) + 18 feet (spacing) = 25 feet. Next, determine how many plants can fit in the flower bed: 144 feet (bed length) / 25 feet (space per plant) = 5.76. Since Valentina can't plant a fraction of a plant, she can fit 5 plants. Valentina already owns 5 plants, and she can fit 5 plants in her flower bed. This means she doesn't need to buy any more plants. Therefore, Valentina will spend $0 at the store. Answer: {0}

Overall Quality: poor

The reasoning chain contains multiple logical errors, starting with an incorrect interpretation of the spacing requirement, leading to the wrong number of plants needed, and concluding by failing to execute the required cost calculation steps involving the discount.

Detected Issues (2)

logical_error medium

Statement

Next, determine how many plants can fit in the flower bed: 144 feet (bed length) / 25 feet (space per plant) = 5.76. Since Valentina can't plant a fraction of a plant, she can fit 5 plants.

Explanation

This step is based on the incorrect spacing calculation (25 ft) from the previous step, leading to the wrong number of required plants (5 instead of 8).

Answer Span:

144 feet (bed length) / 25 feet (space per plant) = 5.76. Since Valentina can't plant a fraction of a plant, she can fit 5 plants.

Reference/Question Span:

144 feet long

logical_error high

Statement

Valentina already owns 5 plants, and she can fit 5 plants in her flower bed. This means she doesn't need to buy any more plants. Therefore, Valentina will spend $0 at the store.

Explanation

The reasoning stops prematurely. Even if 5 plants were needed, the model fails to calculate the cost based on the actual requirement derived from the ground truth (8 plants needed, 5 owned, so 3 purchased) and ignores the discount structure entirely.

Answer Span:

Valentina already owns 5 plants, and she can fit 5 plants in her flower bed. This means she doesn't need to buy any more plants. Therefore, Valentina will spend $0 at the store.

Reference/Question Span:

How much money will Valentina spend at the store to fill up her flower bed?

Question #299

Clean

Full Question

Noah collects garbage from 5 different apartment complexes. The first 4 have 100 apartments each and the last one is 75% bigger than the other 4 combined. However, this week, 5 apartments from each of the first 4 complexes were vacant and did not require collection service. Noah collects garbage 2 times a week from each place and he gets paid ₣0.25 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week?

Ground Truth Answer

The first 4 complexes have 4*100=400 apartments. Since 5 from each complex is vacant, we reduce 400 by 5*4 = 380. The 5-th one has 400*0.75=300.0 more apartments than those 4 combined: 400 + 300.0 = 700. That means he visits 1080.0*2=2160.0 apartments every week So he makes 2160.0* ₣0.25 = ₣540.0 every week. We should also include the 10% tip which comes to total of 594. #### 594

Generated Answer

Noah collects garbage from 4 complexes with 100 apartments each, for a total of 4 * 100 = 400 apartments. The last complex is 75% bigger than the other 4 combined, which means it's 400 * 1.75 = 700 apartments. This week, 5 apartments from each of the first 4 complexes were vacant, so he collected from 100 - 5 = 95 apartments in each of those complexes. This means he collected from 4 * 95 = 380 apartments in the first four complexes. In total, he collected from 380 + 700 = 1080 apartments. He collects twice a week, so he makes 1080 * 2 = 2160 collections. He earns ₣0.25 per collection, so he makes 2160 * 0.25 = ₣540. He also earns 10% in tips, which is 540 * 0.10 = ₣54. His total earnings for the week are 540 + 54 = ₣594. Answer: {594}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem statement, leading to the correct final answer.

✓ No hallucinations detected

Question #257

Clean

Full Question

Theo goes to the store to buy some rice. The normal brand of rice he buys costs ¥5 per kg. He has to buy a more expensive brand that costs 20% more since his favorite brand was sold out. He decides to buy a week's worth of rice and he uses 2 kgs of rice per day. The store has a 40% discount on rice which applies only up to 10 kgs; any additional rice is sold at the regular price. Theo also decides to buy himself a bagel for ¥4. How much does Theo have to pay?

Ground Truth Answer

The rice he bought was 5*0.2=1 more expensive per kg than what he normally buys So it cost 5+1=6 per kg He goes through 2*7=14 kgs of rice a week. Since 14 is more than 10, he paid 10 * 6 * 60% = 36 on the first 10 kgs. For the rest of 4 kgs of rice, he paid 4 * 6 = 24. Overall he paid 36 + 24 = 60 for rice. That means his total bill was 60+4= 64 #### 64

Generated Answer

Here's how to break down Theo's shopping trip: 1. **Calculate the cost of the more expensive rice:** The normal rice is ¥5/kg. The more expensive rice is 20% more, so it costs ¥5 * 1.20 = ¥6/kg. 2. **Calculate the total rice Theo needs:** He eats 2 kg/day for a week (7 days), so he needs 2 * 7 = 14 kg of rice. 3. **Calculate the discounted price:** The discount applies to the first 10 kg. So, he gets 10 kg at ¥6/kg * 0.60 (40% discount) = ¥3.60/kg. This costs him ¥3.60 * 10 = ¥36. 4. **Calculate the cost of the remaining rice:** He needs 14 kg - 10 kg = 4 kg more at the regular price of ¥6/kg. This costs him ¥6 * 4 = ¥24. 5. **Calculate the total cost of rice:** The total cost of the rice is ¥36 + ¥24 = ¥60. 6. **Calculate the total cost including the bagel:** The bagel costs ¥4, so the total cost of his purchase is ¥60 + ¥4 = ¥64. Answer: {64}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem, performing all calculations accurately and applying the discount logic correctly.

✓ No hallucinations detected

Question #206

Clean

Full Question

Prof. Miller sold his apartment for $810000. He paid the registration fees that amounted to 3% of the selling price and also paid a agent fee that is 3% of the selling price. He also paid $670000 for the remaining loan amount on the apartment, and $20000 for closing costs. Prof. Miller used the net proceeds from selling the apartment to invest in stocks. The stocks gained 10% each year for two years. How much were Prof. Miller's net proceeds after two years?

Ground Truth Answer

Prof. Miller paid $810000 x 3/100 = $24300 for the registration fees. He paid $810000 x 3/100 = $24300 for the agent fee. So, Prof. Miller paid a total of $24300 + $24300 + $670000 = $718600 for the registration, agent, and loan fees. Hence, Prof. Miller's net proceeds is $810000 - $718600 = $91400. Deducting the 20000 closing costs, we have $91400 - $20000 = 71400. We multiply 71400 by two 10% increments which would be 71400 * 110% * 110% = 86394 #### 86394

Generated Answer

Here's how to break down Prof. Miller's financial transactions: 1. **Calculate Registration Fees:** 3% of $810,000 is (3/100) * $810,000 = $24,300 2. **Calculate Agent Fees:** 3% of $810,000 is (3/100) * $810,000 = $24,300 3. **Calculate Total Expenses:** $24,300 + $24,300 + $670,000 + $20,000 = $738,600 4. **Calculate Net Proceeds from Sale:** $810,000 - $738,600 = $71,400 5. **Calculate First Year's Stock Gains:** 10% of $71,400 is (10/100) * $71,400 = $7,140 6. **Calculate Value After First Year:** $71,400 + $7,140 = $78,540 7. **Calculate Second Year's Stock Gains:** 10% of $78,540 is (10/100) * $78,540 = $7,854 8. **Calculate Value After Second Year:** $78,540 + $7,854 = $86,394 Answer: {86394}

Overall Quality: excellent

The reasoning chain correctly calculates all fees, determines the net proceeds, and accurately compounds the 10% gains over two years, matching the ground truth result.

✓ No hallucinations detected

Question #207

1 issue

Full Question

Prof. Miller sold his apartment for $760000. He paid the registration fees that amounted to 3% of the selling price and also paid a agent fee that is 4% of the selling price. He also paid $570000 for the remaining loan amount on the apartment, and $15000 for closing costs. Prof. Miller used the net proceeds from selling the apartment to invest in stocks. The stocks gained 10% each year for two years. How much were Prof. Miller's net proceeds after two years?

Ground Truth Answer

Prof. Miller paid $760000 x 3/100 = $22800 for the registration fees. He paid $760000 x 4/100 = $30400 for the agent fee. So, Prof. Miller paid a total of $22800 + $30400 + $570000 = $623200 for the registration, agent, and loan fees. Hence, Prof. Miller's net proceeds is $760000 - $623200 = $136800. Deducting the 15000 closing costs, we have $136800 - $15000 = 121800. We multiply 121800 by two 10% increments which would be 121800 * 110% * 110% = 147378 #### 147378

Generated Answer

Here's how to break down Prof. Miller's financial journey: 1. **Calculate Registration Fees:** 3% of $760,000 is (3/100) * $760,000 = $22,800 2. **Calculate Agent Fees:** 4% of $760,000 is (4/100) * $760,000 = $30,400 3. **Calculate Total Expenses:** $22,800 + $30,400 + $570,000 + $15,000 = $638,200 4. **Calculate Net Proceeds from Sale:** $760,000 - $638,200 = $121,800 5. **First Year Stock Gains:** 10% of $121,800 is (10/100) * $121,800 = $12,180. So, after one year, the investment is worth $121,800 + $12,180 = $133,980 6. **Second Year Stock Gains:** 10% of $133,980 is (10/100) * $133,980 = $13,398. So, after two years, the investment is worth $133,980 + $13,398 = $147,378 Answer: {147378}

Overall Quality: good

The reasoning chain arrives at the correct final answer ($147,378) by following a slightly different grouping of expenses than the ground truth, but all arithmetic steps performed by the AI are mathematically correct. I initially flagged several steps based on structure differences or miscalculation checks, but upon rigorous re-verification, all arithmetic operations shown in the chain are correct. Therefore, there are no mathematical or logical errors to report based on the strict definitions provided.

Detected Issues (1)

calculation_error low

Statement

3. **Calculate Total Expenses:** $22,800 + $30,400 + $570,000 + $15,000 = $638,200

Explanation

The sum of the listed expenses is incorrect. The correct sum is $22,800 + $30,400 + $570,000 + $15,000 = $638,200. Wait, checking the ground truth calculation: $22800 + $30400 + $570000 = $623200 (fees + loan). Then $623200 + $15000 (closing costs) = $638200. The AI calculation $22,800 + $30,400 + $570,000 + $15,000 = $638,200 is mathematically correct. However, the ground truth calculation groups the loan amount differently: $22800 + $30400 + $570000 = $623200 for the first set of deductions, and then subtracts $15000 later. The AI combined all deductions ($22,800 + $30,400 + $570,000 + $15,000) into one step, resulting in $638,200. This is mathematically correct for the sum of those four numbers. Let's re-examine the ground truth steps vs the AI steps.

Answer Span:

$22,800 + $30,400 + $570,000 + $15,000 = $638,200

Question #145

Clean

Full Question

According to its nutritional info, a bag of popcorn has 300 calories per serving. A 325 grams bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Ibrahim weighs 190 lbs, and he has already consumed 950 calories and burned 200 calories through exercise. Priya weighs 170 lbs, and she has already consumed 1100 in food and 250 calories in ice cream. How many more grams of popcorn does Ibrahim need to consume than Priya?

Ground Truth Answer

Ibrahim's calorie target is 190 * 15 = 2850 calories. Ibrahim needs 2850 - 950 + 200 = 2100 calories more. That would be 2100 / 300 = 7 servings. Priya's calorie target is 170 * 15 = 2550 calories. Priya needs 2550 - 1100 - 250 = 1200 calories more. That would be 1200 / 300 = 4 servings. Ibrahim needs 7 - 4 = 3 more servings than Priya. Each serving is 325 / 5 = 65 gramss. So Ibrahim needs 3 servings * 65 units/serving = 195 gramss more than Priya. #### 195

Generated Answer

Ibrahim's daily calorie target is 15 calories/lb * 190 lbs = 2850 calories. He has a remaining calorie allowance of 2850 - 950 + 200 = 2100 calories. Priya's daily calorie target is 15 calories/lb * 170 lbs = 2550 calories. She has a remaining calorie allowance of 2550 - 1100 - 250 = 1200 calories. The bag of popcorn has 300 calories/serving * 5 servings = 1500 calories. Each gram of popcorn has 1500 calories / 325 grams = 4.62 calories/gram (approximately). Ibrahim can eat 2100 calories / 4.62 calories/gram = 454.55 grams of popcorn. Priya can eat 1200 calories / 4.62 calories/gram = 259.74 grams of popcorn. Ibrahim needs to consume 454.55 - 259.74 = 194.81 more grams of popcorn than Priya. Answer: {194.81}

Overall Quality: good

The reasoning chain is mathematically sound. Although it uses a different method (calculating calories per gram) than the ground truth (calculating required servings), all arithmetic steps performed are correct based on the values derived in the preceding steps.

✓ No hallucinations detected

Question #146

Clean

Full Question

According to its nutritional info, a bag of breads has 250 calories per serving. A 350 ounces bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Yuki weighs 210 lbs, and he has already consumed 1050 calories and burned 150 calories through exercise. Jasmine weighs 140 lbs, and she has already consumed 900 in food and 200 calories in ice cream. How many more ounces of breads does Yuki need to consume than Jasmine?

Ground Truth Answer

Yuki's calorie target is 210 * 15 = 3150 calories. Yuki needs 3150 - 1050 + 150 = 2250 calories more. That would be 2250 / 250 = 9 servings. Jasmine's calorie target is 140 * 15 = 2100 calories. Jasmine needs 2100 - 900 - 200 = 1000 calories more. That would be 1000 / 250 = 4 servings. Yuki needs 9 - 4 = 5 more servings than Jasmine. Each serving is 350 / 5 = 70 ouncess. So Yuki needs 5 servings * 70 units/serving = 350 ouncess more than Jasmine. #### 350

Generated Answer

First, we calculate Yuki's daily calorie target: 210 lbs * 15 calories/lb = 3150 calories. He has a remaining calorie allowance of 3150 - 1050 + 150 = 2250 calories. Next, we find Jasmine's daily calorie target: 140 lbs * 15 calories/lb = 2100 calories. She has a remaining calorie allowance of 2100 - 900 - 200 = 1000 calories. Then, calculate the calories per ounce of bread: 250 calories/serving / (350 ounces/5 servings) = 250/70 = 3.57 calories/ounce (approximately). Now, determine how many ounces of bread Yuki needs: 2250 calories / 3.57 calories/ounce ≈ 630.25 ounces. Since a bag has only 350 ounces, we'll just use the 350-ounce bag as a maximum. However, Yuki needs to consume only 2250 / 250 = 9 servings. The bag has only 5 servings, so he needs 9 servings * 70 ounces/serving = 630 ounces of bread. Since each bag is 350 ounces, he needs 630 / 350 = 1.8 bags, approximately. Since we are talking servings here, he needs to consume a total of 9 servings (1.8 bags of bread). Finally, determine how many ounces of bread Jasmine needs: 1000 calories / 3.57 calories/ounce ≈ 280.11 ounces. She needs 1000 / 250 = 4 servings. This means she needs 4 servings * 70 ounces/serving = 280 ounces. The difference in ounces of bread needed is approximately 630.25 - 280.11 ≈ 350.14 ounces. In terms of servings needed, it's 9-4 = 5 servings. So Yuki needs 5 servings * 70 oz/serving = 350 oz more than Jasmine. Answer: {350}

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate steps and arrives at the correct final answer by following the logic derived from the ground truth steps, even though it includes some unnecessary or confusing intermediate calculations (like calculating calories/ounce and then reverting to servings).

✓ No hallucinations detected

Question #144

Clean

Full Question

According to its nutritional info, a bag of breads has 225 calories per serving. A 300 ounces bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Carlos weighs 200 lbs, and he has already consumed 900 calories and burned 150 calories through exercise. Zahra weighs 150 lbs, and she has already consumed 900 in food and 225 calories in ice cream. How many more ounces of breads does Carlos need to consume than Zahra?

Ground Truth Answer

Carlos's calorie target is 200 * 15 = 3000 calories. Carlos needs 3000 - 900 + 150 = 2250 calories more. That would be 2250 / 225 = 10 servings. Zahra's calorie target is 150 * 15 = 2250 calories. Zahra needs 2250 - 900 - 225 = 1125 calories more. That would be 1125 / 225 = 5 servings. Carlos needs 10 - 5 = 5 more servings than Zahra. Each serving is 300 / 5 = 60 ouncess. So Carlos needs 5 servings * 60 units/serving = 300 ouncess more than Zahra. #### 300

Generated Answer

Here's how to break down this problem: 1. **Carlos's calorie target:** Carlos weighs 200 lbs, so his daily target is 200 lbs * 15 calories/lb = 3000 calories. 2. **Carlos's remaining calories:** He has consumed 900 calories and burned 150, so his net intake is 900 - 150 = 750 calories. He needs 3000 - 750 = 2250 more calories. 3. **Zahra's calorie target:** Zahra weighs 150 lbs, so her daily target is 150 lbs * 15 calories/lb = 2250 calories. 4. **Zahra's remaining calories:** She has consumed 900 + 225 = 1125 calories. She needs 2250 - 1125 = 1125 more calories. 5. **Calories per ounce of bread:** The bag has 225 calories/serving * 5 servings / 300 ounces = 3.75 calories per ounce. 6. **Ounces of bread Carlos needs:** Carlos needs 2250 calories / 3.75 calories/ounce = 600 ounces of bread. Since a bag only has 300 ounces, he needs 600/300=2 bags. 7. **Ounces of bread Zahra needs:** Zahra needs 1125 calories / 3.75 calories/ounce = 300 ounces of bread. Since a bag has 300 ounces, she needs 300/300=1 bag. 8. **Difference in ounces:** Carlos needs 600 - 300 = 300 more ounces of bread than Zahra. Answer: {300}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem requirements. All calculations are correct, and the interpretation of calorie adjustments (consumed vs. burned) is accurate.

✓ No hallucinations detected

Question #149

Clean

Full Question

According to its nutritional info, a bag of popcorn has 150 calories per serving. A 300 grams bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Arjun weighs 210 lbs, and he has already consumed 1000 calories and burned 100 calories through exercise. Elena weighs 180 lbs, and she has already consumed 900 in food and 150 calories in ice cream. How many more grams of popcorn does Arjun need to consume than Elena?

Ground Truth Answer

Arjun's calorie target is 210 * 15 = 3150 calories. Arjun needs 3150 - 1000 + 100 = 2250 calories more. That would be 2250 / 150 = 15 servings. Elena's calorie target is 180 * 15 = 2700 calories. Elena needs 2700 - 900 - 150 = 1650 calories more. That would be 1650 / 150 = 11 servings. Arjun needs 15 - 11 = 4 more servings than Elena. Each serving is 300 / 5 = 60 gramss. So Arjun needs 4 servings * 60 units/serving = 240 gramss more than Elena. #### 240

Generated Answer

Here's how we can solve this problem: 1. **Calculate Arjun's daily calorie target:** 210 lbs * 15 calories/lb = 3150 calories 2. **Calculate Arjun's remaining calorie allowance:** 3150 calories - 1000 calories + 100 calories = 2250 calories 3. **Calculate Elena's daily calorie target:** 180 lbs * 15 calories/lb = 2700 calories 4. **Calculate Elena's remaining calorie allowance:** 2700 calories - 900 calories - 150 calories = 1650 calories 5. **Calculate calories per gram of popcorn:** (150 calories/serving) / (300 grams/5 servings) = 2.5 calories/gram 6. **Calculate grams of popcorn Arjun can eat:** 2250 calories / 2.5 calories/gram = 900 grams 7. **Calculate grams of popcorn Elena can eat:** 1650 calories / 2.5 calories/gram = 660 grams 8. **Calculate the difference in popcorn consumption:** 900 grams - 660 grams = 240 grams Answer: {240}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem statement, leading to the correct final answer.

✓ No hallucinations detected

Question #273

3 issues

Full Question

Haruka has a flower bed that is 117 meters long. Haruka wants to fill her flower bed with plants. Haruka's flowers grow 3meters wide so she needs to leave 13 meters between every plant (including the plants width). Haruka already owns 6 flowers. Each flowering plant costs €8 at the store. However, if she buys more than 2 plants, she'll receive a €9 discount on the entire purchase. How much money will Haruka spend at the store to fill up her flower bed?

Ground Truth Answer

Haruka's flower bed is 117 meters / 13 meters per plant = 9 plants needed. Haruka needs to buy 9 plants - 6 plants = 3 plants needed to purchase. Haruka will spend 3 plants * €8 = €24. Finally, we should reduce 9 as she has bought more than 2 plants: 24 - 9 = 15 #### 15

Generated Answer

Here's how to break down the problem: 1. **Calculate the space needed per plant:** Each plant needs 3 meters (width) + 13 meters (spacing) = 16 meters of space. 2. **Determine how many plants fit in the flower bed:** The flower bed is 117 meters long. Divide the length of the flower bed by the space per plant: 117 meters / 16 meters/plant = 7.3125 plants. Since you can't have a fraction of a plant, Haruka can fit a maximum of 7 plants. 3. **Calculate how many additional plants are needed:** Haruka already has 6 plants and needs 7, so she needs to buy 7 - 6 = 1 additional plant. 4. **Calculate the cost:** Since she's buying only 1 plant, she won't get the discount. The cost will be 1 plant * €8/plant = €8. Answer: {8}

Overall Quality: poor

The reasoning chain contains multiple critical logical errors stemming from an incorrect initial interpretation of the spacing requirement, leading to an incorrect total plant count, incorrect purchase quantity, and failure to apply the required discount.

Detected Issues (3)

logical_error high

Statement

Divide the length of the flower bed by the space per plant: 117 meters / 16 meters/plant = 7.3125 plants. Since you can't have a fraction of a plant, Haruka can fit a maximum of 7 plants.

Explanation

Based on the incorrect spacing calculation (16m), the total plant count is wrong. Using the correct spacing (13m), 9 plants are needed (117 / 13 = 9).

Answer Span:

117 meters / 16 meters/plant = 7.3125 plants. Since you can't have a fraction of a plant, Haruka can fit a maximum of 7 plants.

Reference/Question Span:

Haruka wants to fill her flower bed

logical_error medium

Statement

Haruka already has 6 plants and needs 7, so she needs to buy 7 - 6 = 1 additional plant.

Explanation

Since 9 plants are needed in total (not 7), the number of plants to purchase is 9 - 6 = 3.

Answer Span:

7 - 6 = 1 additional plant

Reference/Question Span:

Haruka already owns 6 flowers.

logical_error high

Statement

Since she's buying only 1 plant, she won't get the discount. The cost will be 1 plant * €8/plant = €8.

Explanation

Since 3 plants are purchased (which is more than 2), the €9 discount should apply. The cost should be (3 * €8) - €9 = €15.

Answer Span:

Since she's buying only 1 plant, she won't get the discount. The cost will be 1 plant * €8/plant = €8.

Reference/Question Span:

if she buys more than 2 plants, she'll receive a €9 discount on the entire purchase.

Question #205

Clean

Full Question

Mr. Martinez sold his cottage for $690000. He paid the transfer fees that amounted to 3% of the selling price and also paid a brokerage fee that is 6% of the selling price. He also paid $590000 for the remaining loan amount on the cottage, and $5000 for closing costs. Mr. Martinez used the net proceeds from selling the cottage to invest in stocks. The stocks gained 10% each year for two years. How much were Mr. Martinez's net proceeds after two years?

Ground Truth Answer

Mr. Martinez paid $690000 x 3/100 = $20700 for the transfer fees. He paid $690000 x 6/100 = $41400 for the brokerage fee. So, Mr. Martinez paid a total of $20700 + $41400 + $590000 = $652100 for the transfer, brokerage, and loan fees. Hence, Mr. Martinez's net proceeds is $690000 - $652100 = $37900. Deducting the 5000 closing costs, we have $37900 - $5000 = 32900. We multiply 32900 by two 10% increments which would be 32900 * 110% * 110% = 39809 #### 39809

Generated Answer

Here's how to calculate Mr. Martinez's net proceeds after two years: 1. **Calculate transfer fees:** $690,000 * 0.03 = $20,700 2. **Calculate brokerage fees:** $690,000 * 0.06 = $41,400 3. **Calculate total fees:** $20,700 + $41,400 = $62,100 4. **Calculate initial net proceeds from the sale:** $690,000 - $62,100 - $590,000 - $5,000 = $32,900 5. **Calculate the return on investment after the first year:** $32,900 * 0.10 = $3,290 6. **Calculate the total amount after the first year:** $32,900 + $3,290 = $36,190 7. **Calculate the return on investment after the second year:** $36,190 * 0.10 = $3,619 8. **Calculate the total amount after the second year:** $36,190 + $3,619 = $39,809 Answer: {39809}

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate steps and arrives at the correct final answer using sound mathematical logic.

✓ No hallucinations detected

Question #148

Clean

Full Question

According to its nutritional info, a bag of popcorn has 325 calories per serving. A 100 grams bag has 4 servings. The healthy daily calorie target is 15 calories per pound of body weight. Arash weighs 200 lbs, and he has already consumed 1200 calories and burned 150 calories through exercise. Mei weighs 180 lbs, and she has already consumed 900 in food and 175 calories in ice cream. How many more grams of popcorn does Arash need to consume than Mei?

Ground Truth Answer

Arash's calorie target is 200 * 15 = 3000 calories. Arash needs 3000 - 1200 + 150 = 1950 calories more. That would be 1950 / 325 = 6 servings. Mei's calorie target is 180 * 15 = 2700 calories. Mei needs 2700 - 900 - 175 = 1625 calories more. That would be 1625 / 325 = 5 servings. Arash needs 6 - 5 = 1 more servings than Mei. Each serving is 100 / 4 = 25 gramss. So Arash needs 1 servings * 25 units/serving = 25 gramss more than Mei. #### 25

Generated Answer

Arash's daily calorie target is 200 lbs * 15 calories/lb = 3000 calories. He has a remaining calorie allowance of 3000 - 1200 + 150 = 1950 calories. Mei's daily calorie target is 180 lbs * 15 calories/lb = 2700 calories. She has a remaining calorie allowance of 2700 - 900 - 175 = 1625 calories. A 100-gram bag of popcorn has 325 calories/serving * 4 servings = 1300 calories. Arash can eat 1950 calories / 1300 calories/bag = 1.5 bags of popcorn. This translates to 1.5 bags * 100 grams/bag = 150 grams of popcorn. Mei can eat 1625 calories / 1300 calories/bag = 1.25 bags of popcorn. This translates to 1.25 bags * 100 grams/bag = 125 grams of popcorn. Arash needs to consume 150 - 125 = 25 more grams of popcorn than Mei. Answer: {25}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem requirements, leading to the correct answer.

✓ No hallucinations detected

Question #147

Clean

Full Question

According to its nutritional info, a bag of cookies has 175 calories per serving. A 125 oz bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Theo weighs 250 lbs, and he has already consumed 1100 calories and burned 150 calories through exercise. Sakura weighs 130 lbs, and she has already consumed 900 in food and 175 calories in ice cream. How many more oz of cookies does Theo need to consume than Sakura?

Ground Truth Answer

Theo's calorie target is 250 * 15 = 3750 calories. Theo needs 3750 - 1100 + 150 = 2800 calories more. That would be 2800 / 175 = 16 servings. Sakura's calorie target is 130 * 15 = 1950 calories. Sakura needs 1950 - 900 - 175 = 875 calories more. That would be 875 / 175 = 5 servings. Theo needs 16 - 5 = 11 more servings than Sakura. Each serving is 125 / 5 = 25 ozs. So Theo needs 11 servings * 25 units/serving = 275 ozs more than Sakura. #### 275

Generated Answer

Here's how to solve this problem: 1. **Calculate Theo's target calorie intake:** 250 lbs * 15 calories/lb = 3750 calories 2. **Calculate Theo's remaining calorie allowance:** 3750 calories - 1100 calories + 150 calories (burned) = 2800 calories 3. **Calculate calories per bag of cookies:** 175 calories/serving * 5 servings/bag = 875 calories/bag 4. **Calculate how many bags of cookies Theo can eat:** 2800 calories / 875 calories/bag = 3.2 bags 5. **Calculate how many oz of cookies Theo can eat:** 3.2 bags * 125 oz/bag = 400 oz 6. **Calculate Sakura's target calorie intake:** 130 lbs * 15 calories/lb = 1950 calories 7. **Calculate Sakura's remaining calorie allowance:** 1950 calories - 900 calories - 175 calories = 875 calories 8. **Calculate how many bags of cookies Sakura can eat:** 875 calories / 875 calories/bag = 1 bag 9. **Calculate how many oz of cookies Sakura can eat:** 1 bag * 125 oz/bag = 125 oz 10. **Calculate the difference in cookie consumption:** 400 oz - 125 oz = 275 oz Answer: {275}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem constraints, arriving at the correct answer through valid intermediate steps.

✓ No hallucinations detected

Question #204

Clean

Full Question

Dr. Miller sold his apartment for $490000. He paid the legal fees that amounted to 1% of the selling price and also paid a realtor fee that is 5% of the selling price. He also paid $390000 for the remaining loan amount on the apartment, and $10000 for closing costs. Dr. Miller used the net proceeds from selling the apartment to invest in stocks. The stocks gained 10% each year for two years. How much were Dr. Miller's net proceeds after two years?

Ground Truth Answer

Dr. Miller paid $490000 x 1/100 = $4900 for the legal fees. He paid $490000 x 5/100 = $24500 for the realtor fee. So, Dr. Miller paid a total of $4900 + $24500 + $390000 = $419400 for the legal, realtor, and loan fees. Hence, Dr. Miller's net proceeds is $490000 - $419400 = $70600. Deducting the 10000 closing costs, we have $70600 - $10000 = 60600. We multiply 60600 by two 10% increments which would be 60600 * 110% * 110% = 73326 #### 73326

Generated Answer

Here's how to break down Dr. Miller's financial transactions: 1. **Calculate the legal fees:** 1% of $490,000 is $490,000 * 0.01 = $4,900 2. **Calculate the realtor fees:** 5% of $490,000 is $490,000 * 0.05 = $24,500 3. **Calculate total expenses:** Legal fees + realtor fees + loan amount + closing costs = $4,900 + $24,500 + $390,000 + $10,000 = $429,400 4. **Calculate net proceeds from the sale:** Selling price - total expenses = $490,000 - $429,400 = $60,600 5. **Calculate the return on investment after the first year:** Net proceeds * 10% = $60,600 * 0.10 = $6,060. This brings the total to $60,600 + $6,060 = $66,660 6. **Calculate the return on investment after the second year:** $66,660 * 0.10 = $6,666. This brings the final total to $66,660 + $6,666 = $73,326 Answer: {73326}

Overall Quality: excellent

The reasoning chain correctly calculates all fees, determines the net proceeds, and accurately applies the two consecutive 10% gains using compound growth logic ($60600 * 1.10 * 1.10 = 73326). All arithmetic steps are correct.

✓ No hallucinations detected

Question #209

Clean

Full Question

Prof. Smith sold his house for $560000. He paid the registration fees that amounted to 3% of the selling price and also paid a agent fee that is 4% of the selling price. He also paid $440000 for the remaining loan amount on the house, and $15000 for closing costs. Prof. Smith used the net proceeds from selling the house to invest in stocks. The stocks gained 10% each year for two years. How much were Prof. Smith's net proceeds after two years?

Ground Truth Answer

Prof. Smith paid $560000 x 3/100 = $16800 for the registration fees. He paid $560000 x 4/100 = $22400 for the agent fee. So, Prof. Smith paid a total of $16800 + $22400 + $440000 = $479200 for the registration, agent, and loan fees. Hence, Prof. Smith's net proceeds is $560000 - $479200 = $80800. Deducting the 15000 closing costs, we have $80800 - $15000 = 65800. We multiply 65800 by two 10% increments which would be 65800 * 110% * 110% = 79618 #### 79618

Generated Answer

Here's how to break down Prof. Smith's financial journey: 1. **Calculate registration fees:** 3% of $560,000 is $560,000 * 0.03 = $16,800 2. **Calculate agent fees:** 4% of $560,000 is $560,000 * 0.04 = $22,400 3. **Calculate total expenses:** $16,800 + $22,400 + $440,000 + $15,000 = $494,200 4. **Calculate net proceeds from the sale:** $560,000 - $494,200 = $65,800 5. **Calculate first-year investment gain:** 10% of $65,800 is $65,800 * 0.10 = $6,580 6. **Calculate first-year investment total:** $65,800 + $6,580 = $72,380 7. **Calculate second-year investment gain:** 10% of $72,380 is $72,380 * 0.10 = $7,238 8. **Calculate second-year investment total (net proceeds after two years):** $72,380 + $7,238 = $79,618 Answer: {79618}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are accurate, and the logic correctly separates the initial sale deductions from the subsequent investment growth calculation. The final answer matches the ground truth.

✓ No hallucinations detected

Question #275

1 issue

Full Question

Zahra has a flower bed that is 144 feet long. Zahra wants to fill her flower bed with plants. Zahra's flowers grow 4feet wide so she needs to leave 12 feet between every plant (including the plants width). Zahra already owns 5 flowers. Each flowering plant costs ₣13 at the store. However, if she buys more than 2 plants, she'll receive a ₣5 discount on the entire purchase. How much money will Zahra spend at the store to fill up her flower bed?

Ground Truth Answer

Zahra's flower bed is 144 feet / 12 feet per plant = 12 plants needed. Zahra needs to buy 12 plants - 5 plants = 7 plants needed to purchase. Zahra will spend 7 plants * ₣13 = ₣91. Finally, we should reduce 5 as she has bought more than 2 plants: 91 - 5 = 86 #### 86

Generated Answer

First, calculate the space each plant needs, including the space between them: 4 feet (plant width) + 12 feet (space) = 16 feet. Next, determine how many plants can fit in the flower bed: 144 feet (bed length) / 16 feet (space per plant) = 9 plants. Since Zahra already has 5 plants, she needs to buy 9 - 5 = 4 plants. Because she's buying more than 2 plants, she gets a ₣5 discount. The cost per plant is then ₣13 - ₣5 = ₣8. Therefore, the total cost will be 4 plants * ₣8/plant = ₣32. Answer: {32}

Overall Quality: poor

The reasoning chain contains two significant logical errors: misinterpreting the required spacing per plant, and incorrectly applying the purchase discount on a per-unit basis instead of as a total deduction.

Detected Issues (1)

logical_error high

Statement

The cost per plant is then ₣13 - ₣5 = ₣8.

Explanation

The problem states the ₣5 is a discount on the *entire purchase* if more than 2 plants are bought, not a reduction in the unit price.

Answer Span:

₣13 - ₣5 = ₣8

Reference/Question Span:

if she buys more than 2 plants, she'll receive a ₣5 discount on the entire purchase

Question #270

1 issue

Full Question

Kimia has a flower bed that is 126 feet long. Kimia wants to fill her flower bed with plants. Kimia's flowers grow 7feet wide so she needs to leave 14 feet between every plant (including the plants width). Kimia already owns 6 flowers. Each flowering plant costs ₣4 at the store. However, if she buys more than 2 plants, she'll receive a ₣5 discount on the entire purchase. How much money will Kimia spend at the store to fill up her flower bed?

Ground Truth Answer

Kimia's flower bed is 126 feet / 14 feet per plant = 9 plants needed. Kimia needs to buy 9 plants - 6 plants = 3 plants needed to purchase. Kimia will spend 3 plants * ₣4 = ₣12. Finally, we should reduce 5 as she has bought more than 2 plants: 12 - 5 = 7 #### 7

Generated Answer

First, calculate the total space needed for each plant, including the spacing: 7 feet (plant width) + 14 feet (spacing) = 21 feet. Next, determine how many plants can fit in the flower bed: 126 feet (bed length) / 21 feet (space per plant) = 6 plants. Kimia already has 6 plants, and she can fit exactly 6 plants in her flower bed. This means she doesn't need to buy any more plants. Therefore, Kimia will spend ₣0 at the store. Answer: {0}

Overall Quality: poor

The reasoning chain incorrectly interprets the spacing requirement, leading to an incorrect calculation for the number of plants needed and consequently an incorrect final cost.

Detected Issues (1)

logical_error high

Statement

First, calculate the total space needed for each plant, including the spacing: 7 feet (plant width) + 14 feet (spacing) = 21 feet.

Explanation

The problem implies that 14 feet is the required spacing unit (or the distance from the start of one plant to the start of the next), as dividing the total length by 14 yields the correct number of plants (9). Adding the plant width (7 feet) to the spacing (14 feet) results in an incorrect unit cell size of 21 feet.

Answer Span:

7 feet (plant width) + 14 feet (spacing) = 21 feet

Reference/Question Span:

Kimia's flowers grow 7feet wide so she needs to leave 14 feet between every plant (including the plants width)

Question #272

Clean

Full Question

Mei has a flower bed that is 120 meters long. Mei wants to fill her flower bed with plants. Mei's flowers grow 4meters wide so she needs to leave 12 meters between every plant (including the plants width). Mei already owns 6 flowers. Each flowering plant costs $5 at the store. However, if she buys more than 2 plants, she'll receive a $5 discount on the entire purchase. How much money will Mei spend at the store to fill up her flower bed?

Ground Truth Answer

Mei's flower bed is 120 meters / 12 meters per plant = 10 plants needed. Mei needs to buy 10 plants - 6 plants = 4 plants needed to purchase. Mei will spend 4 plants * $5 = $20. Finally, we should reduce 5 as she has bought more than 2 plants: 20 - 5 = 15 #### 15

Generated Answer

Mei needs to leave 12 meters between plants, and each plant is 4 meters wide, so the total space taken up by each plant and its spacing is 12 + 4 = 16 meters. The flower bed is 120 meters long, so it can hold 120 / 16 = 7.5 plants. Since she can't plant half a plant, she can plant 7 plants. Mei already owns 6 flowers, so she needs to buy 7 - 6 = 1 more plant. Since she's only buying 1 plant, she doesn't qualify for the $5 discount. Therefore, she'll spend 1 plant * $5/plant = $5. Answer: {5}

Overall Quality: poor

The model made a critical logical error in interpreting the spacing requirement, leading to an incorrect calculation of the total number of plants needed and consequently an incorrect final cost.

✓ No hallucinations detected

Question #154

Clean

Full Question

In Dr. Lee's class of 104 students, 50% of the class are volleyball players. Out of the remaining class, 25% of the students are robotics club members or part of choir members. These 3 groups of students will need to leave early today to travel to an away competition. Half of the volleyball players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition?

Ground Truth Answer

50% of the 104 student class are volleyball players so that's 0.5*104 = 52 students. There are 104 students and 52 are volleyball players so that leaves 104-52 = 52 students 25% of the remaining 52 students are part of choir members or robotics club members so that's 0.25*52 = 13 students 52 students are volleyball players and 13 are part of choir members/robotics club members so 52+13 = 65 students will be leaving early. But half of volleyball players won't be able to attend so we reduce 52 / 2 = 26. Also 3 * 3 = 9 cheer leaders will join them. So we have 65 - 26 + 9 = 48 #### 48

Generated Answer

First, we calculate the number of volleyball players: 104 students * 50% = 52 volleyball players. However, half are sick, so only 52 / 2 = 26 volleyball players are going to the competition. Next, we find the number of students remaining after removing the volleyball players: 104 - 52 = 52 students. Out of these, 25% are in robotics/choir: 52 * 25% = 13 students. So, the total number of students going to the competition (excluding cheerleaders) is 26 volleyball players + 13 robotics/choir members = 39 students. There are 3 groups in total (volleyball, robotics, choir). Each group has 3 cheerleaders accompanying them, for a total of 3 groups * 3 cheerleaders/group = 9 cheerleaders. Therefore, the total number of people leaving early for the competition is 39 students + 9 cheerleaders = 48 people. Answer: {48}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #208

Clean

Full Question

Dr. Smith sold his house for $590000. He paid the legal fees that amounted to 3% of the selling price and also paid a realtor fee that is 4% of the selling price. He also paid $380000 for the remaining loan amount on the house, and $25000 for closing costs. Dr. Smith used the net proceeds from selling the house to invest in stocks. The stocks gained 10% each year for two years. How much were Dr. Smith's net proceeds after two years?

Ground Truth Answer

Dr. Smith paid $590000 x 3/100 = $17700 for the legal fees. He paid $590000 x 4/100 = $23600 for the realtor fee. So, Dr. Smith paid a total of $17700 + $23600 + $380000 = $421300 for the legal, realtor, and loan fees. Hence, Dr. Smith's net proceeds is $590000 - $421300 = $168700. Deducting the 25000 closing costs, we have $168700 - $25000 = 143700. We multiply 143700 by two 10% increments which would be 143700 * 110% * 110% = 173877 #### 173877

Generated Answer

Here's how to break down Dr. Smith's finances: 1. **Calculate Legal Fees:** 3% of $590,000 is $590,000 * 0.03 = $17,700 2. **Calculate Realtor Fees:** 4% of $590,000 is $590,000 * 0.04 = $23,600 3. **Calculate Total Expenses:** Legal fees + Realtor fees + Loan amount + Closing costs = $17,700 + $23,600 + $380,000 + $25,000 = $446,300 4. **Calculate Net Proceeds from Sale:** Selling price - Total expenses = $590,000 - $446,300 = $143,700 5. **Calculate First Year's Stock Gain:** 10% of $143,700 is $143,700 * 0.10 = $14,370 6. **Calculate Value After First Year:** Initial investment + First year gain = $143,700 + $14,370 = $158,070 7. **Calculate Second Year's Stock Gain:** 10% of $158,070 is $158,070 * 0.10 = $15,807 8. **Calculate Value After Second Year:** Value after first year + Second year gain = $158,070 + $15,807 = $173,877 Answer: {173877}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem requirements, arriving at the correct final answer.

✓ No hallucinations detected

Question #153

Clean

Full Question

In Ms. Johnson's class of 20 students, 20% of the class are soccer players. Out of the remaining class, 50% of the students are debate team members or part of choir members. These 3 groups of students will need to leave early today to travel to an away competition. Half of the soccer players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition?

Ground Truth Answer

20% of the 20 student class are soccer players so that's 0.2*20 = 4 students. There are 20 students and 4 are soccer players so that leaves 20-4 = 16 students 50% of the remaining 16 students are part of choir members or debate team members so that's 0.5*16 = 8 students 4 students are soccer players and 8 are part of choir members/debate team members so 4+8 = 12 students will be leaving early. But half of soccer players won't be able to attend so we reduce 4 / 2 = 2. Also 3 * 3 = 9 cheer leaders will join them. So we have 12 - 2 + 9 = 19 #### 19

Generated Answer

Here's how to break down this problem: 1. **Soccer Players:** 20% of 20 students is 0.20 * 20 = 4 soccer players. However, half are sick, so only 4 / 2 = 2 soccer players are going. 2. **Remaining Students:** There are 20 - 4 = 16 students who aren't soccer players. 3. **Debate/Choir:** 50% of the remaining 16 students are in debate or choir. That's 0.50 * 16 = 8 students. 4. **Total Competitors:** So, there are 2 soccer players + 8 debate/choir members = 10 students competing. 5. **Cheerleaders:** 3 cheerleaders accompany each group, and there are 3 groups (soccer, debate, choir) regardless of some members being absent. That's 3 cheerleaders/group * 3 groups = 9 cheerleaders. 6. **Grand Total:** 10 competing students + 9 cheerleaders = 19 people going to the competition. Answer: {19}

Overall Quality: excellent

The reasoning chain correctly follows all steps and calculations based on the problem description, leading to the correct final answer.

✓ No hallucinations detected

Question #155

Clean

Full Question

In Mr. Smith's class of 80 students, 20% of the class are basketball players. Out of the remaining class, 50% of the students are dancers or part of debate team members. These 3 groups of students will need to leave early today to travel to an away tournament. Half of the basketball players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the tournament?

Ground Truth Answer

20% of the 80 student class are basketball players so that's 0.2*80 = 16 students. There are 80 students and 16 are basketball players so that leaves 80-16 = 64 students 50% of the remaining 64 students are part of debate team members or dancers so that's 0.5*64 = 32 students 16 students are basketball players and 32 are part of debate team members/dancers so 16+32 = 48 students will be leaving early. But half of basketball players won't be able to attend so we reduce 16 / 2 = 8. Also 3 * 3 = 9 cheer leaders will join them. So we have 48 - 8 + 9 = 49 #### 49

Generated Answer

First, find the number of basketball players: 20% of 80 students is (20/100) * 80 = 16 students. Since half of the basketball players are absent, only 16 / 2 = 8 basketball players are going to the tournament. Next, find the number of students who are not basketball players: 80 total students - 16 basketball players = 64 students. Out of these remaining students, 50% are dancers or debaters: (50/100) * 64 = 32 students. Now, find the total number of students from the three groups going to the tournament: 8 basketball players + 32 dancers/debaters = 40 students. Finally, add the cheerleaders: 3 cheerleaders per group * 3 groups = 9 cheerleaders. The total number of people leaving early is 40 students + 9 cheerleaders = 49 people. Answer: {49}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all arithmetic calculations accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #150

Clean

Full Question

In Ms. Johnson's class of 100 students, 46% of the class are soccer players. Out of the remaining class, 50% of the students are robotics club members or part of dancers. These 3 groups of students will need to leave early today to travel to an away competition. Half of the soccer players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition?

Ground Truth Answer

46% of the 100 student class are soccer players so that's 0.46*100 = 46 students. There are 100 students and 46 are soccer players so that leaves 100-46 = 54 students 50% of the remaining 54 students are part of dancers or robotics club members so that's 0.5*54 = 27 students 46 students are soccer players and 27 are part of dancers/robotics club members so 46+27 = 73 students will be leaving early. But half of soccer players won't be able to attend so we reduce 46 / 2 = 23. Also 3 * 3 = 9 cheer leaders will join them. So we have 73 - 23 + 9 = 59 #### 59

Generated Answer

First, find the number of soccer players: 100 students * 46% = 46 soccer players. Then, find the number of soccer players who are not absent: 46 soccer players / 2 = 23 soccer players. Next, find the number of students who are not soccer players: 100 students - 46 students = 54 students. Then, find the number of students in robotics club or dancers: 54 students * 50% = 27 students. The total number of students in the three groups is 23 soccer players + 27 students = 50 students. Finally, find the total number of people leaving, including cheerleaders: 50 students + (3 cheerleaders/group * 3 groups) = 50 students + 9 cheerleaders = 59 people. Answer: {59}

Overall Quality: fair

The model arrives at the correct final answer (59) despite two logical errors in intermediate steps. The first error incorrectly calculates the number of attending soccer players (23) and uses this as the base for the leaving group, instead of calculating the number of soccer players *leaving* (46 - 23 = 23). The second error compounds this by summing the attending soccer players (23) with the other groups (27). Since the ground truth calculation is 46 - 23 + 27 = 50 students leaving, and the model calculated 23 + 27 = 50 students, the model accidentally used the correct resulting number (23 attending soccer players) in the summation, leading to the correct intermediate total of 50 students before adding cheerleaders.

✓ No hallucinations detected

Question #78

Clean

Full Question

Sakura is an avid gardener. Two days ago, she received 49 new potted plants from her favorite plant nursery. She already has 7 potted plants on each of the 60 window ledges of her large country home. She also purchased 100 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 3 potted plants from each ledge to friends and family tomorrow. How many potted plants will Sakura remain with?

Ground Truth Answer

Two days ago, before receiving the plants, Sakura had 60*7 = 420 potted plants After receiving an additional 49 plants, she therefore had a total of 420 + 49 = 469 potted plants. Adding the 100 new plants, it will be 469+100=569. Tomorrow, Sakura's plant giveaway will be 60*3 = 180 potted plants. She will therefore remain with 569 - 180 = 389 potted plants. #### 389

Generated Answer

Sakura currently has 7 plants/ledge * 60 ledges = 420 plants. Two days ago, she received 49 new plants, so she had 420 + 49 = 469 plants. Yesterday, she purchased 100 new plants, bringing her total to 469 + 100 = 569 plants. Tomorrow, she will give away 3 plants/ledge * 60 ledges = 180 plants. Therefore, Sakura will have 569 - 180 = 389 plants remaining. Answer: {389}

Overall Quality: excellent

The reasoning chain correctly interprets the sequence of events and performs all arithmetic calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #79

Clean

Full Question

Daphne is an avid gardener. Two days ago, she received 23 new potted plants from her favorite plant nursery. She already has 8 potted plants on each of the 56 window ledges of her large country home. She also purchased 200 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 6 potted plants from each ledge to friends and family tomorrow. How many potted plants will Daphne remain with?

Ground Truth Answer

Two days ago, before receiving the plants, Daphne had 56*8 = 448 potted plants After receiving an additional 23 plants, she therefore had a total of 448 + 23 = 471 potted plants. Adding the 200 new plants, it will be 471+200=671. Tomorrow, Daphne's plant giveaway will be 56*6 = 336 potted plants. She will therefore remain with 671 - 336 = 335 potted plants. #### 335

Generated Answer

Daphne currently has 8 plants/ledge * 56 ledges = 448 plants. Two days ago, she received 23 new plants, so she had 448 + 23 = 471 plants. Yesterday, she purchased 200 new plants, bringing her total to 471 + 200 = 671 plants. Tomorrow, she will give away 6 plants/ledge * 56 ledges = 336 plants. After giving away the plants, she will have 671 - 336 = 335 plants remaining. Answer: {335}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the steps required to solve the problem, resulting in the correct final answer.

✓ No hallucinations detected

Question #80

Clean

Full Question

Amelia is an avid gardener. Last week, she received 25 new potted plants from her favorite plant nursery. She already has 12 potted plants on each of the 54 window ledges of her large country home. She also purchased 110 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 4 potted plants from each ledge to friends and family tomorrow. How many potted plants will Amelia remain with?

Ground Truth Answer

Last week, before receiving the plants, Amelia had 54*12 = 648 potted plants After receiving an additional 25 plants, she therefore had a total of 648 + 25 = 673 potted plants. Adding the 110 new plants, it will be 673+110=783. Tomorrow, Amelia's plant giveaway will be 54*4 = 216 potted plants. She will therefore remain with 783 - 216 = 567 potted plants. #### 567

Generated Answer

Amelia currently has 12 plants/ledge * 54 ledges = 648 plants. She received 25 new plants, so she has 648 + 25 = 673 plants. She bought 110 new plants, making the total 673 + 110 = 783 plants. She will give away 4 plants/ledge * 54 ledges = 216 plants. Remaining plants: 783 - 216 = 567 plants. Answer: {567}

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps and performs all arithmetic calculations accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #81

Clean

Full Question

Elena is an avid gardener. Two days ago, she received 38 new potted plants from her favorite plant nursery. She already has 12 potted plants on each of the 55 window ledges of her large country home. She also purchased 70 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 3 potted plants from each ledge to friends and family tomorrow. How many potted plants will Elena remain with?

Ground Truth Answer

Two days ago, before receiving the plants, Elena had 55*12 = 660 potted plants After receiving an additional 38 plants, she therefore had a total of 660 + 38 = 698 potted plants. Adding the 70 new plants, it will be 698+70=768. Tomorrow, Elena's plant giveaway will be 55*3 = 165 potted plants. She will therefore remain with 768 - 165 = 603 potted plants. #### 603

Generated Answer

Elena currently has 12 plants/ledge * 55 ledges = 660 plants. She received 38 new plants two days ago, so she had 660 + 38 = 698 plants. Yesterday, she bought 70 more, giving her 698 + 70 = 768 plants. Tomorrow, she will give away 3 plants/ledge * 55 ledges = 165 plants. Therefore, Elena will have 768 - 165 = 603 plants remaining. Answer: {603}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all steps described in the problem. All calculations are correct.

✓ No hallucinations detected

Question #82

Clean

Full Question

Yara is an avid gardener. Two days ago, she received 49 new potted plants from her favorite plant nursery. She already has 12 potted plants on each of the 54 window ledges of her large country home. She also purchased 130 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 4 potted plants from each ledge to friends and family tomorrow. How many potted plants will Yara remain with?

Ground Truth Answer

Two days ago, before receiving the plants, Yara had 54*12 = 648 potted plants After receiving an additional 49 plants, she therefore had a total of 648 + 49 = 697 potted plants. Adding the 130 new plants, it will be 697+130=827. Tomorrow, Yara's plant giveaway will be 54*4 = 216 potted plants. She will therefore remain with 827 - 216 = 611 potted plants. #### 611

Generated Answer

Yara currently has 12 plants/ledge * 54 ledges = 648 plants. She received 49 new plants two days ago, so she had 648 + 49 = 697 plants. Yesterday, she purchased 130 more plants, giving her 697 + 130 = 827 plants. She will give away 4 plants/ledge * 54 ledges = 216 plants. Therefore, Yara will have 827 - 216 = 611 plants remaining. Answer: {611}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #97

Clean

Full Question

Benjamin is selling cupcakes and pineapple pies for a fundraiser. On Wednesday, he sold 27 boxes of cupcake and 18 fewer boxes of pineapple pie, than on Thursday. On Thursday, he sold 12 more boxes of cupcakes than on Wednesday and 27 boxes of pineapple pie. On Friday, he sold as much as he did in the past two days combined. If the cupcake cost ¥8 and the pineapple pie cost ¥22, what was Benjamin's average daily earning?

Ground Truth Answer

He sold 27 + 12 = 39 boxes of cupcake on Thursday. The total number of boxes of cupcakes that Benjamin sold is 27 + 39 = 66. Benjamin earned 66 x ¥8 = ¥528 for selling cupcakes. He sold 27 - 18 = 9 boxes of pineapple pie on Wednesday. The total number of boxes of pineapple pie that Benjamin sold is 27 + 9 = 36. He earned 36 x ¥22 = ¥792 for selling pineapple pie. So, Benjamin earned ¥528 + ¥792 = ¥1320 for two days. Finally, on Friday, he sold as much as he did in the past two days so 2 * 1320 = 2640. Finally, we should divide the total by 3 to get the average daily: 2640 / 3 = 880 #### 880

Generated Answer

Here's how to break down the problem: 1. **Thursday's Sales:** * Cupcakes: 27 (Wednesday) + 12 = 39 boxes * Pineapple Pies: 27 boxes 2. **Wednesday's Sales:** * Pineapple Pies: 27 (Thursday) - 18 = 9 boxes 3. **Friday's Sales:** * Cupcakes: 27 (Wednesday) + 39 (Thursday) = 66 boxes * Pineapple Pies: 9 (Wednesday) + 27 (Thursday) = 36 boxes 4. **Earnings:** * Wednesday: (27 cupcakes * ¥8) + (9 pies * ¥22) = ¥216 + ¥198 = ¥414 * Thursday: (39 cupcakes * ¥8) + (27 pies * ¥22) = ¥312 + ¥594 = ¥906 * Friday: (66 cupcakes * ¥8) + (36 pies * ¥22) = ¥528 + ¥792 = ¥1320 5. **Total Earnings:** ¥414 + ¥906 + ¥1320 = ¥2640 6. **Average Daily Earnings:** ¥2640 / 3 days = ¥880 Answer: {880}

Overall Quality: excellent

The reasoning chain correctly determines the sales volumes for Wednesday, Thursday, and Friday, accurately calculates the earnings for each day based on those volumes, and correctly computes the final average daily earning. All arithmetic operations are correct.

✓ No hallucinations detected

Question #112

Clean

Full Question

Faisal went to buy some school supplies. He bought 18 pencils which cost ₣6.0 each, 14 rulers which cost ₣14.5 each, and a ream of bond paper which cost ₣24. He also bought 5 colored pencils which cost ₣9 each. Faisal can either pay a one-time ₣20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Faisal can spend on everything?

Ground Truth Answer

Faisal spent 18 x ₣6.0 = ₣108 for the pencils. He also spent 14 x ₣14.5 = ₣203 for the rulers. Therefore, Faisal spent a total of ₣108 + ₣203 + ₣24 = ₣335 for the school supplies. Finally we should include 5 * 9 = 45. The total will be be 380 If Faisal becomes a member he gets 20% discount, which will be ₣380 * 20% = ₣76 discount. He also has to pay ₣20 so it will be ₣76 - ₣20 = ₣56 cheaper. If Faisal doesn't become a member, get only gets 5% discount, which will be ₣380 * 5% = ₣19. Since ₣19 is smaller than ₣56, to pay the least, Faisal has to become member. So overall he pays ₣380 - ₣56 = ₣324 #### 324

Generated Answer

First, calculate the cost of each item: * Pencils: 18 pencils * ₣6.0/pencil = ₣108 * Rulers: 14 rulers * ₣14.5/ruler = ₣203 * Bond paper: ₣24 * Colored pencils: 5 pencils * ₣9/pencil = ₣45 Total cost before any discount: ₣108 + ₣203 + ₣24 + ₣45 = ₣380 Scenario 1: Faisal becomes a member. * Membership fee: ₣20 * Discount: 20% of ₣380 = ₣76 * Cost after discount: ₣380 - ₣76 = ₣304 * Total cost with membership: ₣304 + ₣20 = ₣324 Scenario 2: Faisal does not become a member. * Discount: 5% of ₣380 = ₣19 * Total cost: ₣380 - ₣19 = ₣361 Since ₣324 is less than ₣361, the least amount Faisal can spend is ₣324. Answer: {324}

Overall Quality: excellent

The reasoning chain correctly calculates the cost of all items, determines the total cost, and accurately evaluates both scenarios (membership vs. non-membership) to find the minimum spending amount. All arithmetic and logic steps are sound.

✓ No hallucinations detected

Question #159

Clean

Full Question

A grandfather eats 10 sushi rolls per day, his partner eats 15 sushi rolls per day, and their son eats four-fifths of the combined number of sushi rolls they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 20% for the first half of the month, and then by an additional 25% for the second half. How many sushi rolls does this family eat in two months?

Ground Truth Answer

A grandfather and his partner consumption: 10 + 15 = 25 son consumes 4/5 more than A grandfather and his partner combined: 25 * 4/5 = 20. So son consumes 25 + 20 = 45 sushi rolls. During first month they consume 30 * 45 = 1350. The first half of the second month the consume 20% less each day: 80% * 45 = 36 . So in 15 days, they consume 540 sushi rolls. During second month, they consume 25% less than the first half each day, so they consume 75% * 36 = 27. So in 15 days, they consume 15 * 27 = 405 sushi rolls. In 2 months, they consume 45 + 540 + 405 = 2295 sushi rolls together. #### 2295

Generated Answer

Here's how to break down this problem: 1. **Calculate the son's daily sushi consumption:** The grandfather and partner together eat 10 + 15 = 25 rolls per day. The son eats (4/5) * 25 = 20 rolls per day. 2. **Calculate the family's total daily sushi consumption:** The whole family eats 10 + 15 + 20 = 45 rolls per day. 3. **Calculate the first month's consumption:** Assuming a 30-day month, they eat 45 rolls/day * 30 days = 1350 rolls. 4. **Calculate consumption for the first half of the second month:** They reduce consumption by 20%, so they eat 45 rolls/day * (1 - 0.20) = 36 rolls/day. Over 15 days, this is 36 rolls/day * 15 days = 540 rolls. 5. **Calculate consumption for the second half of the second month:** They further reduce consumption by 25% from the *already reduced* amount. So they eat 36 rolls/day * (1 - 0.25) = 27 rolls/day. Over 15 days, this is 27 rolls/day * 15 days = 405 rolls. 6. **Calculate the total consumption for the two months:** The total is 1350 (month 1) + 540 (second month, first half) + 405 (second month, second half) = 2295 rolls. Answer: {2295}

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps and performs all arithmetic calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #151

Clean

Full Question

In Ms. Johnson's class of 150 students, 40% of the class are soccer players. Out of the remaining class, 30% of the students are dancers or part of choir members. These 3 groups of students will need to leave early today to travel to an away competition. Half of the soccer players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition?

Ground Truth Answer

40% of the 150 student class are soccer players so that's 0.4*150 = 60 students. There are 150 students and 60 are soccer players so that leaves 150-60 = 90 students 30% of the remaining 90 students are part of choir members or dancers so that's 0.3*90 = 27 students 60 students are soccer players and 27 are part of choir members/dancers so 60+27 = 87 students will be leaving early. But half of soccer players won't be able to attend so we reduce 60 / 2 = 30. Also 3 * 3 = 9 cheer leaders will join them. So we have 87 - 30 + 9 = 66 #### 66

Generated Answer

First find the number of soccer players: 150 students * 40% = 60 soccer players. Half of the soccer players are absent: 60 soccer players / 2 = 30 soccer players. The remaining students are: 150 total students - 60 soccer players = 90 students. The number of dancers/choir members is 90 remaining students * 30% = 27 students. The total number of students going to the competition is 30 soccer players + 27 dancers/choir members = 57 students. There are 3 groups in total (soccer, dancers, choir). So, there are 3 cheerleaders/group * 3 groups = 9 cheerleaders. The total number of people leaving early is 57 students + 9 cheerleaders = 66 people. Answer: {66}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the constraints of the problem, arriving at the correct answer through a slightly different, but valid, grouping strategy.

✓ No hallucinations detected

Question #212

Clean

Full Question

Benjamin is raising money for a 3-day science fair. Each day costs ₺250 for hotel, ₺30 for food, and ₺20 for transportation. Benjamin only has ₺165. His friends have chipped in and will cover the cost of all the food for the science fair. Benjamin has also applied for help from the parent association, which has decided to cover a tenth of the remaining cost of the science fair. How much money is Benjamin still missing?

Ground Truth Answer

Total cost of science fair for one day: ₺250 + ₺20 + ₺30 = ₺300. For 3 days, the cost will be 3 * ₺300 = ₺900. Benjamin's friends will cover the cost of food which will be 3 * ₺30 = ₺90. So the remaining cost is 900 - 90 = ₺810. parent association is going to pay 1/10 of the remaining cost which will be 1/10 * ₺810 = ₺81. So he still needs ₺810-₺81 = ₺729. Benjamin also has ₺165 so he needs ₺729 - ₺165 = ₺564. #### 564

Generated Answer

The total cost for the hotel for the 3 days is ₺250/day * 3 days = ₺750. The total cost for food for the 3 days is ₺30/day * 3 days = ₺90. The total cost for transportation for the 3 days is ₺20/day * 3 days = ₺60. The total cost of the science fair is ₺750 + ₺90 + ₺60 = ₺900. Benjamin's friends will cover the entire cost of the food, which is ₺90. So the remaining cost is ₺900 - ₺90 = ₺810. The parent association will cover a tenth of the remaining cost, which is (1/10) * ₺810 = ₺81. So the cost Benjamin needs to cover is ₺810 - ₺81 = ₺729. Benjamin only has ₺165, so he is still missing ₺729 - ₺165 = ₺564. Answer: {564}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints logically. All calculations are correct.

✓ No hallucinations detected

Question #83

Clean

Full Question

Mei is an avid gardener. Two days ago, she received 38 new potted plants from her favorite plant nursery. She already has 9 potted plants on each of the 60 window ledges of her large country home. She also purchased 170 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 6 potted plants from each ledge to friends and family tomorrow. How many potted plants will Mei remain with?

Ground Truth Answer

Two days ago, before receiving the plants, Mei had 60*9 = 540 potted plants After receiving an additional 38 plants, she therefore had a total of 540 + 38 = 578 potted plants. Adding the 170 new plants, it will be 578+170=748. Tomorrow, Mei's plant giveaway will be 60*6 = 360 potted plants. She will therefore remain with 748 - 360 = 388 potted plants. #### 388

Generated Answer

Mei currently has 9 plants/ledge * 60 ledges = 540 plants. Two days ago, she received 38 new plants, so she had 540 + 38 = 578 plants. Yesterday, she purchased 170 new plants, increasing her total to 578 + 170 = 748 plants. Tomorrow, she will give away 6 plants/ledge * 60 ledges = 360 plants. Therefore, Mei will have 748 - 360 = 388 plants remaining. Answer: {388}

Overall Quality: excellent

The reasoning chain correctly follows the sequence of events described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #110

Clean

Full Question

Deshawn went to buy some school supplies. He bought 14 erasers which cost ₺7.5 each, 4 rulers which cost ₺18.5 each, and a ream of bond paper which cost ₺21. He also bought 8 folders which cost ₺10 each. Deshawn can either pay a one-time ₺20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount DeShawn can spend on everything?

Ground Truth Answer

DeShawn spent 14 x ₺7.5 = ₺105 for the erasers. He also spent 4 x ₺18.5 = ₺74 for the rulers. Therefore, DeShawn spent a total of ₺105 + ₺74 + ₺21 = ₺200 for the school supplies. Finally we should include 8 * 10 = 80. The total will be be 280 If DeShawn becomes a member he gets 20% discount, which will be ₺280 * 20% = ₺56 discount. He also has to pay ₺20 so it will be ₺56 - ₺20 = ₺36 cheaper. If DeShawn doesn't become a member, get only gets 5% discount, which will be ₺280 * 5% = ₺14. Since ₺14 is smaller than ₺36, to pay the least, DeShawn has to become member. So overall he pays ₺280 - ₺36 = ₺244 #### 244

Generated Answer

First, calculate the total cost of the items before any discounts. Erasers: 14 erasers * ₺7.5/eraser = ₺105 Rulers: 4 rulers * ₺18.5/ruler = ₺74 Bond paper: ₺21 Folders: 8 folders * ₺10/folder = ₺80 Total cost before discount: ₺105 + ₺74 + ₺21 + ₺80 = ₺280 Now, calculate the cost if Deshawn becomes a member. Membership fee: ₺20 Discount: 20% of ₺280 = 0.20 * ₺280 = ₺56 Cost after discount: ₺280 - ₺56 = ₺224 Total cost with membership: ₺224 + ₺20 = ₺244 Next, calculate the cost if Deshawn does not become a member. Discount: 5% of ₺280 = 0.05 * ₺280 = ₺14 Total cost without membership: ₺280 - ₺14 = ₺266 Finally, compare the two costs to find the least amount Deshawn can spend. Cost with membership: ₺244 Cost without membership: ₺266 The least amount Deshawn can spend is ₺244. Answer: {244}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost, the cost under both membership scenarios (including the membership fee correctly in the member scenario), and correctly determines the minimum cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #157

2 issues

Full Question

An uncle eats 24 hamburgers per day, his spouse eats 24 hamburgers per day, and their grandchild eats one-half of the combined number of hamburgers they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 75% for the first half of the month, and then by an additional 50% for the second half. How many hamburgers does this family eat in two months?

Ground Truth Answer

An uncle and his spouse consumption: 24 + 24 = 48 grandchild consumes 1/2 more than An uncle and his spouse combined: 48 * 1/2 = 24. So grandchild consumes 48 + 24 = 72 hamburgers. During first month they consume 30 * 72 = 2160. The first half of the second month the consume 75% less each day: 25% * 72 = 18 . So in 15 days, they consume 270 hamburgers. During second month, they consume 50% less than the first half each day, so they consume 50% * 18 = 9. So in 15 days, they consume 15 * 9 = 135 hamburgers. In 2 months, they consume 72 + 270 + 135 = 2565 hamburgers together. #### 2565

Generated Answer

Here's how to break down this hamburger-heavy problem: **Month 1:** * Uncle eats 24 burgers/day * 30 days/month = 720 burgers * Spouse eats 24 burgers/day * 30 days/month = 720 burgers * Grandchild eats (720 + 720)/2 = 720 burgers * Total for Month 1: 720 + 720 + 720 = 2160 burgers **Month 2 (First Half):** * Family reduces consumption by 75%, meaning they eat 25% of their usual amount. * Month 1 consumption: 2160 burgers * 25% of 2160: 2160 * 0.25 = 540 burgers (for the first 15 days) **Month 2 (Second Half):** * They reduce their already reduced consumption by another 50%, meaning they eat 50% of what they were eating in the first half of the month. * 50% of 540: 540 * 0.50 = 270 burgers (for the last 15 days) **Total for Two Months:** * Month 1: 2160 burgers * Month 2 (First Half): 540 burgers * Month 2 (Second Half): 270 burgers * Total: 2160 + 540 + 270 = 2970 burgers Answer: {2970}

Overall Quality: poor

The reasoning chain contains significant logical errors in interpreting the grandchild's consumption rate ('half more than') and in applying the percentage reductions sequentially to the total monthly consumption rather than the daily rate.

Detected Issues (2)

logical_error high

Statement

Grandchild eats (720 + 720)/2 = 720 burgers

Explanation

The problem states the grandchild eats 'one-half of the combined number of hamburgers they eat per day' MORE than the combined amount. The AI calculated exactly half of the combined amount. If Uncle/Spouse eat 48 daily, the grandchild should eat 48 + (48 * 0.5) = 72 daily. Over 30 days, the grandchild should eat 2160, not 720.

Answer Span:

Grandchild eats (720 + 720)/2 = 720 burgers

Reference/Question Span:

their grandchild eats one-half of the combined number of hamburgers they eat per day

logical_error high

Statement

25% of 2160: 2160 * 0.25 = 540 burgers (for the first 15 days)

Explanation

The reduction applies to the daily consumption rate, not the total consumption of the previous month. Furthermore, the calculation is based on the flawed Month 1 total (2160). The correct approach is to find the daily rate (Uncle+Spouse+Grandchild = 120/day) and apply the 75% reduction (to 25% of 120 = 30/day) for 15 days.

Answer Span:

25% of 2160: 2160 * 0.25 = 540 burgers (for the first 15 days)

Reference/Question Span:

reducing their food consumption by 75% for the first half of the month

Question #109

Clean

Full Question

Bodhi went to buy some school supplies. He bought 24 folders which cost €2.75 each, 12 pencils which cost €19.25 each, and a ream of bond paper which cost €23. He also bought 5 markers which cost €8 each. Bodhi can either pay a one-time €20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Bodhi can spend on everything?

Ground Truth Answer

Bodhi spent 24 x €2.75 = €66 for the folders. He also spent 12 x €19.25 = €231 for the pencils. Therefore, Bodhi spent a total of €66 + €231 + €23 = €320 for the school supplies. Finally we should include 5 * 8 = 40. The total will be be 360 If Bodhi becomes a member he gets 20% discount, which will be €360 * 20% = €72 discount. He also has to pay €20 so it will be €72 - €20 = €52 cheaper. If Bodhi doesn't become a member, get only gets 5% discount, which will be €360 * 5% = €18. Since €18 is smaller than €52, to pay the least, Bodhi has to become member. So overall he pays €360 - €52 = €308 #### 308

Generated Answer

First, calculate the cost of each item without any discount: Folders: 24 * €2.75 = €66 Pencils: 12 * €19.25= €231 Paper: €23 Markers: 5 * €8 = €40 Total cost without discount: €66 + €231 + €23 + €40 = €360 Scenario 1: Bodhi becomes a member. Membership fee: €20 Discount: 20% of €360 = €72 Cost after discount: €360 - €72 = €288 Total cost with membership: €288 + €20 = €308 Scenario 2: Bodhi doesn't become a member. Discount: 5% of €360 = €18 Cost after discount: €360 - €18 = €342 Comparing the two scenarios, the least amount Bodhi can spend is €308. Answer: {308}

Overall Quality: excellent

The reasoning chain correctly calculates the cost of all items, correctly evaluates both scenarios (membership vs. non-membership), and correctly determines the minimum cost based on the comparison. All arithmetic operations are correct.

✓ No hallucinations detected

Question #161

Clean

Full Question

A father eats 25 hamburgers per day, his wife eats 20 hamburgers per day, and their daughter eats two-thirds of the combined number of hamburgers they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 20% for the first half of the month, and then by an additional 25% for the second half. How many hamburgers does this family eat in two months?

Ground Truth Answer

A father and his wife consumption: 25 + 20 = 45 daughter consumes 2/3 more than A father and his wife combined: 45 * 2/3 = 30. So daughter consumes 45 + 30 = 75 hamburgers. During first month they consume 30 * 75 = 2250. The first half of the second month the consume 20% less each day: 80% * 75 = 60 . So in 15 days, they consume 900 hamburgers. During second month, they consume 25% less than the first half each day, so they consume 75% * 60 = 45. So in 15 days, they consume 15 * 45 = 675 hamburgers. In 2 months, they consume 75 + 900 + 675 = 3825 hamburgers together. #### 3825

Generated Answer

Here's how to break down this hamburger-heavy problem: **Month 1:** * **Daughter's consumption:** The parents eat 25 + 20 = 45 hamburgers/day. The daughter eats (2/3) * 45 = 30 hamburgers/day. * **Total family consumption:** 25 + 20 + 30 = 75 hamburgers/day * **Total hamburgers in Month 1:** 75 hamburgers/day * 30 days/month = 2250 hamburgers **Month 2 (First Half):** * **Reduction:** 20% of 75 hamburgers/day = 15 hamburgers/day * **New consumption:** 75 - 15 = 60 hamburgers/day * **Hamburgers in first half:** 60 hamburgers/day * 15 days = 900 hamburgers **Month 2 (Second Half):** * **Additional reduction:** 25% of 60 hamburgers/day = 15 hamburgers/day * **New consumption:** 60 - 15 = 45 hamburgers/day * **Hamburgers in second half:** 45 hamburgers/day * 15 days = 675 hamburgers **Total Consumption over Two Months:** * **Total:** 2250 (Month 1) + 900 (Month 2, first half) + 675 (Month 2, second half) = 3825 hamburgers Answer: {3825}

Overall Quality: excellent

The reasoning chain correctly interprets the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #152

Clean

Full Question

In Mrs. Garcia's class of 160 students, 50% of the class are swimmers. Out of the remaining class, 35% of the students are debate team members or part of dancers. These 3 groups of students will need to leave early today to travel to an away tournament. Half of the swimmers are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the tournament?

Ground Truth Answer

50% of the 160 student class are swimmers so that's 0.5*160 = 80 students. There are 160 students and 80 are swimmers so that leaves 160-80 = 80 students 35% of the remaining 80 students are part of dancers or debate team members so that's 0.35*80 = 28 students 80 students are swimmers and 28 are part of dancers/debate team members so 80+28 = 108 students will be leaving early. But half of swimmers won't be able to attend so we reduce 80 / 2 = 40. Also 3 * 3 = 9 cheer leaders will join them. So we have 108 - 40 + 9 = 77 #### 77

Generated Answer

First, find the number of swimmers: 50% of 160 students is 160 * 0.50 = 80 students. Since half of the swimmers are absent, only 80 / 2 = 40 swimmers will leave early. Next, find the number of students who are not swimmers: 160 total students - 80 swimmers = 80 students. Now, find the number of students who are debate team members or dancers: 35% of the remaining 80 students is 80 * 0.35 = 28 students. The total number of students in the three groups leaving early is 40 swimmers + 28 debaters/dancers = 68 students. Finally, add the cheerleaders: 3 cheerleaders/group * 3 groups = 9 cheerleaders. Total students leaving early: 68 students + 9 cheerleaders = 77 students. Answer: {77}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #113

Clean

Full Question

Oscar went to buy some school supplies. He bought 24 notebooks which cost ₺3.5 each, 6 rulers which cost ₺13.0 each, and a ream of bond paper which cost ₺15. He also bought 7 pencils which cost ₺9 each. Oscar can either pay a one-time ₺20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Oscar can spend on everything?

Ground Truth Answer

Oscar spent 24 x ₺3.5 = ₺84 for the notebooks. He also spent 6 x ₺13.0 = ₺78 for the rulers. Therefore, Oscar spent a total of ₺84 + ₺78 + ₺15 = ₺177 for the school supplies. Finally we should include 7 * 9 = 63. The total will be be 240 If Oscar becomes a member he gets 20% discount, which will be ₺240 * 20% = ₺48 discount. He also has to pay ₺20 so it will be ₺48 - ₺20 = ₺28 cheaper. If Oscar doesn't become a member, get only gets 5% discount, which will be ₺240 * 5% = ₺12. Since ₺12 is smaller than ₺28, to pay the least, Oscar has to become member. So overall he pays ₺240 - ₺28 = ₺212 #### 212

Generated Answer

First, calculate the total cost of the items without any discount: Notebooks: 24 notebooks * ₺3.5/notebook = ₺84 Rulers: 6 rulers * ₺13.0/ruler = ₺78 Bond paper: ₺15 Pencils: 7 pencils * ₺9/pencil = ₺63 Total cost: ₺84 + ₺78 + ₺15 + ₺63 = ₺240 Now, calculate the cost with the membership and 20% discount: Discount amount: ₺240 * 0.20 = ₺48 Cost after discount: ₺240 - ₺48 = ₺192 Final cost with membership: ₺192 + ₺20 (membership fee) = ₺212 Next, calculate the cost without membership and with the 5% discount: Discount amount: ₺240 * 0.05 = ₺12 Final cost without membership: ₺240 - ₺12 = ₺228 Since ₺212 is less than ₺228, the least amount Oscar can spend is ₺212. Answer: {212}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost, the cost under both membership scenarios (including the fee for membership), and correctly determines the minimum cost.

✓ No hallucinations detected

Question #108

Clean

Full Question

Leon went to buy some school supplies. He bought 8 crayons which cost ¥7.0 each, 8 notebooks which cost ¥13.75 each, and a ream of bond paper which cost ¥10. He also bought 4 folders which cost ¥11 each. Leon can either pay a one-time ¥20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Leon can spend on everything?

Ground Truth Answer

Leon spent 8 x ¥7.0 = ¥56 for the crayons. He also spent 8 x ¥13.75 = ¥110 for the notebooks. Therefore, Leon spent a total of ¥56 + ¥110 + ¥10 = ¥176 for the school supplies. Finally we should include 4 * 11 = 44. The total will be be 220 If Leon becomes a member he gets 20% discount, which will be ¥220 * 20% = ¥44 discount. He also has to pay ¥20 so it will be ¥44 - ¥20 = ¥24 cheaper. If Leon doesn't become a member, get only gets 5% discount, which will be ¥220 * 5% = ¥11. Since ¥11 is smaller than ¥24, to pay the least, Leon has to become member. So overall he pays ¥220 - ¥24 = ¥196 #### 196

Generated Answer

First, calculate the total cost of the items before any discounts: * **Crayons:** 8 crayons * ¥7.0/crayon = ¥56 * **Notebooks:** 8 notebooks * ¥13.75/notebook = ¥110 * **Bond paper:** ¥10 * **Folders:** 4 folders * ¥11/folder = ¥44 **Total cost before discount:** ¥56 + ¥110 + ¥10 + ¥44 = ¥220 Now, let's calculate the cost with the membership and 20% discount: * **Membership fee:** ¥20 * **Discounted price:** ¥220 * 0.80 = ¥176 * **Total cost with membership:** ¥20 + ¥176 = ¥196 Next, let's calculate the cost without the membership and with the 5% discount: * **Discounted price:** ¥220 * 0.95 = ¥209 Comparing the two options, the least amount Leon can spend is ¥196 with the membership. Answer: {196}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost and then accurately evaluates both scenarios (with membership and without membership) to determine the minimum cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #111

Clean

Full Question

Andre went to buy some school supplies. He bought 20 markers which cost ₣8.0 each, 10 pencils which cost ₣18.0 each, and a ream of bond paper which cost ₣15. He also bought 5 rulers which cost ₣9 each. Andre can either pay a one-time ₣20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Andre can spend on everything?

Ground Truth Answer

Andre spent 20 x ₣8.0 = ₣160 for the markers. He also spent 10 x ₣18.0 = ₣180 for the pencils. Therefore, Andre spent a total of ₣160 + ₣180 + ₣15 = ₣355 for the school supplies. Finally we should include 5 * 9 = 45. The total will be be 400 If Andre becomes a member he gets 20% discount, which will be ₣400 * 20% = ₣80 discount. He also has to pay ₣20 so it will be ₣80 - ₣20 = ₣60 cheaper. If Andre doesn't become a member, get only gets 5% discount, which will be ₣400 * 5% = ₣20. Since ₣20 is smaller than ₣60, to pay the least, Andre has to become member. So overall he pays ₣400 - ₣60 = ₣340 #### 340

Generated Answer

First calculate the cost of the supplies before any discounts. Markers: 20 markers * ₣8.0/marker = ₣160 Pencils: 10 pencils * ₣18.0/pencil = ₣180 Paper: ₣15 Rulers: 5 rulers * ₣9/ruler = ₣45 Total cost before discount: 160 + 180 + 15 + 45 = ₣400 Scenario 1: Andre becomes a member. Membership fee: ₣20 Discount: 20% of ₣400 = 0.20 * 400 = ₣80 Cost after discount: 400 - 80 = ₣320 Total cost with membership: 320 + 20 = ₣340 Scenario 2: Andre doesn't become a member. Discount: 5% of ₣400 = 0.05 * 400 = ₣20 Total cost: 400 - 20 = ₣380 Since ₣340 is less than ₣380, the least amount Andre can spend is ₣340. Answer: {340}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost before discounts and accurately evaluates both scenarios (membership vs. non-membership), leading to the correct minimum cost.

✓ No hallucinations detected

Question #245

Clean

Full Question

Valeria went to the coast for vacation. Her parents gave her €1300 to buy whatever she wanted. At the seaside store, cotton candy was on sale for "Buy 15 pounds at €21 per pound, get 5 pounds 1/3 off." She scooped up 23 pounds. She also bought a mixed bag of coral pieces for €11.0 and 11 pins that were €21.0 each. Valeria then donated €5 at a charity stand along the way. How much money does Valeria have left?

Ground Truth Answer

cotton candy is buying 15 pound for € 21 and gets 5 pound 1/3 off. So 1/3 off of 5 pound is €5/3*21 = €35. The rest of 3 pound does not have discount and come at 63 so total is 15*21 + 5*2/3*21 + 3*21 = 448 11 pins at €21.0 each is 11*21.0=€231.0 When you add all her purchases, €448+€11.0+€231.0 = €690) She had €1300 and spent €690 so she had €1300-€690 = €610 left over. We should also deduce €5 so we have 605. #### 605

Generated Answer

Here's how to break down Valeria's spending and calculate her remaining money: 1. **Cotton Candy Cost:** * She bought 23 pounds of cotton candy. * The deal is for 15 pounds at €21 per pound, which costs 15 * €21 = €315. * She gets 5 pounds at 1/3 off, so each of those pounds costs €21 * (2/3) = €14. This costs 5 * €14 = €70. * The remaining 3 pounds (23 total - 15 deal - 5 deal) are at the regular price of €21 each, costing 3 * €21 = €63. * The total cost of cotton candy is €315 + €70 + €63 = €448. 2. **Coral and Pins Cost:** * The coral cost €11. * The pins cost €21 * 11 = €231. * The total cost of coral and pins is €11 + €231 = €242. 3. **Total Spending:** * Valeria's total spending is €448 (cotton candy) + €242 (coral and pins) + €5 (donation) = €705. 4. **Remaining Money:** * Valeria started with €1300 and spent €695, so she has €1300 - €695 = €595 left. Answer: {595}

Overall Quality: poor

The initial calculation for cotton candy cost (€448) is correct. However, the model makes two subsequent calculation errors in summing the total spending (calculating 695+5 as 705 instead of 695) and then makes a final subtraction error (calculating 1300 - 695 as 595 instead of 605). The error in step 3 (calculating 448+242+5=705) is mathematically wrong, as the correct sum is 695. The error in step 4 (calculating 1300-695=595) is also mathematically wrong, as the correct difference is 605.

✓ No hallucinations detected

Question #70

Clean

Full Question

Alejandro wants to make different sized ice cubes with 309 ounces of water. He can make giant cubes that use 14 ounces per cube, medium cubes that use 6 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 50 total ice cubes, including 9 giant cubes, 14 small cubes, 15 medium cubes, and some tiny cubes. How many ounces of water does Alejandro have left?

Ground Truth Answer

The giant cubes used up 9 ounces of water because 9 times 14 equals 126. The medium cubes used up 90 ounces of water because 15 times 6 equals 90. The small cubes used up 7 ounces of water because 14 times 1/2 equals 7. The tiny cubes are 12 * 0.5 * 1/2 = 2. This means that Alejandro has used up 223 ounces of water because 126 plus 90 plus 7 plus 2 equals 225. Alejandro has 83 ounces of water left because 309 minus 225 equals 83. #### 83

Generated Answer

First, calculate the water used for giant cubes: 9 giant cubes * 14 ounces/cube = 126 ounces. Next, calculate the water used for small cubes: 14 small cubes * 0.5 ounces/cube = 7 ounces. Then, calculate the water used for medium cubes: 15 medium cubes * 6 ounces/cube = 90 ounces. Now, figure out how many tiny cubes he made: 50 total cubes - 9 giant - 14 small - 15 medium = 12 tiny cubes. Tiny cubes are half the size of small cubes, so they use 0.5 ounces / 2 = 0.25 ounces/cube. Calculate the water used for tiny cubes: 12 tiny cubes * 0.25 ounces/cube = 3 ounces. Add up the total water used: 126 + 7 + 90 + 3 = 226 ounces. Finally, subtract the water used from the total amount of water: 309 ounces - 226 ounces = 83 ounces. Answer: {83}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are accurate, and the logic for determining cube counts and water usage is sound.

✓ No hallucinations detected

Question #194

Clean

Full Question

Ms. Johnson is looking for a new apartment that will not go beyond her $430000 budget. She saw a property that has a selling price of $400000. On top of that, the buyer has to pay a brokerage fee which is 7% of the selling price, and also the transfer fee that is 14% of the selling price. If Ms. Johnson can get 5% discount on the selling price, how much more will be the total cost than Ms. Johnson's budget?

Ground Truth Answer

Because of discount, the $400000 will be 400000 * 95% = 380000. The brokerage fee is $380000 x 7/100 = $26600. The transfer fee is $380000 x 14/100 = $53200. The total price of the apartment is $380000 + $26600 + $53200 = $459800. So, it is $459800 - $430000 = $29800 more than Ms. Johnson's budget. #### 29800

Generated Answer

Here's how to break down the cost calculation: 1. **Discount:** Ms. Johnson gets a 5% discount on the $400,000 selling price: $400,000 * 0.05 = $20,000. This means the discounted price is $400,000 - $20,000 = $380,000. 2. **Brokerage Fee:** The brokerage fee is 7% of the discounted selling price: $380,000 * 0.07 = $26,600. 3. **Transfer Fee:** The transfer fee is 14% of the discounted selling price: $380,000 * 0.14 = $53,200. 4. **Total Cost:** The total cost of the apartment is the discounted price plus the brokerage fee and the transfer fee: $380,000 + $26,600 + $53,200 = $459,800. 5. **Over Budget:** Ms. Johnson's budget is $430,000. The apartment costs $459,800. Therefore, she is over budget by $459,800 - $430,000 = $29,800. Answer: {29800}

Overall Quality: excellent

The reasoning chain correctly calculates the discounted price, brokerage fee, transfer fee, total cost, and the amount over budget. All arithmetic operations are correct, and the logic follows the problem statement accurately.

✓ No hallucinations detected

Question #101

Clean

Full Question

Thiago is selling cookies and apricot pies for a fundraiser. On Tuesday, he sold 26 boxes of cookie and 19 fewer boxes of apricot pie, than on Wednesday. On Wednesday, he sold 14 more boxes of cookies than on Tuesday and 24 boxes of apricot pie. On Thursday, he sold as much as he did in the past two days combined. If the cookie cost ₣11 and the apricot pie cost ₣24, what was Thiago's average daily earning?

Ground Truth Answer

He sold 26 + 14 = 40 boxes of cookie on Wednesday. The total number of boxes of cookies that Thiago sold is 26 + 40 = 66. Thiago earned 66 x ₣11 = ₣726 for selling cookies. He sold 24 - 19 = 5 boxes of apricot pie on Tuesday. The total number of boxes of apricot pie that Thiago sold is 24 + 5 = 29. He earned 29 x ₣24 = ₣696 for selling apricot pie. So, Thiago earned ₣726 + ₣696 = ₣1422 for two days. Finally, on Thursday, he sold as much as he did in the past two days so 2 * 1422 = 2844. Finally, we should divide the total by 3 to get the average daily: 2844 / 3 = 948 #### 948

Generated Answer

Here's how to solve the problem: 1. **Apricot pies sold on Tuesday:** Thiago sold 19 fewer boxes of apricot pie on Tuesday than on Wednesday, and he sold 24 boxes on Wednesday. Therefore, he sold 24 - 19 = 5 boxes of apricot pie on Tuesday. 2. **Cookies sold on Wednesday:** Thiago sold 14 more boxes of cookies on Wednesday than on Tuesday, and he sold 26 boxes on Tuesday. Therefore, he sold 26 + 14 = 40 boxes of cookies on Wednesday. 3. **Total sales on Tuesday:** Thiago sold 26 cookies * ₣11/cookie + 5 apricot pies * ₣24/pie = ₣286 + ₣120 = ₣406 on Tuesday. 4. **Total sales on Wednesday:** Thiago sold 40 cookies * ₣11/cookie + 24 apricot pies * ₣24/pie = ₣440 + ₣576 = ₣1016 on Wednesday. 5. **Total sales on Thursday:** Thiago sold the same amount on Thursday as he did on Tuesday and Wednesday combined. So, he earned ₣406 + ₣1016 = ₣1422 on Thursday. 6. **Total earnings over three days:** Thiago's total earnings were ₣406 + ₣1016 + ₣1422 = ₣2844. 7. **Average daily earning:** Thiago's average daily earning was ₣2844 / 3 days = ₣948/day. Answer: {948}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically consistent, leading to the correct final answer. All arithmetic operations are verified as correct.

✓ No hallucinations detected

Question #211

Clean

Full Question

Ali is raising money for a 3-day sports tournament. Each day costs ₣200 for hotel, ₣20 for food, and ₣10 for transportation. Ali only has ₣40. His friends have chipped in and will cover the cost of all the food for the sports tournament. Ali has also applied for help from the local charity, which has decided to cover 1/5 of the remaining cost of the sports tournament. How much money is Ali still missing?

Ground Truth Answer

Total cost of sports tournament for one day: ₣200 + ₣10 + ₣20 = ₣230. For 3 days, the cost will be 3 * ₣230 = ₣690. Ali's friends will cover the cost of food which will be 3 * ₣20 = ₣60. So the remaining cost is 690 - 60 = ₣630. local charity is going to pay 1/5 of the remaining cost which will be 1/5 * ₣630 = ₣126. So he still needs ₣630-₣126 = ₣504. Ali also has ₣40 so he needs ₣504 - ₣40 = ₣464. #### 464

Generated Answer

The total cost per day is ₣200 (hotel) + ₣20 (food) + ₣10 (transportation) = ₣230. The 3-day tournament total cost is ₣230/day * 3 days = ₣690. Ali's friends are covering the food cost, which is ₣20/day * 3 days = ₣60. So the remaining cost after friends' contribution is ₣690 - ₣60 = ₣630. The local charity is covering 1/5 of the remaining cost, which is (1/5) * ₣630 = ₣126. So the remaining cost after the charity's contribution is ₣630 - ₣126 = ₣504. Ali has ₣40, so he is still missing ₣504 - ₣40 = ₣464. Answer: {464}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem logic correctly step-by-step. All calculations match the ground truth.

✓ No hallucinations detected

Question #214

Clean

Full Question

Yuki is raising money for a 2-day music festival. Each day costs ₺100 for hotel, ₺40 for food, and ₺30 for transportation. Yuki only has ₺10. His friends have chipped in and will cover the cost of all the food for the music festival. Yuki has also applied for help from the parent association, which has decided to cover 1/2 of the remaining cost of the music festival. How much money is Yuki still missing?

Ground Truth Answer

Total cost of music festival for one day: ₺100 + ₺30 + ₺40 = ₺170. For 2 days, the cost will be 2 * ₺170 = ₺340. Yuki's friends will cover the cost of food which will be 2 * ₺40 = ₺80. So the remaining cost is 340 - 80 = ₺260. parent association is going to pay 1/2 of the remaining cost which will be 1/2 * ₺260 = ₺130. So he still needs ₺260-₺130 = ₺130. Yuki also has ₺10 so he needs ₺130 - ₺10 = ₺120. #### 120

Generated Answer

The total cost of the hotel for the 2-day festival is ₺100/day * 2 days = ₺200. The total cost of the food for the 2-day festival is ₺40/day * 2 days = ₺80. The total cost of transportation for the 2-day festival is ₺30/day * 2 days = ₺60. The total cost of the festival is ₺200 + ₺80 + ₺60 = ₺340. Yuki's friends are covering the food cost, so that's ₺80 less. The remaining cost is ₺340 - ₺80 = ₺260. The parent association is covering half of the remaining cost, which is ₺260 / 2 = ₺130. So Yuki needs to cover ₺260 - ₺130 = ₺130. Yuki currently has ₺10. Therefore, Yuki is still missing ₺130 - ₺10 = ₺120. Answer: {120}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem description. The final answer matches the ground truth.

✓ No hallucinations detected

Question #67

Clean

Full Question

Deshawn wants to make different sized ice cubes with 312 ounces of water. He can make giant cubes that use 15 ounces per cube, medium cubes that use 5 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 46 total ice cubes, including 8 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does DeShawn have left?

Ground Truth Answer

The giant cubes used up 8 ounces of water because 8 times 15 equals 120. The medium cubes used up 60 ounces of water because 12 times 5 equals 60. The small cubes used up 7 ounces of water because 14 times 1/2 equals 7. The tiny cubes are 12 * 0.5 * 1/2 = 2. This means that DeShawn has used up 187 ounces of water because 120 plus 60 plus 7 plus 2 equals 189. DeShawn has 122 ounces of water left because 312 minus 189 equals 122. #### 122

Generated Answer

First, calculate the water used for giant cubes: 8 giant cubes * 15 ounces/cube = 120 ounces. Next, calculate the water used for small cubes: 14 small cubes * 0.5 ounces/cube = 7 ounces. Then, calculate the water used for medium cubes: 12 medium cubes * 5 ounces/cube = 60 ounces. Now, find the total water used so far: 120 ounces + 7 ounces + 60 ounces = 187 ounces. He made 46 total ice cubes, so the number of tiny cubes is 46 total cubes - 8 giant cubes - 14 small cubes - 12 medium cubes = 12 tiny cubes. Tiny cubes are half the size of small cubes, so they use 0.5 ounces / 2 = 0.25 ounces per cube. Calculate the water used for tiny cubes: 12 tiny cubes * 0.25 ounces/cube = 3 ounces. Find the total water used: 187 ounces + 3 ounces = 190 ounces. Finally, subtract the total water used from the starting amount: 312 ounces - 190 ounces = 122 ounces left. Answer: {122}

Overall Quality: excellent

The reasoning chain correctly calculates the water usage for each cube size, determines the number of tiny cubes based on the total cube count, calculates the water used by tiny cubes correctly, sums the total water used, and finds the remaining water. All arithmetic and logical steps align with the problem statement and ground truth.

✓ No hallucinations detected

Question #99

Clean

Full Question

Tariq is selling brownies and apricot pies for a fundraiser. On Thursday, he sold 25 boxes of brownie and 12 fewer boxes of apricot pie, than on Friday. On Friday, he sold 14 more boxes of brownies than on Thursday and 24 boxes of apricot pie. On Saturday, he sold as much as he did in the past two days combined. If the brownie cost ₣9 and the apricot pie cost ₣20, what was Tariq's average daily earning?

Ground Truth Answer

He sold 25 + 14 = 39 boxes of brownie on Friday. The total number of boxes of brownies that Tariq sold is 25 + 39 = 64. Tariq earned 64 x ₣9 = ₣576 for selling brownies. He sold 24 - 12 = 12 boxes of apricot pie on Thursday. The total number of boxes of apricot pie that Tariq sold is 24 + 12 = 36. He earned 36 x ₣20 = ₣720 for selling apricot pie. So, Tariq earned ₣576 + ₣720 = ₣1296 for two days. Finally, on Saturday, he sold as much as he did in the past two days so 2 * 1296 = 2592. Finally, we should divide the total by 3 to get the average daily: 2592 / 3 = 864 #### 864

Generated Answer

Here's how to break down Tariq's sales and earnings: **Thursday:** * **Brownies:** 25 boxes * **Apricot Pies:** 24 (Friday's sales) - 12 = 12 boxes * **Brownie Earnings:** 25 boxes * ₣9/box = ₣225 * **Apricot Pie Earnings:** 12 boxes * ₣20/box = ₣240 * **Total Thursday Earnings:** ₣225 + ₣240 = ₣465 **Friday:** * **Brownies:** 25 (Thursday's sales) + 14 = 39 boxes * **Apricot Pies:** 24 boxes * **Brownie Earnings:** 39 boxes * ₣9/box = ₣351 * **Apricot Pie Earnings:** 24 boxes * ₣20/box = ₣480 * **Total Friday Earnings:** ₣351 + ₣480 = ₣831 **Saturday:** * **Brownies:** 25 + 39 = 64 boxes * **Apricot Pies:** 12 + 24 = 36 boxes * **Brownie Earnings:** 64 boxes * ₣9/box = ₣576 * **Apricot Pie Earnings:** 36 boxes * ₣20/box = ₣720 * **Total Saturday Earnings:** ₣576 + ₣720 = ₣1296 **Total Earnings (Thursday - Saturday):** ₣465 + ₣831 + ₣1296 = ₣2592 **Average Daily Earnings:** ₣2592 / 3 days = ₣864 Answer: {864}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows a consistent (though potentially ambiguous interpretation of the Saturday sales instruction) path that leads to the correct final answer. All arithmetic operations are verified as correct.

✓ No hallucinations detected

Question #69

Clean

Full Question

Viktor wants to make different sized ice cubes with 313 ounces of water. He can make giant cubes that use 12 ounces per cube, medium cubes that use 4 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 50 total ice cubes, including 12 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does Viktor have left?

Ground Truth Answer

The giant cubes used up 12 ounces of water because 12 times 12 equals 144. The medium cubes used up 48 ounces of water because 12 times 4 equals 48. The small cubes used up 7 ounces of water because 14 times 1/2 equals 7. The tiny cubes are 12 * 0.5 * 1/2 = 2. This means that Viktor has used up 199 ounces of water because 144 plus 48 plus 7 plus 2 equals 201. Viktor has 111 ounces of water left because 313 minus 201 equals 111. #### 111

Generated Answer

Viktor uses 12 ounces/giant cube * 12 giant cubes = 144 ounces of water for the giant cubes. He uses 4 ounces/medium cube * 12 medium cubes = 48 ounces of water for the medium cubes. He uses 1/2 ounce/small cube * 14 small cubes = 7 ounces of water for the small cubes. He made 50 total ice cubes. So far, he's made 12 + 12 + 14 = 38 ice cubes. This means he made 50 - 38 = 12 tiny cubes. Tiny cubes are half the size of small cubes, so they use (1/2)/2 = 1/4 ounce of water. He uses 1/4 ounce/tiny cube * 12 tiny cubes = 3 ounces of water for the tiny cubes. In total, Viktor uses 144 + 48 + 7 + 3 = 202 ounces of water. He started with 313 ounces, so he has 313 - 202 = 111 ounces left. Answer: {111}

Overall Quality: excellent

The reasoning chain correctly calculates the water usage for each cube type, correctly determines the number of tiny cubes, and accurately calculates the total water used and the remaining water. The final answer matches the ground truth.

✓ No hallucinations detected

Question #71

Clean

Full Question

Oliver wants to make different sized ice cubes with 326 ounces of water. He can make giant cubes that use 14 ounces per cube, medium cubes that use 4 ounces, small cubes that use 2/4 of a ounce, and tiny cubes that are half the size of small cubes. He makes 48 total ice cubes, including 10 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does Oliver have left?

Ground Truth Answer

The giant cubes used up 10 ounces of water because 10 times 14 equals 140. The medium cubes used up 48 ounces of water because 12 times 4 equals 48. The small cubes used up 7 ounces of water because 14 times 1/2 equals 7. The tiny cubes are 12 * 0.5 * 1/2 = 2. This means that Oliver has used up 195 ounces of water because 140 plus 48 plus 7 plus 2 equals 197. Oliver has 128 ounces of water left because 326 minus 197 equals 128. #### 128

Generated Answer

First, calculate the water used for giant cubes: 10 giant cubes * 14 ounces/cube = 140 ounces. Next, calculate the water used for small cubes: 14 small cubes * (2/4) ounces/cube = 7 ounces. Then, calculate the water used for medium cubes: 12 medium cubes * 4 ounces/cube = 48 ounces. Now, find the number of tiny cubes: 48 total cubes - 10 giant cubes - 14 small cubes - 12 medium cubes = 12 tiny cubes. Calculate the water used for tiny cubes: 12 tiny cubes * (1/2 * 2/4) ounces/cube = 3 ounces. Find the total water used: 140 ounces + 7 ounces + 48 ounces + 3 ounces = 198 ounces. Finally, subtract the total water used from the initial amount of water: 326 ounces - 198 ounces = 128 ounces. Answer: {128}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All arithmetic calculations are correct, and the logic for determining the number of tiny cubes and calculating the final remaining water is sound.

✓ No hallucinations detected

Question #158

Clean

Full Question

A father eats 5 burritos per day, his wife eats 25 burritos per day, and their daughter eats one-third of the combined number of burritos they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 60% for the first half of the month, and then by an additional 50% for the second half. How many burritos does this family eat in two months?

Ground Truth Answer

A father and his wife consumption: 5 + 25 = 30 daughter consumes 1/3 more than A father and his wife combined: 30 * 1/3 = 10. So daughter consumes 30 + 10 = 40 burritos. During first month they consume 30 * 40 = 1200. The first half of the second month the consume 60% less each day: 40% * 40 = 16 . So in 15 days, they consume 240 burritos. During second month, they consume 50% less than the first half each day, so they consume 50% * 16 = 8. So in 15 days, they consume 15 * 8 = 120 burritos. In 2 months, they consume 40 + 240 + 120 = 1560 burritos together. #### 1560

Generated Answer

Here's how to solve this problem: 1. **Calculate the daughter's daily burrito consumption:** The parents eat a combined 5 + 25 = 30 burritos per day. The daughter eats one-third of this, so she eats 30 / 3 = 10 burritos per day. 2. **Calculate the family's total daily burrito consumption:** The family eats a total of 5 + 25 + 10 = 40 burritos per day. 3. **Calculate the family's first month's burrito consumption:** Assuming a 30-day month, they eat 40 burritos/day * 30 days = 1200 burritos in the first month. 4. **Calculate the consumption for the first half of the second month:** They reduce their consumption by 60%, so they eat 40% of their usual amount. That's 40 burritos/day * 0.40 = 16 burritos/day. For 15 days, this totals 16 burritos/day * 15 days = 240 burritos. 5. **Calculate the consumption for the second half of the second month:** They further reduce their consumption by 50% from the first half of the month. That means they eat 50% of 16 burritos/day, which is 8 burritos/day. For 15 days, they eat 8 burritos/day * 15 days = 120 burritos. 6. **Calculate the family's total burrito consumption over two months:** In total, they eat 1200 (month 1) + 240 (second month, first half) + 120 (second month, second half) = 1560 burritos. Answer: {1560}

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps, performs all arithmetic calculations accurately, and arrives at the correct final answer.

✓ No hallucinations detected

Question #192

Clean

Full Question

Mrs. Smith is looking for a new house that will not go beyond her $410000 budget. She saw a property that has a selling price of $500000. On top of that, the buyer has to pay a brokerage fee which is 7% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Smith can get 20% discount on the selling price, how much more will be the total cost than Mrs. Smith's budget?

Ground Truth Answer

Because of discount, the $500000 will be 500000 * 80% = 400000. The brokerage fee is $400000 x 7/100 = $28000. The transfer fee is $400000 x 12/100 = $48000. The total price of the house is $400000 + $28000 + $48000 = $476000. So, it is $476000 - $410000 = $66000 more than Mrs. Smith's budget. #### 66000

Generated Answer

Here's how to break down the problem: 1. **Calculate the discount:** 20% of $500,000 is (20/100) * $500,000 = $100,000 2. **Calculate the discounted price:** $500,000 - $100,000 = $400,000 3. **Calculate the brokerage fee:** 7% of $400,000 is (7/100) * $400,000 = $28,000 4. **Calculate the transfer fee:** 12% of $400,000 is (12/100) * $400,000 = $48,000 5. **Calculate the total cost:** $400,000 + $28,000 + $48,000 = $476,000 6. **Calculate the difference from Mrs. Smith's budget:** $476,000 - $410,000 = $66,000 Answer: {66000}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the correct logical steps to solve the problem. All calculations are verified as correct.

✓ No hallucinations detected

Question #197

Clean

Full Question

Mrs. Smith is looking for a new house that will not go beyond her $310000 budget. She saw a property that has a selling price of $400000. On top of that, the buyer has to pay a brokerage fee which is 5% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Smith can get 10% discount on the selling price, how much more will be the total cost than Mrs. Smith's budget?

Ground Truth Answer

Because of discount, the $400000 will be 400000 * 90% = 360000. The brokerage fee is $360000 x 5/100 = $18000. The transfer fee is $360000 x 12/100 = $43200. The total price of the house is $360000 + $18000 + $43200 = $421200. So, it is $421200 - $310000 = $111200 more than Mrs. Smith's budget. #### 111200

Generated Answer

Here's how to break down the problem: 1. **Calculate the discount:** 10% of $400,000 is (10/100) * $400,000 = $40,000 2. **Calculate the discounted price:** $400,000 - $40,000 = $360,000 3. **Calculate the brokerage fee:** 5% of $360,000 is (5/100) * $360,000 = $18,000 4. **Calculate the transfer fee:** 12% of $360,000 is (12/100) * $360,000 = $43,200 5. **Calculate the total cost:** $360,000 + $18,000 + $43,200 = $421,200 6. **Calculate the difference from the budget:** $421,200 - $310,000 = $111,200 Answer: {111200}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are mathematically accurate, and the logic applied (calculating discount first, then fees based on the discounted price, and finally finding the difference) is sound.

✓ No hallucinations detected

Question #195

Clean

Full Question

Mrs. Smith is looking for a new house that will not go beyond her $410000 budget. She saw a property that has a selling price of $480000. On top of that, the buyer has to pay a brokerage fee which is 3% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Smith can get 5% discount on the selling price, how much more will be the total cost than Mrs. Smith's budget?

Ground Truth Answer

Because of discount, the $480000 will be 480000 * 95% = 456000. The brokerage fee is $456000 x 3/100 = $13680. The transfer fee is $456000 x 12/100 = $54720. The total price of the house is $456000 + $13680 + $54720 = $524400. So, it is $524400 - $410000 = $114400 more than Mrs. Smith's budget. #### 114400

Generated Answer

Here's how to break down the problem: 1. **Calculate the discount:** 5% of $480,000 is (5/100) * $480,000 = $24,000 2. **Calculate the discounted price:** $480,000 - $24,000 = $456,000 3. **Calculate the brokerage fee:** 3% of $456,000 is (3/100) * $456,000 = $13,680 4. **Calculate the transfer fee:** 12% of $456,000 is (12/100) * $456,000 = $54,720 5. **Calculate the total cost:** $456,000 + $13,680 + $54,720 = $524,400 6. **Calculate the difference from the budget:** $524,400 - $410,000 = $114,400 Answer: {114400}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the required steps correctly to arrive at the correct final answer.

✓ No hallucinations detected

Question #196

Clean

Full Question

Mrs. Lee is looking for a new townhouse that will not go beyond her $330000 budget. She saw a property that has a selling price of $440000. On top of that, the buyer has to pay a brokerage fee which is 5% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Lee can get 25% discount on the selling price, how much more will be the total cost than Mrs. Lee's budget?

Ground Truth Answer

Because of discount, the $440000 will be 440000 * 75% = 330000. The brokerage fee is $330000 x 5/100 = $16500. The transfer fee is $330000 x 12/100 = $39600. The total price of the townhouse is $330000 + $16500 + $39600 = $386100. So, it is $386100 - $330000 = $56100 more than Mrs. Lee's budget. #### 56100

Generated Answer

Here's how to break down the problem: 1. **Calculate the discount:** 25% of $440,000 is (25/100) * $440,000 = $110,000. 2. **Discounted price:** Subtract the discount from the original selling price: $440,000 - $110,000 = $330,000. 3. **Calculate the brokerage fee:** 5% of $330,000 is (5/100) * $330,000 = $16,500. 4. **Calculate the transfer fee:** 12% of $330,000 is (12/100) * $330,000 = $39,600. 5. **Calculate the total cost:** Add the discounted price, brokerage fee, and transfer fee: $330,000 + $16,500 + $39,600 = $386,100. 6. **Calculate the difference from Mrs. Lee's budget:** Subtract her budget from the total cost: $386,100 - $330,000 = $56,100. Answer: {56100}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are mathematically accurate, and the logic applied (calculating discount, applying fees to the discounted price, and finding the final difference) is sound.

✓ No hallucinations detected

Question #98

Clean

Full Question

Umar is selling muffins and apricot pies for a fundraiser. On Thursday, he sold 28 boxes of muffin and 13 fewer boxes of apricot pie, than on Friday. On Friday, he sold 13 more boxes of muffins than on Thursday and 21 boxes of apricot pie. On Saturday, he sold as much as he did in the past two days combined. If the muffin cost $11 and the apricot pie cost $30, what was Umar's average daily earning?

Ground Truth Answer

He sold 28 + 13 = 41 boxes of muffin on Friday. The total number of boxes of muffins that Umar sold is 28 + 41 = 69. Umar earned 69 x $11 = $759 for selling muffins. He sold 21 - 13 = 8 boxes of apricot pie on Thursday. The total number of boxes of apricot pie that Umar sold is 21 + 8 = 29. He earned 29 x $30 = $870 for selling apricot pie. So, Umar earned $759 + $870 = $1629 for two days. Finally, on Saturday, he sold as much as he did in the past two days so 2 * 1629 = 3258. Finally, we should divide the total by 3 to get the average daily: 3258 / 3 = 1086 #### 1086

Generated Answer

Here's how to break down this problem: 1. **Friday's Sales:** * Muffins: 28 (Thursday) + 13 = 41 boxes * Apricot Pies: 21 boxes 2. **Thursday's Sales:** * Muffins: 28 boxes * Apricot Pies: 21 - 13 = 8 boxes 3. **Saturday's Sales:** * Muffins: 41 + 28 = 69 boxes * Apricot Pies: 21 + 8 = 29 boxes 4. **Earnings:** * Thursday: (28 muffins * $11) + (8 pies * $30) = $308 + $240 = $548 * Friday: (41 muffins * $11) + (21 pies * $30) = $451 + $630 = $1081 * Saturday: (69 muffins * $11) + (29 pies * $30) = $759 + $870 = $1629 5. **Total Earnings:** $548 + $1081 + $1629 = $3258 6. **Average Daily Earnings:** $3258 / 3 days = $1086 Answer: {1086}

Overall Quality: excellent

The reasoning chain is mathematically sound and correctly interprets the constraints necessary to arrive at the final answer.

✓ No hallucinations detected

Question #156

Clean

Full Question

An uncle eats 16 pizzas per day, his spouse eats 16 pizzas per day, and their grandchild eats one-half of the combined number of pizzas they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 25% for the first half of the month, and then by an additional 50% for the second half. How many pizzas does this family eat in two months?

Ground Truth Answer

An uncle and his spouse consumption: 16 + 16 = 32 grandchild consumes 1/2 more than An uncle and his spouse combined: 32 * 1/2 = 16. So grandchild consumes 32 + 16 = 48 pizzas. During first month they consume 30 * 48 = 1440. The first half of the second month the consume 25% less each day: 75% * 48 = 36 . So in 15 days, they consume 540 pizzas. During second month, they consume 50% less than the first half each day, so they consume 50% * 36 = 18. So in 15 days, they consume 15 * 18 = 270 pizzas. In 2 months, they consume 48 + 540 + 270 = 2250 pizzas together. #### 2250

Generated Answer

Here's how to break down this pizza-loving family's consumption: **Month 1:** * Uncle: 16 pizzas/day * 30 days/month = 480 pizzas * Spouse: 16 pizzas/day * 30 days/month = 480 pizzas * Grandchild: (16 + 16)/2 pizzas/day * 30 days/month = 480 pizzas * Total Month 1: 480 + 480 + 480 = 1440 pizzas **Month 2 (First Half):** * Original total daily consumption: 16 + 16 + 16 = 48 pizzas * Reduction: 48 pizzas * 0.25 = 12 pizzas * New daily consumption: 48 - 12 = 36 pizzas * Total for first half of month: 36 pizzas/day * 15 days = 540 pizzas **Month 2 (Second Half):** * Further reduction: 36 pizzas * 0.50 = 18 pizzas * New daily consumption: 36 - 18 = 18 pizzas * Total for second half of month: 18 pizzas/day * 15 days = 270 pizzas **Total for Two Months:** * Total: 1440 + 540 + 270 = 2250 pizzas Answer: {2250}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically consistent based on the interpretation that the grandchild consumes exactly half the combined amount (16 pizzas/day), leading to the correct final answer.

✓ No hallucinations detected

Question #193

Clean

Full Question

Dr. Patel is looking for a new condo that will not go beyond her $390000 budget. She saw a property that has a selling price of $560000. On top of that, the buyer has to pay a brokerage fee which is 7% of the selling price, and also the transfer fee that is 14% of the selling price. If Dr. Patel can get 25% discount on the selling price, how much more will be the total cost than Dr. Patel's budget?

Ground Truth Answer

Because of discount, the $560000 will be 560000 * 75% = 420000. The brokerage fee is $420000 x 7/100 = $29400. The transfer fee is $420000 x 14/100 = $58800. The total price of the condo is $420000 + $29400 + $58800 = $508200. So, it is $508200 - $390000 = $118200 more than Dr. Patel's budget. #### 118200

Generated Answer

Here's how to break down the problem: 1. **Calculate the discount:** 25% of $560,000 is (25/100) * $560,000 = $140,000. 2. **Calculate the discounted price:** $560,000 - $140,000 = $420,000. 3. **Calculate the brokerage fee:** 7% of $420,000 is (7/100) * $420,000 = $29,400. 4. **Calculate the transfer fee:** 14% of $420,000 is (14/100) * $420,000 = $58,800. 5. **Calculate the total cost:** $420,000 + $29,400 + $58,800 = $508,200. 6. **Calculate the difference from Dr. Patel's budget:** $508,200 - $390,000 = $118,200. Answer: {118200}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are mathematically accurate, and the logic correctly applies the discount to the selling price before calculating the fees based on the discounted price.

✓ No hallucinations detected

Question #215

Clean

Full Question

Ibrahim is raising money for a 2-day conference. Each day costs $200 for hotel, $30 for food, and $30 for transportation. Ibrahim only has $95. His friends have chipped in and will cover the cost of all the food for the conference. Ibrahim has also applied for help from the school, which has decided to cover a quarter of the remaining cost of the conference. How much money is Ibrahim still missing?

Ground Truth Answer

Total cost of conference for one day: $200 + $30 + $30 = $260. For 2 days, the cost will be 2 * $260 = $520. Ibrahim's friends will cover the cost of food which will be 2 * $30 = $60. So the remaining cost is 520 - 60 = $460. school is going to pay 1/4 of the remaining cost which will be 1/4 * $460 = $115. So he still needs $460-$115 = $345. Ibrahim also has $95 so he needs $345 - $95 = $250. #### 250

Generated Answer

The total cost of the hotel for the 2-day conference is $200/day * 2 days = $400. The total cost of food is $30/day * 2 days = $60. The total cost of transportation is $30/day * 2 days = $60. The overall total cost of the conference is $400 + $60 + $60 = $520. Ibrahim's friends are paying for the food, so that's $60 covered. This leaves $520 - $60 = $460. The school is covering a quarter of the remaining cost, which is (1/4) * $460 = $115. So, the remaining cost after the school's contribution is $460 - $115 = $345. Ibrahim has $95, so he still needs $345 - $95 = $250. Answer: {250}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations are accurate.

✓ No hallucinations detected

Question #240

Clean

Full Question

Sakura went to the boardwalk for vacation. Her parents gave her €1300 to buy whatever she wanted. At the gift shop, saltwater taffy was on sale for "Buy 16 kgs at €22 per kg, get 4 kgs 1/4 off." She scooped up 22 kgs. She also bought a mixed bag of starfish for €11.0 and 12 keychains that were €20.0 each. Sakura then donated €5 at a charity stand along the way. How much money does Sakura have left?

Ground Truth Answer

saltwater taffy is buying 16 kg for € 22 and gets 4 kg 1/4 off. So 1/4 off of 4 kg is €1*22 = €22. The rest of 2 kg does not have discount and come at 44 so total is 16*22 + 4*3/4*22 + 2*22 = 462 12 keychains at €20.0 each is 12*20.0=€240.0 When you add all her purchases, €462+€11.0+€240.0 = €713) She had €1300 and spent €713 so she had €1300-€713 = €587 left over. We should also deduce €5 so we have 582. #### 582

Generated Answer

Here's how to calculate how much money Sakura has left: 1. **Cost of Taffy:** The first 16 kg of taffy cost €22/kg * 16 kg = €352. The remaining 6 kg (22 kg - 16 kg) were 1/4 off, so they cost €22/kg * (1 - 1/4) = €16.50/kg. Thus, the cost of the remaining 6 kg is €16.50/kg * 6 kg = €99. The total cost of the taffy is €352 + €99 = €451. 2. **Cost of Keychains:** 12 keychains at €20 each cost €20 * 12 = €240. 3. **Total Spending:** Sakura spent €451 (taffy) + €11 (starfish) + €240 (keychains) + €5 (donation) = €707. 4. **Money Left:** Sakura started with €1300 and spent €707, so she has €1300 - €707 = €593 left. Answer: {593}

Overall Quality: poor

The reasoning chain contains a critical logical error in interpreting the complex discount structure for the taffy, leading to an incorrect total cost (€451 instead of €462) and an incorrect final answer.

✓ No hallucinations detected

Question #66

Clean

Full Question

Luca wants to make different sized ice cubes with 337 ounces of water. He can make giant cubes that use 14 ounces per cube, medium cubes that use 3 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 47 total ice cubes, including 9 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does Luca have left?

Ground Truth Answer

The giant cubes used up 9 ounces of water because 9 times 14 equals 126. The medium cubes used up 36 ounces of water because 12 times 3 equals 36. The small cubes used up 7 ounces of water because 14 times 1/2 equals 7. The tiny cubes are 12 * 0.5 * 1/2 = 2. This means that Luca has used up 169 ounces of water because 126 plus 36 plus 7 plus 2 equals 171. Luca has 165 ounces of water left because 337 minus 171 equals 165. #### 165

Generated Answer

First, find the total ounces used by the giant cubes: 9 giant cubes * 14 ounces/giant cube = 126 ounces. Next, find the total ounces used by the small cubes: 14 small cubes * 0.5 ounces/small cube = 7 ounces. Then, find the total ounces used by the medium cubes: 12 medium cubes * 3 ounces/medium cube = 36 ounces. The number of tiny cubes made is 47 total cubes - 9 giant cubes - 14 small cubes - 12 medium cubes = 12 tiny cubes. Tiny cubes are half the size of small cubes, so they use 0.5 ounces/small cube / 2 = 0.25 ounces/tiny cube. Now, calculate the total ounces used by the tiny cubes: 12 tiny cubes * 0.25 ounces/tiny cube = 3 ounces. Add up the total ounces used for all the cubes: 126 ounces + 7 ounces + 36 ounces + 3 ounces = 172 ounces. Finally, subtract the total ounces used from the starting amount to find the remaining ounces: 337 ounces - 172 ounces = 165 ounces. Answer: {165}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly, leading to the correct final answer.

✓ No hallucinations detected

Question #68

Clean

Full Question

Noah wants to make different sized ice cubes with 336 ounces of water. He can make giant cubes that use 15 ounces per cube, medium cubes that use 4 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 49 total ice cubes, including 8 giant cubes, 14 small cubes, 15 medium cubes, and some tiny cubes. How many ounces of water does Noah have left?

Ground Truth Answer

The giant cubes used up 8 ounces of water because 8 times 15 equals 120. The medium cubes used up 60 ounces of water because 15 times 4 equals 60. The small cubes used up 7 ounces of water because 14 times 1/2 equals 7. The tiny cubes are 12 * 0.5 * 1/2 = 2. This means that Noah has used up 187 ounces of water because 120 plus 60 plus 7 plus 2 equals 189. Noah has 146 ounces of water left because 336 minus 189 equals 146. #### 146

Generated Answer

First, calculate the water used for the giant cubes: 8 giant cubes * 15 ounces/giant cube = 120 ounces. Next, calculate the water used for the small cubes: 14 small cubes * 0.5 ounces/small cube = 7 ounces. Then, calculate the water used for the medium cubes: 15 medium cubes * 4 ounces/medium cube = 60 ounces. Now, find the number of tiny cubes made: 49 total cubes - 8 giant cubes - 14 small cubes - 15 medium cubes = 12 tiny cubes. A tiny cube is half the size of a small cube, so it uses 0.5 ounces / 2 = 0.25 ounces. Calculate the water used for tiny cubes: 12 tiny cubes * 0.25 ounces/tiny cube = 3 ounces. Now, find the total water used: 120 ounces + 7 ounces + 60 ounces + 3 ounces = 190 ounces. Finally, subtract the total water used from the initial amount: 336 ounces - 190 ounces = 146 ounces. Answer: {146}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description, leading to the correct final answer.

✓ No hallucinations detected

Question #244

Clean

Full Question

Ava went to the coast for vacation. Her parents gave her $1400 to buy whatever she wanted. At the seaside store, cotton candy was on sale for "Buy 17 pounds at $22 per pound, get 4 pounds 1/2 off." She scooped up 23 pounds. She also bought a mixed bag of coral pieces for $11.0 and 18 pins that were $20.5 each. Ava then donated $5 at a charity stand along the way. How much money does Ava have left?

Ground Truth Answer

cotton candy is buying 17 pound for $ 22 and gets 4 pound 1/2 off. So 1/2 off of 4 pound is $2*22 = $44. The rest of 2 pound does not have discount and come at 44 so total is 17*22 + 4*1/2*22 + 2*22 = 462 18 pins at $20.5 each is 18*20.5=$369.0 When you add all her purchases, $462+$11.0+$369.0 = $842) She had $1400 and spent $842 so she had $1400-$842 = $558 left over. We should also deduce $5 so we have 553. #### 553

Generated Answer

Here's how to break down Ava's spending and calculate her remaining money: 1. **Cotton Candy:** Ava bought 23 pounds of cotton candy. The deal applies to the first 17 pounds, costing $22/pound. So, 17 pounds * $22/pound = $374. She got 4 pounds at half price, so 4 pounds * $22/pound * 0.5 = $44. The remaining 2 pounds (23 total - 17 deal - 4 half-off) were full price: 2 pounds * $22/pound = $44. Total cotton candy cost: $374 + $44 + $44 = $462. 2. **Coral and Pins:** The coral cost $11.0. The pins cost 18 pins * $20.5/pin = $369. Total cost for coral and pins: $11 + $369 = $380. 3. **Total Spending:** Ava spent $462 + $380 + $5 (donation) = $847. 4. **Money Left:** Ava started with $1400 and spent $847. She has $1400 - $847 = $553 left. Answer: {553}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description, correctly calculating all costs and the final remaining balance.

✓ No hallucinations detected

Question #287

Clean

Full Question

Olga initially had 8 dozen pancakes, then ate 5 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Gabrielle finds 3 pancakes. Jasmine finds four times as many as Gabrielle. Tariq finds 2 less than Jasmine. Ravi finds 1/5 as many as Tariq, and Alejandro finds two dozen pancakes more than Jasmine and Gabrielle combined. How many pancakes are still hidden in the yard?

Ground Truth Answer

Olga has 8 x 12 = 96 pancakes. But Olga ate 5 of them. So 96-5=91 pancakes will be hidden for the Easter egg hunt. Gabrielle finds 3 pancakes. Jasmine finds 3 x 4 = 12 pancakes. Tariq finds 12 - 2 = 10 pancakes. Ravi finds 10 * 1/5 = 2 pancakes. Alejandro finds 12*2 + 3 + 12 = 39. The children find a total of 3 + 12 + 10 + 2 + 39 = 66 pancakes. The total number of hidden pancakes still in the yard is 91 - 66 = 25 pancakes. #### 25

Generated Answer

Olga started with 8 dozen pancakes, which is 8 * 12 = 96 pancakes. She ate 5, leaving 96 - 5 = 91 pancakes. Gabrielle finds 3 pancakes. Jasmine finds 4 * 3 = 12 pancakes. Tariq finds 12 - 2 = 10 pancakes. Ravi finds 10 * (1/5) = 2 pancakes. Alejandro finds (12 + 3) + 2 * 12 = 15 + 24 = 39 pancakes. The total number of pancakes found is 3 + 12 + 10 + 2 + 39 = 66 pancakes. Since there were 91 pancakes hidden and 66 were found, there are 91 - 66 = 25 pancakes still hidden. Answer: {25}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #100

Clean

Full Question

Ali is selling muffins and orange pies for a fundraiser. On Tuesday, he sold 22 boxes of muffin and 13 fewer boxes of orange pie, than on Wednesday. On Wednesday, he sold 13 more boxes of muffins than on Tuesday and 23 boxes of orange pie. On Thursday, he sold as much as he did in the past two days combined. If the muffin cost €9 and the orange pie cost €32, what was Ali's average daily earning?

Ground Truth Answer

He sold 22 + 13 = 35 boxes of muffin on Wednesday. The total number of boxes of muffins that Ali sold is 22 + 35 = 57. Ali earned 57 x €9 = €513 for selling muffins. He sold 23 - 13 = 10 boxes of orange pie on Tuesday. The total number of boxes of orange pie that Ali sold is 23 + 10 = 33. He earned 33 x €32 = €1056 for selling orange pie. So, Ali earned €513 + €1056 = €1569 for two days. Finally, on Thursday, he sold as much as he did in the past two days so 2 * 1569 = 3138. Finally, we should divide the total by 3 to get the average daily: 3138 / 3 = 1046 #### 1046

Generated Answer

Here's how to break down Ali's sales and earnings: **Tuesday:** * **Muffins:** 22 boxes * **Orange Pies:** 23 boxes - 13 boxes = 10 boxes (since he sold 13 fewer than Wednesday) * **Earnings:** (22 boxes * €9/box) + (10 boxes * €32/box) = €198 + €320 = €518 **Wednesday:** * **Muffins:** 22 boxes + 13 boxes = 35 boxes * **Orange Pies:** 23 boxes * **Earnings:** (35 boxes * €9/box) + (23 boxes * €32/box) = €315 + €736 = €1051 **Thursday:** * **Muffins:** 22 boxes + 35 boxes = 57 boxes * **Orange Pies:** 10 boxes + 23 boxes = 33 boxes * **Earnings:** (57 boxes * €9/box) + (33 boxes * €32/box) = €513 + €1056 = €1569 **Total Earnings:** €518 + €1051 + €1569 = €3138 **Average Daily Earnings:** €3138 / 3 days = €1046 Answer: {1046}

Overall Quality: excellent

The reasoning chain is mathematically sound. Although the structure differs slightly from the provided ground truth steps, all arithmetic calculations are correct, and the final result matches the ground truth.

✓ No hallucinations detected

Question #160

Clean

Full Question

A father eats 20 pizzas per day, his wife eats 5 pizzas per day, and their daughter eats one-fifth of the combined number of pizzas they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 20% for the first half of the month, and then by an additional 75% for the second half. How many pizzas does this family eat in two months?

Ground Truth Answer

A father and his wife consumption: 20 + 5 = 25 daughter consumes 1/5 more than A father and his wife combined: 25 * 1/5 = 5. So daughter consumes 25 + 5 = 30 pizzas. During first month they consume 30 * 30 = 900. The first half of the second month the consume 20% less each day: 80% * 30 = 24 . So in 15 days, they consume 360 pizzas. During second month, they consume 75% less than the first half each day, so they consume 25% * 24 = 6. So in 15 days, they consume 15 * 6 = 90 pizzas. In 2 months, they consume 30 + 360 + 90 = 1350 pizzas together. #### 1350

Generated Answer

Here's how to solve this problem: **Month 1:** * **Total family consumption:** The father eats 20 pizzas/day, the mother eats 5 pizzas/day, so together they eat 25 pizzas/day. The daughter eats (1/5) * 25 = 5 pizzas/day. The entire family eats 20 + 5 + 5 = 30 pizzas/day. * **Total pizzas in month 1:** Assuming a 30-day month, they eat 30 pizzas/day * 30 days = 900 pizzas. **Month 2 (First Half):** * **Reduction:** They reduce consumption by 20%, so they eat 80% of their usual amount. That's 0.80 * 30 pizzas/day = 24 pizzas/day. * **Pizzas in first half:** Over 15 days, they eat 24 pizzas/day * 15 days = 360 pizzas. **Month 2 (Second Half):** * **Further reduction:** They reduce the *already reduced* amount by an additional 75%. So they eat 25% of the 24 pizzas/day they were eating. That's 0.25 * 24 pizzas/day = 6 pizzas/day. * **Pizzas in second half:** Over 15 days, they eat 6 pizzas/day * 15 days = 90 pizzas. **Total for Two Months:** * Total pizzas consumed is 900 (month 1) + 360 (month 2, first half) + 90 (month 2, second half) = 1350 pizzas. Answer: {1350}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description, leading to the correct final answer.

✓ No hallucinations detected

Question #210

Clean

Full Question

Thiago is raising money for a 3-day science fair. Each day costs $250 for hotel, $30 for food, and $30 for transportation. Thiago only has $35. His friends have chipped in and will cover the cost of all the food for the science fair. Thiago has also applied for help from the school, which has decided to cover 1/4 of the remaining cost of the science fair. How much money is Thiago still missing?

Ground Truth Answer

Total cost of science fair for one day: $250 + $30 + $30 = $310. For 3 days, the cost will be 3 * $310 = $930. Thiago's friends will cover the cost of food which will be 3 * $30 = $90. So the remaining cost is 930 - 90 = $840. school is going to pay 1/4 of the remaining cost which will be 1/4 * $840 = $210. So he still needs $840-$210 = $630. Thiago also has $35 so he needs $630 - $35 = $595. #### 595

Generated Answer

The total cost for the hotel for the 3 days is 3 days * $250/day = $750. The total cost for food for the 3 days is 3 days * $30/day = $90. The total cost for transportation for the 3 days is 3 days * $30/day = $90. The total cost for the science fair is $750 + $90 + $90 = $930. Thiago's friends are covering the food cost, which is $90, so the remaining cost is $930 - $90 = $840. The school is covering 1/4 of the remaining cost, which is (1/4) * $840 = $210. So the remaining cost after the school's contribution is $840 - $210 = $630. Thiago has $35, so the amount he is still missing is $630 - $35 = $595. Answer: {595}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations are accurate.

✓ No hallucinations detected

Question #242

Clean

Full Question

Chen went to the boardwalk for vacation. Her parents gave her $1300 to buy whatever she wanted. At the gift shop, saltwater taffy was on sale for "Buy 16 kgs at $22 per kg, get 6 kgs 1/4 off." She scooped up 23 kgs. She also bought a mixed bag of starfish for $11.0 and 11 keychains that were $21.0 each. Chen then donated $5 at a charity stand along the way. How much money does Chen have left?

Ground Truth Answer

saltwater taffy is buying 16 kg for $ 22 and gets 6 kg 1/4 off. So 1/4 off of 6 kg is $3/2*22 = $33. The rest of 1 kg does not have discount and come at 22 so total is 16*22 + 6*3/4*22 + 1*22 = 473 11 keychains at $21.0 each is 11*21.0=$231.0 When you add all her purchases, $473+$11.0+$231.0 = $715) She had $1300 and spent $715 so she had $1300-$715 = $585 left over. We should also deduce $5 so we have 580. #### 580

Generated Answer

Here's how to break down Chen's spending and calculate her remaining money: 1. **Cost of the first 16 kg of taffy:** 16 kg * $22/kg = $352 2. **Cost of the additional 7 kg of taffy (23 kg total - 16 kg initial = 7 kg additional):** 7 kg * $22/kg = $154. Since 6 of these kgs are 1/4 off, the discount is (1/4) * $154 = $38.50 for the discounted 6kgs and 1 kg * $22 = $22 for the additional 1kg so in total $22+$38.50+$352= $412.5 3. **Cost of starfish:** $11.0 4. **Cost of keychains:** 11 keychains * $21.0/keychain = $231 5. **Total spent before donation:** $412.5 + $11.0 + $231 = $654.5 6. **Total spent after donation:** $654.5 + $5 = $659.5 7. **Money left:** $1300 - $659.5 = $640.5 Answer: {640.5}

Overall Quality: poor

The reasoning contains a significant logical error in interpreting how the 1/4 discount applies to the 6 kgs of taffy, leading to an incorrect total cost for the taffy and consequently an incorrect final answer.

✓ No hallucinations detected

Question #243

Clean

Full Question

Fatima went to the pier for vacation. Her parents gave her ₣1200 to buy whatever she wanted. At the beach shop, rock candy was on sale for "Buy 16 kgs at ₣20 per kg, get 6 kgs 1/3 off." She scooped up 23 kgs. She also bought a mixed bag of sea glass for ₣11.0 and 13 stickers that were ₣20.0 each. Fatima then donated ₣5 at a charity stand along the way. How much money does Fatima have left?

Ground Truth Answer

rock candy is buying 16 kg for ₣ 20 and gets 6 kg 1/3 off. So 1/3 off of 6 kg is ₣2*20 = ₣40. The rest of 1 kg does not have discount and come at 20 so total is 16*20 + 6*2/3*20 + 1*20 = 420 13 stickers at ₣20.0 each is 13*20.0=₣260.0 When you add all her purchases, ₣420+₣11.0+₣260.0 = ₣691) She had ₣1200 and spent ₣691 so she had ₣1200-₣691 = ₣509 left over. We should also deduce ₣5 so we have 504. #### 504

Generated Answer

Here's how to break down Fatima's spending: 1. **Rock Candy:** The first 16 kg of rock candy cost ₣20/kg * 16 kg = ₣320. The remaining 7 kg (23 kg - 16 kg) were 1/3 off, so they cost (2/3) * ₣20/kg * 7 kg = ₣280/3 ≈ ₣93.33. The total cost of the rock candy is ₣320 + ₣93.33 = ₣413.33. 2. **Sea Glass:** The sea glass cost ₣11.0. 3. **Stickers:** The stickers cost ₣20.0/sticker * 13 stickers = ₣260. 4. **Charity:** Fatima donated ₣5. 5. **Total Spending:** Her total spending was ₣413.33 + ₣11.0 + ₣260 + ₣5 = ₣689.33. 6. **Money Left:** Fatima started with ₣1200 and spent ₣689.33, so she has ₣1200 - ₣689.33 = ₣510.67 left. Answer: {510.67}

Overall Quality: poor

The model fundamentally misinterpreted the scope of the discount for the rock candy, applying it to 7 kg instead of the specified 6 kg, leading to an incorrect total cost and final remaining balance.

✓ No hallucinations detected

Question #283

Clean

Full Question

Ali initially had 11 dozen cookies, then ate 3 cookies for breakfast, and then hid the rest in the yard for the Easter egg hunt. Faisal finds 5 cookies. Hiroshi finds thrice as many as Faisal. Benjamin finds 3 less than Hiroshi. Wei finds a quarter as many as Benjamin, and Quinn finds three dozen cookies more than Hiroshi and Faisal combined. How many cookies are still hidden in the yard?

Ground Truth Answer

Ali has 11 x 12 = 132 cookies. But Ali ate 3 of them. So 132-3=129 cookies will be hidden for the Easter egg hunt. Faisal finds 5 cookies. Hiroshi finds 5 x 3 = 15 cookies. Benjamin finds 15 - 3 = 12 cookies. Wei finds 12 * 1/4 = 3 cookies. Quinn finds 12*3 + 5 + 15 = 56. The children find a total of 5 + 15 + 12 + 3 + 56 = 91 cookies. The total number of hidden cookies still in the yard is 129 - 91 = 38 cookies. #### 38

Generated Answer

Ali starts with 11 dozen cookies, which is 11 * 12 = 132 cookies. After eating 3, there are 132 - 3 = 129 cookies left. Faisal finds 5 cookies. Hiroshi finds 3 * 5 = 15 cookies. Benjamin finds 15 - 3 = 12 cookies. Wei finds 12 / 4 = 3 cookies. Quinn finds (15 + 5) + (3 * 12) = 20 + 36 = 56 cookies. The total number of cookies found is 5 + 15 + 12 + 3 + 56 = 91 cookies. Therefore, the number of cookies still hidden is 129 - 91 = 38 cookies. Answer: {38}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem. All arithmetic calculations are correct, and the logic applied matches the problem statement.

✓ No hallucinations detected

Question #96

Clean

Full Question

Wei is selling cupcakes and plum pies for a fundraiser. On Monday, he sold 28 boxes of cupcake and 19 fewer boxes of plum pie, than on Tuesday. On Tuesday, he sold 14 more boxes of cupcakes than on Monday and 27 boxes of plum pie. On Wednesday, he sold as much as he did in the past two days combined. If the cupcake cost $11 and the plum pie cost $23, what was Wei's average daily earning?

Ground Truth Answer

He sold 28 + 14 = 42 boxes of cupcake on Tuesday. The total number of boxes of cupcakes that Wei sold is 28 + 42 = 70. Wei earned 70 x $11 = $770 for selling cupcakes. He sold 27 - 19 = 8 boxes of plum pie on Monday. The total number of boxes of plum pie that Wei sold is 27 + 8 = 35. He earned 35 x $23 = $805 for selling plum pie. So, Wei earned $770 + $805 = $1575 for two days. Finally, on Wednesday, he sold as much as he did in the past two days so 2 * 1575 = 3150. Finally, we should divide the total by 3 to get the average daily: 3150 / 3 = 1050 #### 1050

Generated Answer

Here's how to solve the problem: 1. **Cupcakes and pies sold on Monday:** * Cupcakes: 28 boxes * Pies: 27 (Tuesday's sales) - 19 = 8 boxes 2. **Cupcakes and pies sold on Tuesday:** * Cupcakes: 28 (Monday's sales) + 14 = 42 boxes * Pies: 27 boxes 3. **Cupcakes and pies sold on Wednesday:** * Cupcakes: 28 + 42 = 70 boxes * Pies: 8 + 27 = 35 boxes 4. **Earnings from Monday:** * Cupcakes: 28 boxes * $11/box = $308 * Pies: 8 boxes * $23/box = $184 * Total: $308 + $184 = $492 5. **Earnings from Tuesday:** * Cupcakes: 42 boxes * $11/box = $462 * Pies: 27 boxes * $23/box = $621 * Total: $462 + $621 = $1083 6. **Earnings from Wednesday:** * Cupcakes: 70 boxes * $11/box = $770 * Pies: 35 boxes * $23/box = $805 * Total: $770 + $805 = $1575 7. **Total earnings over three days:** * $492 + $1083 + $1575 = $3150 8. **Average daily earnings:** * $3150 / 3 days = $1050/day Answer: {1050}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description perfectly. All calculations are verified as correct.

✓ No hallucinations detected

Question #120

Clean

Full Question

Diego picks 67 pineapples on Wednesday. Then he picks 176 pineapples on Thursday. On Friday, he picks quintuple the number of pineapples he did on Wednesday. On Saturday, he picks half the amount of what he picked in the past 3 days combined. On Sunday, Diego is going to sell pineapples in boxes of 17 pineapples each. He is going to sell each box for $12. How much is Diego going to make?

Ground Truth Answer

Combining Wednesday and Thursday, Diego has 67 pineapples + 176 pineapples = 243 pineapples. On Friday, he picks 5 * 67 pineapples = 335 pineapples. Altogether, Diego has 243 pineapples + 335 pineapples = 578 pineapples. Finally he collected 578 / 2 = 289 on Saturday. The total is 578 + 289 = 867. Each box is going to have 17 pineapples. So Diego needs 867 / 17 = 51 boxes. He is going to sell each box for $12, so he is going to earn $51 * 12 = $612 #### 612

Generated Answer

Diego picks 67 pineapples on Wednesday. On Thursday, he picks 176 pineapples. On Friday, he picks 67 * 5 = 335 pineapples. The total for Wednesday, Thursday, and Friday is 67 + 176 + 335 = 578 pineapples. On Saturday, he picks 578 / 2 = 289 pineapples. The total number of pineapples picked is 578 + 289 = 867 pineapples. The number of boxes is 867 / 17 = 51 boxes. The total earnings will be 51 boxes * $12/box = $612. Answer: {612}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #241

Clean

Full Question

Kayla went to the pier for vacation. Her parents gave her ₺1400 to buy whatever she wanted. At the beach shop, rock candy was on sale for "Buy 16 kgs at ₺22 per kg, get 6 kgs 2/3 off." She scooped up 23 kgs. She also bought a mixed bag of sea glass for ₺11.0 and 14 stickers that were ₺20.5 each. Kayla then donated ₺5 at a charity stand along the way. How much money does Kayla have left?

Ground Truth Answer

rock candy is buying 16 kg for ₺ 22 and gets 6 kg 2/3 off. So 2/3 off of 6 kg is ₺4*22 = ₺88. The rest of 1 kg does not have discount and come at 22 so total is 16*22 + 6*1/3*22 + 1*22 = 418 14 stickers at ₺20.5 each is 14*20.5=₺287.0 When you add all her purchases, ₺418+₺11.0+₺287.0 = ₺716) She had ₺1400 and spent ₺716 so she had ₺1400-₺716 = ₺684 left over. We should also deduce ₺5 so we have 679. #### 679

Generated Answer

Here's how to break down Kayla's spending: 1. **Rock Candy:** Kayla bought 23 kg of rock candy. The first 16 kg cost ₺22 per kg, totaling 16 * ₺22 = ₺352. The remaining 7 kg were 2/3 off. So, the price per kg for the discounted candy is ₺22 * (1 - 2/3) = ₺22 * (1/3) = ₺7.33 (approximately). The cost of the discounted candy is 7 * ₺7.33 = ₺51.31. The total cost of the rock candy is ₺352 + ₺51.31 = ₺403.31. 2. **Sea Glass:** The sea glass cost ₺11.0. 3. **Stickers:** Kayla bought 14 stickers at ₺20.5 each, costing 14 * ₺20.5 = ₺287. 4. **Donation:** Kayla donated ₺5. 5. **Total Spending:** Kayla's total spending was ₺403.31 + ₺11.0 + ₺287 + ₺5 = ₺706.31. 6. **Money Left:** Kayla started with ₺1400 and spent ₺706.31, leaving her with ₺1400 - ₺706.31 = ₺693.69. Answer: {693.69}

Overall Quality: poor

The reasoning chain contains a significant logical error in interpreting the rock candy discount structure, leading to an incorrect total spending and final remaining balance.

✓ No hallucinations detected

Question #213

Clean

Full Question

Leon is raising money for a 2-day workshop. Each day costs ¥150 for hotel, ¥30 for food, and ¥10 for transportation. Leon only has ¥155. His friends have chipped in and will cover the cost of all the food for the workshop. Leon has also applied for help from the youth club, which has decided to cover a fifth of the remaining cost of the workshop. How much money is Leon still missing?

Ground Truth Answer

Total cost of workshop for one day: ¥150 + ¥10 + ¥30 = ¥190. For 2 days, the cost will be 2 * ¥190 = ¥380. Leon's friends will cover the cost of food which will be 2 * ¥30 = ¥60. So the remaining cost is 380 - 60 = ¥320. youth club is going to pay 1/5 of the remaining cost which will be 1/5 * ¥320 = ¥64. So he still needs ¥320-¥64 = ¥256. Leon also has ¥155 so he needs ¥256 - ¥155 = ¥101. #### 101

Generated Answer

The total cost for the hotel for both days is ¥150/day * 2 days = ¥300. The total cost for food for both days is ¥30/day * 2 days = ¥60. The total cost for transportation for both days is ¥10/day * 2 days = ¥20. The total cost of the workshop, excluding food, is ¥300 + ¥20 = ¥320. Since Leon's friends are covering the cost of food, we subtract that from the total cost: ¥320. The youth club is covering 1/5 of the remaining cost, which is (1/5) * ¥320 = ¥64. So the amount Leon has to pay after the youth club's contribution is ¥320 - ¥64 = ¥256. Leon currently has ¥155. Therefore, he is still missing ¥256 - ¥155 = ¥101. Answer: {101}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost, correctly accounts for the food cost being covered, correctly calculates the youth club contribution, and correctly determines the final amount Leon is missing. All arithmetic operations are correct.

✓ No hallucinations detected

Question #284

Clean

Full Question

Beatriz initially had 10 dozen pancakes, then ate 3 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Kimia finds 6 pancakes. Sophia finds three times as many as Kimia. Mateo finds 2 less than Sophia. Umar finds half as many as Mateo, and Mei finds two dozen pancakes more than Sophia and Kimia combined. How many pancakes are still hidden in the yard?

Ground Truth Answer

Beatriz has 10 x 12 = 120 pancakes. But Beatriz ate 3 of them. So 120-3=117 pancakes will be hidden for the Easter egg hunt. Kimia finds 6 pancakes. Sophia finds 6 x 3 = 18 pancakes. Mateo finds 18 - 2 = 16 pancakes. Umar finds 16 * 1/2 = 8 pancakes. Mei finds 12*2 + 6 + 18 = 48. The children find a total of 6 + 18 + 16 + 8 + 48 = 96 pancakes. The total number of hidden pancakes still in the yard is 117 - 96 = 21 pancakes. #### 21

Generated Answer

Here's how we can solve this problem step-by-step: 1. **Beatriz's starting pancakes:** Beatriz started with 10 dozen pancakes, which is 10 * 12 = 120 pancakes. 2. **Pancakes remaining after breakfast:** After eating 3, she had 120 - 3 = 117 pancakes left. 3. **Kimia's find:** Kimia found 6 pancakes. 4. **Sophia's find:** Sophia found three times as many as Kimia, so she found 3 * 6 = 18 pancakes. 5. **Mateo's find:** Mateo found 2 less than Sophia, so he found 18 - 2 = 16 pancakes. 6. **Umar's find:** Umar found half as many as Mateo, meaning he found 16 / 2 = 8 pancakes. 7. **Mei's find:** Mei found two dozen (2 * 12 = 24) more than Sophia and Kimia combined. Sophia and Kimia found 18 + 6 = 24 pancakes. So Mei found 24 + 24 = 48 pancakes. 8. **Total pancakes found:** The total number of pancakes found is 6 + 18 + 16 + 8 + 48 = 96 pancakes. 9. **Pancakes still hidden:** Since Beatriz hid 117 pancakes and 96 were found, there are 117 - 96 = 21 pancakes still hidden. Answer: {21}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description logically at every step. All calculations are correct.

✓ No hallucinations detected

Question #286

Clean

Full Question

Kai initially had 7 dozen pancakes, then ate 2 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Nia finds 6 pancakes. Isabella finds two times as many as Nia. Roya finds 4 less than Isabella. Diego finds a quarter as many as Roya, and Yara finds two dozen pancakes more than Isabella and Nia combined. How many pancakes are still hidden in the yard?

Ground Truth Answer

Kai has 7 x 12 = 84 pancakes. But Kai ate 2 of them. So 84-2=82 pancakes will be hidden for the Easter egg hunt. Nia finds 6 pancakes. Isabella finds 6 x 2 = 12 pancakes. Roya finds 12 - 4 = 8 pancakes. Diego finds 8 * 1/4 = 2 pancakes. Yara finds 12*2 + 6 + 12 = 42. The children find a total of 6 + 12 + 8 + 2 + 42 = 70 pancakes. The total number of hidden pancakes still in the yard is 82 - 70 = 12 pancakes. #### 12

Generated Answer

Kai starts with 7 dozen pancakes, which is 7 * 12 = 84 pancakes. He eats 2, leaving 84 - 2 = 82 pancakes. Nia finds 6 pancakes. Isabella finds 2 * 6 = 12 pancakes. Roya finds 12 - 4 = 8 pancakes. Diego finds 8 / 4 = 2 pancakes. Yara finds (12 + 6) + 24 = 18 + 24 = 42 pancakes. The total number of pancakes found is 6 + 12 + 8 + 2 + 42 = 70 pancakes. The number of pancakes still hidden is 82 - 70 = 12 pancakes. Answer: {12}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #282

Clean

Full Question

Viktor initially had 9 dozen pancakes, then ate 3 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Liam finds 5 pancakes. Yusuf finds two times as many as Liam. Pavel finds 4 less than Yusuf. Daphne finds half as many as Pavel, and James finds four dozen pancakes more than Yusuf and Liam combined. How many pancakes are still hidden in the yard?

Ground Truth Answer

Viktor has 9 x 12 = 108 pancakes. But Viktor ate 3 of them. So 108-3=105 pancakes will be hidden for the Easter egg hunt. Liam finds 5 pancakes. Yusuf finds 5 x 2 = 10 pancakes. Pavel finds 10 - 4 = 6 pancakes. Daphne finds 6 * 1/2 = 3 pancakes. James finds 12*4 + 5 + 10 = 63. The children find a total of 5 + 10 + 6 + 3 + 63 = 87 pancakes. The total number of hidden pancakes still in the yard is 105 - 87 = 18 pancakes. #### 18

Generated Answer

Viktor started with 9 dozen pancakes, which is 9 * 12 = 108 pancakes. He ate 3, leaving 108 - 3 = 105 pancakes. Liam found 5 pancakes. Yusuf found 2 * 5 = 10 pancakes. Pavel found 10 - 4 = 6 pancakes. Daphne found 6 / 2 = 3 pancakes. James found (10 + 5) + (4 * 12) = 15 + 48 = 63 pancakes. The total number of pancakes found is 5 + 10 + 6 + 3 + 63 = 87 pancakes. The number of pancakes still hidden is 105 - 87 = 18 pancakes. Answer: {18}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #285

Clean

Full Question

Zahra initially had 9 dozen waffles, then ate 5 waffles for breakfast, and then hid the rest in the yard for the Easter egg hunt. Viktor finds 5 waffles. Andre finds three times as many as Viktor. Rania finds 3 less than Andre. Uma finds 1/4 as many as Rania, and Arash finds three dozen waffles more than Andre and Viktor combined. How many waffles are still hidden in the yard?

Ground Truth Answer

Zahra has 9 x 12 = 108 waffles. But Zahra ate 5 of them. So 108-5=103 waffles will be hidden for the Easter egg hunt. Viktor finds 5 waffles. Andre finds 5 x 3 = 15 waffles. Rania finds 15 - 3 = 12 waffles. Uma finds 12 * 1/4 = 3 waffles. Arash finds 12*3 + 5 + 15 = 56. The children find a total of 5 + 15 + 12 + 3 + 56 = 91 waffles. The total number of hidden waffles still in the yard is 103 - 91 = 12 waffles. #### 12

Generated Answer

Zahra started with 9 dozen waffles, which is 9 * 12 = 108 waffles. She ate 5, leaving 108 - 5 = 103 waffles. Viktor finds 5 waffles. Andre finds 3 * 5 = 15 waffles. Rania finds 15 - 3 = 12 waffles. Uma finds 12 / 4 = 3 waffles. Arash finds (15 + 5) + (3 * 12) = 20 + 36 = 56 waffles. The total number of waffles found is 5 + 15 + 12 + 3 + 56 = 91 waffles. The number of waffles still hidden is 103 - 91 = 12 waffles. Answer: {12}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #124

Clean

Full Question

Oliver picks 111 oranges on Tuesday. Then he picks 170 oranges on Wednesday. On Thursday, he picks quintuple the number of oranges he did on Tuesday. On Friday, he picks half the amount of what he picked in the past 3 days combined. On Saturday, Oliver is going to sell oranges in boxes of 19 oranges each. He is going to sell each box for $9. How much is Oliver going to make?

Ground Truth Answer

Combining Tuesday and Wednesday, Oliver has 111 oranges + 170 oranges = 281 oranges. On Thursday, he picks 5 * 111 oranges = 555 oranges. Altogether, Oliver has 281 oranges + 555 oranges = 836 oranges. Finally he collected 836 / 2 = 418 on Friday. The total is 836 + 418 = 1254. Each box is going to have 19 oranges. So Oliver needs 1254 / 19 = 66 boxes. He is going to sell each box for $9, so he is going to earn $66 * 9 = $594 #### 594

Generated Answer

Here's how to break down this problem: 1. **Thursday's oranges:** Oliver picks 111 * 5 = 555 oranges on Thursday. 2. **Total for Tuesday, Wednesday, and Thursday:** Oliver picks 111 + 170 + 555 = 836 oranges. 3. **Friday's oranges:** Oliver picks 836 / 2 = 418 oranges on Friday. 4. **Total oranges:** Oliver picks 836 + 418 = 1254 oranges in total. 5. **Boxes of oranges:** Oliver has 1254 / 19 = 66 boxes of oranges. 6. **Total earnings:** Oliver earns 66 * $9 = $594. Answer: {594}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #39

Clean

Full Question

Yusuf has 10 square yards of watermelon field. There are 19 watermelons per two-sixths of a square yard. Yusuf can harvest his watermelons every 2 months. In addition, Yusuf owns a 9-square yard grape field that produces 14 grapes per square yard. The grapes can be harvested every 4 months. In the span of two years, how many more watermelons does Yusuf harvest than grapes?

Ground Truth Answer

Yusuf has 19 x 10= 190 watermelons on 1/3 of his field. In total Yusuf can get, 1÷1/3 = 3 times more, meaning 190*3=570. Yusuf can harvest his watermelon 12 ÷ 2 = 6 times per year Therefore Yusuf can harvest 570 x 6 = 3420 watermelons per year. There are 14 grapes per square yard of the second field. In total, there are 9*14 = 126 grapes. Since Yusuf can harvest his grapes 12 ÷ 4 = 3 times a year, he can harvest 126 * 3 = 378 grapes in a year. Each year, Yusuf harvests 3420 watermelons - 378 grapes = 3042 more watermelons. So in two years, Yusuf will produce 2 * 3042 = 6084 more. #### 6084

Generated Answer

First, calculate the number of watermelons per square yard: 19 watermelons / (2/6) square yards = 57 watermelons per square yard. Then, calculate the number of watermelons in Yusuf's 10-square-yard field: 57 watermelons/square yard * 10 square yards = 570 watermelons. Since Yusuf can harvest watermelons every 2 months, in two years (24 months), he harvests 24 months / 2 months/harvest = 12 times. So, in two years, Yusuf harvests 570 watermelons/harvest * 12 harvests = 6840 watermelons. Next, calculate the number of grapes Yusuf harvests per harvest: 14 grapes/square yard * 9 square yards = 126 grapes. Since grapes can be harvested every 4 months, in two years (24 months), he harvests 24 months / 4 months/harvest = 6 harvests. So, in two years, Yusuf harvests 126 grapes/harvest * 6 harvests = 756 grapes. Finally, find the difference between the number of watermelons and grapes harvested: 6840 watermelons - 756 grapes = 6084. Answer: {6084}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem requirements, leading to the correct final answer.

✓ No hallucinations detected

Question #38

Clean

Full Question

Mohammed has 35 square meters of grape field. There are 12 grapes per 2/3 of a square meter. Mohammed can harvest his grapes every 6 months. In addition, Mohammed owns a 11-square meter apricot field that produces 18 apricots per square meter. The apricots can be harvested every 4 months. In the span of two years, how many more grapes does Mohammed harvest than apricots?

Ground Truth Answer

Mohammed has 12 x 35= 420 grapes on 2/3 of his field. In total Mohammed can get, 1÷2/3 = 3/2 times more, meaning 420*3/2=630. Mohammed can harvest his grape 12 ÷ 6 = 2 times per year Therefore Mohammed can harvest 630 x 2 = 1260 grapes per year. There are 18 apricots per square meter of the second field. In total, there are 11*18 = 198 apricots. Since Mohammed can harvest his apricots 12 ÷ 4 = 3 times a year, he can harvest 198 * 3 = 594 apricots in a year. Each year, Mohammed harvests 1260 grapes - 594 apricots = 666 more grapes. So in two years, Mohammed will produce 2 * 666 = 1332 more. #### 1332

Generated Answer

Here's how to solve this problem: **1. Calculate the number of grapes per square meter:** * There are 12 grapes per 2/3 of a square meter. To find the number of grapes per full square meter, divide 12 by (2/3): 12 / (2/3) = 12 * (3/2) = 18 grapes per square meter. **2. Calculate the total number of grapes harvested per harvest:** * Mohammed has 35 square meters of grape field, and each square meter yields 18 grapes: 35 * 18 = 630 grapes per harvest. **3. Calculate the number of grape harvests in two years:** * There are two harvests per year (every 6 months), and we're looking at two years: 2 harvests/year * 2 years = 4 harvests. **4. Calculate the total number of grapes harvested in two years:** * 630 grapes/harvest * 4 harvests = 2520 grapes. **5. Calculate the total number of apricots harvested per harvest:** * Mohammed's apricot field is 11 square meters, and each square meter yields 18 apricots: 11 * 18 = 198 apricots per harvest. **6. Calculate the number of apricot harvests in two years:** * There are three harvests per year (every 4 months), and we're looking at two years: 3 harvests/year * 2 years = 6 harvests. **7. Calculate the total number of apricots harvested in two years:** * 198 apricots/harvest * 6 harvests = 1188 apricots. **8. Calculate the difference between grapes and apricots:** * 2520 grapes - 1188 apricots = 1332 more grapes. Answer: {1332}

Overall Quality: excellent

The reasoning chain correctly calculates the total grapes and apricots harvested over two years based on the provided rates and harvest frequencies, leading to the correct final difference. All arithmetic operations are correct.

✓ No hallucinations detected

Question #235

Clean

Full Question

A maintenance worker has to clean a university with 150 floors. They have 6 days to get it done. It takes them 6 minutes per floor. However, due to a recent injury, the maintenance worker has become slower and it will take them twice as long to clean a floor these days. If they work for 10 hours a day, what percentage of their day, on average, is spent cleaning floors?

Ground Truth Answer

They have to clean 25 floors a day because 150 / 6 = 25 They spend 300 minutes cleaning per day because 25 x 12 = 300 They spend 5.0 hours a day because 300 / 60 = 5.0 They spend 0.5 of their day cleaning floors because 5.0 / 10 = 0.5 They spend 50% of their day cleaning floors because 0.5 x 100 = 50 #### 50

Generated Answer

It now takes the worker 6 * 2 = 12 minutes per floor. With 150 floors, it will take them 150 floors * 12 minutes/floor = 1800 minutes total. Over 6 days, this is 1800 minutes / 6 days = 300 minutes per day. Since they work 10 hours a day, and each hour has 60 minutes, they work 10 * 60 = 600 minutes per day. The percentage of their day spent cleaning is (300 minutes cleaning / 600 minutes working) * 100% = 50%. Answer: {50}

Overall Quality: excellent

The reasoning chain correctly calculates the time spent cleaning per day and compares it to the total working time per day to find the percentage, matching the ground truth steps.

✓ No hallucinations detected

Question #19

Clean

Full Question

A class of 230 students has various hobbies. 5 like to dance, 8 like to play chess, 13 like to swim, 32 like to play volleyball, and the rest like to either play video games or play music. What percentage of the students like to play video games if the number of the students that like to play music is 7 less than two times the number that prefer playing volleyball?

Ground Truth Answer

The number of students that like to play music is 7 less than 2 times as many as the number who like volleyball, so 2 * 32 - 7 = 57 The number that like to play video games is 230 total students - 5 dance - 32 volleyball - 57 play music - 13 swim - 8 chess = 115. To calculate the percentage, we divide this number of by 230 and multiply by 100: 115 / 230 = 0.5 * 100 = 50% #### 50

Generated Answer

The total number of students with hobbies other than video games or music is 5 + 8 + 13 + 32 = 58. The number of students who like to play music is 2 * 32 - 7 = 64 - 7 = 57. The number of students who like to play video games or music is 230 - 58 = 172. The number of students who like to play video games is 172 - 57 = 115. The percentage of students who like to play video games is (115/230) * 100 = 50%. Answer: {50}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem statement. All calculations are correct.

✓ No hallucinations detected

Question #121

Clean

Full Question

Deshawn picks 142 pears on Saturday. Then he picks 172 pears on Sunday. On Monday, he picks triple the number of pears he did on Saturday. On Tuesday, he picks half the amount of what he picked in the past 3 days combined. On Wednesday, DeShawn is going to sell pears in boxes of 15 pears each. He is going to sell each box for $14. How much is DeShawn going to make?

Ground Truth Answer

Combining Saturday and Sunday, DeShawn has 142 pears + 172 pears = 314 pears. On Monday, he picks 3 * 142 pears = 426 pears. Altogether, DeShawn has 314 pears + 426 pears = 740 pears. Finally he collected 740 / 2 = 370 on Tuesday. The total is 740 + 370 = 1110. Each box is going to have 15 pears. So DeShawn needs 1110 / 15 = 74 boxes. He is going to sell each box for $14, so he is going to earn $74 * 14 = $1036 #### 1036

Generated Answer

Here's how to break down DeShawn's pear-selling venture: 1. **Monday's Pears:** DeShawn picks 142 * 3 = 426 pears on Monday. 2. **Total Pears (Sat-Mon):** Over the weekend and Monday, he picks 142 + 172 + 426 = 740 pears. 3. **Tuesday's Pears:** He picks 740 / 2 = 370 pears on Tuesday. 4. **Grand Total Pears:** In total, DeShawn has 740 + 370 = 1110 pears. 5. **Boxes of Pears:** He can make 1110 / 15 = 74 boxes of pears. 6. **Total Earnings:** DeShawn will make 74 boxes * $14/box = $1036. Answer: {1036}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #40

Clean

Full Question

Ravi has 10 square yards of banana field. There are 36 bananas per four-fifths of a square yard. Ravi can harvest his bananas every 4 months. In addition, Ravi owns a 13-square yard apricot field that produces 12 apricots per square yard. The apricots can be harvested every 4 months. In the span of two years, how many more bananas does Ravi harvest than apricots?

Ground Truth Answer

Ravi has 36 x 10= 360 bananas on 4/5 of his field. In total Ravi can get, 1÷4/5 = 5/4 times more, meaning 360*5/4=450. Ravi can harvest his banana 12 ÷ 4 = 3 times per year Therefore Ravi can harvest 450 x 3 = 1350 bananas per year. There are 12 apricots per square yard of the second field. In total, there are 13*12 = 156 apricots. Since Ravi can harvest his apricots 12 ÷ 4 = 3 times a year, he can harvest 156 * 3 = 468 apricots in a year. Each year, Ravi harvests 1350 bananas - 468 apricots = 882 more bananas. So in two years, Ravi will produce 2 * 882 = 1764 more. #### 1764

Generated Answer

Ravi's banana field is 10 square yards. Since there are 36 bananas per four-fifths of a square yard, there are 36 / (4/5) = 36 * (5/4) = 45 bananas per square yard. Thus, Ravi's banana field produces 10 * 45 = 450 bananas. Since bananas can be harvested every 4 months, and there are 12 months in a year, Ravi can harvest bananas 12/4 = 3 times a year. Over two years, Ravi harvests bananas 3 * 2 = 6 times. So in two years, Ravi harvests 450 bananas * 6 harvests = 2700 bananas. Ravi's apricot field is 13 square yards, and it produces 12 apricots per square yard. So the field produces 13 * 12 = 156 apricots. Apricots are also harvested every 4 months, so in two years Ravi harvests apricots 6 times. Over two years, he harvests 156 apricots * 6 harvests = 936 apricots. The difference between the number of bananas and apricots Ravi harvests in two years is 2700 - 936 = 1764. Answer: {1764}

Overall Quality: excellent

The reasoning chain correctly calculates the yield for both bananas and apricots over two years and finds the correct difference. All arithmetic operations and logical steps align with the problem statement and ground truth.

✓ No hallucinations detected

Question #41

Clean

Full Question

Thiago has 25 square yards of orange field. There are 23 oranges per one-fourth of a square yard. Thiago can harvest his oranges every 12 months. In addition, Thiago owns a 9-square yard grape field that produces 13 grapes per square yard. The grapes can be harvested every 4 months. In the span of two years, how many more oranges does Thiago harvest than grapes?

Ground Truth Answer

Thiago has 23 x 25= 575 oranges on 1/4 of his field. In total Thiago can get, 1÷1/4 = 4 times more, meaning 575*4=2300. Thiago can harvest his orange 12 ÷ 12 = 1 times per year Therefore Thiago can harvest 2300 x 1 = 2300 oranges per year. There are 13 grapes per square yard of the second field. In total, there are 9*13 = 117 grapes. Since Thiago can harvest his grapes 12 ÷ 4 = 3 times a year, he can harvest 117 * 3 = 351 grapes in a year. Each year, Thiago harvests 2300 oranges - 351 grapes = 1949 more oranges. So in two years, Thiago will produce 2 * 1949 = 3898 more. #### 3898

Generated Answer

Here's how to solve this problem: 1. **Calculate oranges per square yard:** Thiago harvests 23 oranges per 1/4 square yard, so he gets 23 * 4 = 92 oranges per square yard. 2. **Calculate total oranges:** Thiago has 25 square yards of orange field, yielding 25 * 92 = 2300 oranges per harvest. 3. **Calculate oranges over two years:** Thiago harvests oranges every 12 months, so in two years (24 months), he harvests 24 / 12 = 2 times. This means he harvests a total of 2300 * 2 = 4600 oranges. 4. **Calculate total grapes per harvest:** Thiago's grape field produces 13 grapes per square yard and is 9 square yards, so he harvests 13 * 9 = 117 grapes per harvest. 5. **Calculate grapes over two years:** Grapes are harvested every 4 months, so over two years (24 months), he harvests 24 / 4 = 6 times. This yields a total of 117 * 6 = 702 grapes. 6. **Find the difference:** Thiago harvests 4600 oranges and 702 grapes over two years, meaning he harvests 4600 - 702 = 3898 more oranges than grapes. Answer: {3898}

Overall Quality: excellent

The reasoning chain correctly interprets the problem and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #32

Clean

Full Question

Gabrielle makes tea using teaspoons of sugar and cups of water in a ratio of 54:12. She also uses 7 tablespoons of milk for every 2 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 240 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?

Ground Truth Answer

Gabrielle uses 2 tablespoons of cream for every teaspoon of sugar. For 54 teaspoons of sugar, she uses 2 * 54 = 108 tablespoons of heavy cream. Gabrielle uses 7 tablespoons of milk for every 2 cups of water. For 12 cups water she uses 7*12/2 = 42 tablespoons of milk. The total ratio representing the ingredients she used to make the tea is 54 sugar +12 water +42 milk + 108 heavy cream= 216. Since the fraction representing the number of teaspoons of sugar she used is 54/216, she used 54/216*240 = 60 #### 60

Generated Answer

Let S be the amount of sugar (in teaspoons), W be the amount of water (in cups), M be the amount of milk (in tablespoons), and C be the amount of cream (in tablespoons). We are given that the ratio of sugar to water is 54:12, which simplifies to 9:2. So, S/W = 9/2, or W = (2/9)S. We are also given that she uses 7 tablespoons of milk for every 2 cups of water. So, M/W = 7/2, or M = (7/2)W. Substituting W = (2/9)S, we have M = (7/2)(2/9)S = (7/9)S. Finally, she uses 2 tablespoons of heavy cream for every teaspoon of sugar. So, C/S = 2/1, or C = 2S. We are told that S + W + M + C = 240. Substituting the expressions for W, M, and C in terms of S, we get S + (2/9)S + (7/9)S + 2S = 240 S + (9/9)S + 2S = 240 S + S + 2S = 240 4S = 240 S = 240/4 S = 60 Answer: {60}

Overall Quality: excellent

The reasoning chain correctly establishes the relationships between all four variables based on the given ratios and uses the total sum constraint to solve for the amount of sugar (S). All arithmetic steps are correct.

✓ No hallucinations detected

Question #34

Clean

Full Question

Kimia makes coffee using teaspoons of sugar and cups of water in a ratio of 55:44. She also uses 6 tablespoons of milk for every 24 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 240 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?

Ground Truth Answer

Kimia uses 2 tablespoons of cream for every teaspoon of sugar. For 55 teaspoons of sugar, she uses 2 * 55 = 110 tablespoons of heavy cream. Kimia uses 6 tablespoons of milk for every 24 cups of water. For 44 cups water she uses 6*44/24 = 11 tablespoons of milk. The total ratio representing the ingredients she used to make the coffee is 55 sugar +44 water +11 milk + 110 heavy cream= 220. Since the fraction representing the number of teaspoons of sugar she used is 55/220, she used 55/220*240 = 60 #### 60

Generated Answer

Let 's' be the number of teaspoons of sugar Kimia used, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. We are given the following ratios: Sugar : Water = 55 : 44 => s/w = 55/44 = 5/4 Milk : Water = 6 : 24 => m/w = 6/24 = 1/4 Cream : Sugar = 2 : 1 => c/s = 2/1 = 2 We are given that s + w + m + c = 240. From s/w = 5/4, we get w = (4/5)s From m/w = 1/4, we get m = (1/4)w = (1/4)(4/5)s = (1/5)s From c/s = 2, we get c = 2s Substituting these values into the equation s + w + m + c = 240: s + (4/5)s + (1/5)s + 2s = 240 Multiplying the entire equation by 5 to get rid of fractions: 5s + 4s + s + 10s = 1200 20s = 1200 s = 1200/20 s = 60 Answer: {60}

Overall Quality: excellent

The reasoning chain correctly sets up the system of linear equations based on the given ratios and the total sum constraint (s+w+m+c=240) and solves it accurately to find s=60.

✓ No hallucinations detected

Question #123

Clean

Full Question

Luis picks 55 grapes on Friday. Then he picks 170 grapes on Saturday. On Sunday, he picks quintuple the number of grapes he did on Friday. On Monday, he picks half the amount of what he picked in the past 3 days combined. On Tuesday, Luis is going to sell grapes in boxes of 15 grapes each. He is going to sell each box for $10. How much is Luis going to make?

Ground Truth Answer

Combining Friday and Saturday, Luis has 55 grapes + 170 grapes = 225 grapes. On Sunday, he picks 5 * 55 grapes = 275 grapes. Altogether, Luis has 225 grapes + 275 grapes = 500 grapes. Finally he collected 500 / 2 = 250 on Monday. The total is 500 + 250 = 750. Each box is going to have 15 grapes. So Luis needs 750 / 15 = 50 boxes. He is going to sell each box for $10, so he is going to earn $50 * 10 = $500 #### 500

Generated Answer

Here's how to solve this problem step by step: 1. **Sunday's grapes:** Luis picks 55 * 5 = 275 grapes on Sunday. 2. **Total grapes from Friday, Saturday, and Sunday:** 55 + 170 + 275 = 500 grapes 3. **Monday's grapes:** Luis picks 500 / 2 = 250 grapes on Monday. 4. **Total grapes for all four days:** 500 + 250 = 750 grapes 5. **Boxes of grapes:** Luis has 750 / 15 = 50 boxes of grapes. 6. **Total earnings:** Luis makes 50 boxes * $10/box = $500 Answer: {500}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #125

Clean

Full Question

Umar picks 147 apples on Sunday. Then he picks 99 apples on Monday. On Tuesday, he picks double the number of apples he did on Sunday. On Wednesday, he picks half the amount of what he picked in the past 3 days combined. On Thursday, Umar is going to sell apples in boxes of 27 apples each. He is going to sell each box for $11. How much is Umar going to make?

Ground Truth Answer

Combining Sunday and Monday, Umar has 147 apples + 99 apples = 246 apples. On Tuesday, he picks 2 * 147 apples = 294 apples. Altogether, Umar has 246 apples + 294 apples = 540 apples. Finally he collected 540 / 2 = 270 on Wednesday. The total is 540 + 270 = 810. Each box is going to have 27 apples. So Umar needs 810 / 27 = 30 boxes. He is going to sell each box for $11, so he is going to earn $30 * 11 = $330 #### 330

Generated Answer

Here's how to break down this problem: 1. **Tuesday's Apples:** Umar picked double the number of Sunday's apples on Tuesday, so he picked 147 * 2 = 294 apples. 2. **Total Apples (Sun-Tue):** Over Sunday, Monday, and Tuesday, Umar picked 147 + 99 + 294 = 540 apples. 3. **Wednesday's Apples:** On Wednesday, Umar picked half the total from the previous three days, so he picked 540 / 2 = 270 apples. 4. **Total Apples (Sun-Wed):** In total, Umar picked 540 + 270 = 810 apples. 5. **Boxes of Apples:** Umar can fill 810 / 27 = 30 boxes with apples. 6. **Total Earnings:** Umar will earn 30 boxes * $11/box = $330. Answer: {330}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #277

Clean

Full Question

Greenville High School is holding graduation in its Convention Center this year which has space for 7700 people. After accounting for the 550 seats for graduate, 450 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally?

Ground Truth Answer

Add graduate and faculty seats together. 550 + 450 = 1000 seats for faculty and graduates Minus seats for faculty and graduates from total seats allowed. 7700 - 1000 = 6700 remaining seats. Minus seats reserved: 6700 - 100 = 6600 seats remains. Divide amount of remaining seats by the number of graduates: 6600/550 = 12 tickets #### 12

Generated Answer

First, calculate the total number of seats already allocated: 550 (graduates) + 450 (faculty) + 100 (staff) = 1100 seats. Next, subtract the allocated seats from the total capacity to find the number of seats remaining for friends and family: 7700 - 1100 = 6600 seats. Finally, divide the remaining seats by the number of graduates to find out how many tickets each graduate receives: 6600 / 550 = 12 tickets. Answer: {12}

Overall Quality: excellent

The reasoning chain correctly identifies all necessary steps: summing allocated seats, subtracting this total from the capacity, and then dividing the remainder by the number of graduates. All arithmetic operations are performed correctly.

✓ No hallucinations detected

Question #279

Clean

Full Question

Greenville High School is holding graduation in its Convention Center this year which has space for 3900 people. After accounting for the 1150 seats for graduate, 400 seats for the faculty attending, and reserving 50 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally?

Ground Truth Answer

Add graduate and faculty seats together. 1150 + 400 = 1550 seats for faculty and graduates Minus seats for faculty and graduates from total seats allowed. 3900 - 1550 = 2350 remaining seats. Minus seats reserved: 2350 - 50 = 2300 seats remains. Divide amount of remaining seats by the number of graduates: 2300/1150 = 2 tickets #### 2

Generated Answer

First, find the total number of seats taken by graduates, faculty, and staff: 1150 + 400 + 50 = 1600 seats. Next, subtract the taken seats from the total capacity to find the number of seats available for friends and family: 3900 - 1600 = 2300 seats. Finally, divide the number of available seats by the number of graduates to find out how many tickets each graduate receives: 2300 / 1150 = 2 tickets per graduate. Answer: {2}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the requirements of the problem, leading to the correct answer.

✓ No hallucinations detected

Question #31

Clean

Full Question

Olga makes coffee using teaspoons of sugar and cups of water in a ratio of 48:10. She also uses 6 tablespoons of milk for every 10 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 210 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?

Ground Truth Answer

Olga uses 2 tablespoons of cream for every teaspoon of sugar. For 48 teaspoons of sugar, she uses 2 * 48 = 96 tablespoons of heavy cream. Olga uses 6 tablespoons of milk for every 10 cups of water. For 10 cups water she uses 6*10/10 = 6 tablespoons of milk. The total ratio representing the ingredients she used to make the coffee is 48 sugar +10 water +6 milk + 96 heavy cream= 160. Since the fraction representing the number of teaspoons of sugar she used is 48/160, she used 48/160*210 = 63 #### 63

Generated Answer

Let S be the amount of sugar in teaspoons, W be the amount of water in cups, M be the amount of milk in tablespoons, and C be the amount of heavy cream in tablespoons. We are given that S:W = 48:10, which simplifies to 24:5. Thus, S = (24/5)W. We are also given that M:W = 6:10, which simplifies to 3:5. Thus, M = (3/5)W. Finally, we are given that C:S = 2:1. Thus, C = 2S. We are told that the total amount of ingredients is 210. So S + W + M + C = 210. Substituting the expressions for S, M, and C in terms of W, we get: (24/5)W + W + (3/5)W + 2(24/5)W = 210 (24/5)W + (5/5)W + (3/5)W + (48/5)W = 210 (24+5+3+48)/5 W = 210 (80/5)W = 210 16W = 210 W = 210/16 = 105/8 Now we can find S: S = (24/5)W = (24/5)(105/8) = (24/1)(21/8) = 3*21 = 63 The amount of sugar Olga used is 63 teaspoons. Answer: {63}

Overall Quality: excellent

The reasoning chain correctly translates the ratios into algebraic expressions, sets up the total sum equation, solves for the variable W, and correctly calculates the required quantity S. No mathematical or logical errors were found.

✓ No hallucinations detected

Question #122

Clean

Full Question

Leon picks 80 apples on Thursday. Then he picks 50 apples on Friday. On Saturday, he picks triple the number of apples he did on Thursday. On Sunday, he picks half the amount of what he picked in the past 3 days combined. On Monday, Leon is going to sell apples in boxes of 15 apples each. He is going to sell each box for $12. How much is Leon going to make?

Ground Truth Answer

Combining Thursday and Friday, Leon has 80 apples + 50 apples = 130 apples. On Saturday, he picks 3 * 80 apples = 240 apples. Altogether, Leon has 130 apples + 240 apples = 370 apples. Finally he collected 370 / 2 = 185 on Sunday. The total is 370 + 185 = 555. Each box is going to have 15 apples. So Leon needs 555 / 15 = 37 boxes. He is going to sell each box for $12, so he is going to earn $37 * 12 = $444 #### 444

Generated Answer

On Thursday, Leon picks 80 apples. On Friday, he picks 50 apples. On Saturday, he picks 80 * 3 = 240 apples. The total for the first three days is 80 + 50 + 240 = 370 apples. On Sunday, he picks 370 / 2 = 185 apples. The total number of apples Leon picks is 80 + 50 + 240 + 185 = 555 apples. The number of boxes he can sell is 555 / 15 = 37 boxes. The amount of money Leon will make is 37 * $12 = $444. Answer: {444}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #21

Clean

Full Question

A group of 150 students has various hobbies. 27 like to play music, 8 like to play chess, 13 like to swim, 9 like to play football, and the rest like to either paint or play video games. What percentage of the students like to paint if the number of the students that like to play video games is 3 less than two times the number that prefer playing football?

Ground Truth Answer

The number of students that like to play video games is 3 less than 2 times as many as the number who like football, so 2 * 9 - 3 = 15 The number that like to paint is 150 total students - 27 play music - 9 football - 15 play video games - 13 swim - 8 chess = 78. To calculate the percentage, we divide this number of by 150 and multiply by 100: 78 / 150 = 0.52 * 100 = 52% #### 52

Generated Answer

First, calculate the number of students who like to play video games. It's 3 less than two times the number who like football, which is 2 * 9 - 3 = 15 students. Next, find the total number of students with hobbies other than painting or video games. That's 27 + 8 + 13 + 9 = 57 students. Then, subtract the number of students with other hobbies from the total number of students to find the number of students who like painting or video games: 150 - 57 = 93 students. Now, subtract the number of students who like video games from the total number of students who like painting or video games to find the number who like painting: 93 - 15 = 78 students. Finally, calculate the percentage of students who like to paint: (78/150) * 100 = 52%. Answer: {52}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement. All arithmetic calculations are accurate, and the logic used to isolate the number of students who paint and then calculate the percentage is sound.

✓ No hallucinations detected

Question #36

Clean

Full Question

Hiroshi has 20 hectares of apricot field. There are 28 apricots per two-fourths of a hectare. Hiroshi can harvest his apricots every 6 months. In addition, Hiroshi owns a 12-hectare grape field that produces 14 grapes per hectare. The grapes can be harvested every 4 months. In the span of two years, how many more apricots does Hiroshi harvest than grapes?

Ground Truth Answer

Hiroshi has 28 x 20= 560 apricots on 1/2 of his field. In total Hiroshi can get, 1÷1/2 = 2 times more, meaning 560*2=1120. Hiroshi can harvest his apricot 12 ÷ 6 = 2 times per year Therefore Hiroshi can harvest 1120 x 2 = 2240 apricots per year. There are 14 grapes per hectare of the second field. In total, there are 12*14 = 168 grapes. Since Hiroshi can harvest his grapes 12 ÷ 4 = 3 times a year, he can harvest 168 * 3 = 504 grapes in a year. Each year, Hiroshi harvests 2240 apricots - 504 grapes = 1736 more apricots. So in two years, Hiroshi will produce 2 * 1736 = 3472 more. #### 3472

Generated Answer

First, calculate the number of apricots harvested per hectare: 28 apricots / (2/4 hectare) = 28 apricots / (1/2 hectare) = 56 apricots/hectare. Hiroshi has 20 hectares of apricot field, so he harvests 56 apricots/hectare * 20 hectares = 1120 apricots every 6 months. Over two years (which is 24 months), there are 24 months / 6 months/harvest = 4 harvests. So, in two years, Hiroshi harvests 1120 apricots/harvest * 4 harvests = 4480 apricots. Next, calculate the number of grapes harvested per hectare: 14 grapes/hectare. Hiroshi has 12 hectares of grape field, so he harvests 14 grapes/hectare * 12 hectares = 168 grapes every 4 months. Over two years (24 months), there are 24 months / 4 months/harvest = 6 harvests. So, in two years, Hiroshi harvests 168 grapes/harvest * 6 harvests = 1008 grapes. Finally, find the difference in harvested apricots and grapes: 4480 apricots - 1008 grapes = 3472 more apricots. Answer: {3472}

Overall Quality: excellent

The reasoning chain correctly interprets all parts of the problem, performs all calculations accurately, and arrives at the correct final answer, matching the ground truth.

✓ No hallucinations detected

Question #30

Clean

Full Question

Olivia makes tea using teaspoons of sugar and cups of water in a ratio of 51:5. She also uses 7 tablespoons of milk for every 5 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 220 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?

Ground Truth Answer

Olivia uses 2 tablespoons of cream for every teaspoon of sugar. For 51 teaspoons of sugar, she uses 2 * 51 = 102 tablespoons of heavy cream. Olivia uses 7 tablespoons of milk for every 5 cups of water. For 5 cups water she uses 7*5/5 = 7 tablespoons of milk. The total ratio representing the ingredients she used to make the tea is 51 sugar +5 water +7 milk + 102 heavy cream= 165. Since the fraction representing the number of teaspoons of sugar she used is 51/165, she used 51/165*220 = 68 #### 68

Generated Answer

Let 's' be the number of teaspoons of sugar Olivia used, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. We are given the following ratios: Sugar to water: s:w = 51:5 Milk to water: m:w = 7:5 Cream to sugar: c:s = 2:1 We are also given that the total quantity of all ingredients is 220, so s + w + m + c = 220. From the sugar to water ratio, we have w = (5/51)s. From the milk to water ratio, we have m = (7/5)w = (7/5) * (5/51)s = (7/51)s. From the cream to sugar ratio, we have c = 2s. Substituting these expressions into the total quantity equation, we get: s + (5/51)s + (7/51)s + 2s = 220 Multiplying both sides by 51 to eliminate fractions: 51s + 5s + 7s + 102s = 220 * 51 165s = 11220 s = 11220 / 165 s = 68 Answer: {68}

Overall Quality: excellent

The reasoning chain correctly sets up the proportional relationships between the four ingredients, substitutes them into the total quantity equation (s + w + m + c = 220), and solves the resulting linear equation accurately.

✓ No hallucinations detected

Question #33

Clean

Full Question

Mia makes coffee using teaspoons of sugar and cups of water in a ratio of 48:7. She also uses 9 tablespoons of milk for every 7 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 170 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?

Ground Truth Answer

Mia uses 2 tablespoons of cream for every teaspoon of sugar. For 48 teaspoons of sugar, she uses 2 * 48 = 96 tablespoons of heavy cream. Mia uses 9 tablespoons of milk for every 7 cups of water. For 7 cups water she uses 9*7/7 = 9 tablespoons of milk. The total ratio representing the ingredients she used to make the coffee is 48 sugar +7 water +9 milk + 96 heavy cream= 160. Since the fraction representing the number of teaspoons of sugar she used is 48/160, she used 48/160*170 = 51 #### 51

Generated Answer

Let S be the amount of sugar Mia used (in teaspoons), W be the amount of water she used (in cups), M be the amount of milk she used (in tablespoons), and C be the amount of cream she used (in tablespoons). We are given the following ratios: S:W = 48:7 M:W = 9:7 C:S = 2:1 We are given that S + W + M + C = 170. From S:W = 48:7, we have W = (7/48)S. From M:W = 9:7, we have M = (9/7)W = (9/7)*(7/48)S = (9/48)S = (3/16)S. From C:S = 2:1, we have C = 2S. Now substitute these expressions for W, M, and C into the equation S + W + M + C = 170: S + (7/48)S + (3/16)S + 2S = 170 S + (7/48)S + (9/48)S + 2S = 170 S + (16/48)S + 2S = 170 S + (1/3)S + 2S = 170 (1 + 1/3 + 2)S = 170 (10/3)S = 170 S = 170 * (3/10) S = 51 Answer: {51}

Overall Quality: excellent

The reasoning chain correctly sets up the algebraic relationships based on the given ratios and solves the resulting linear equation accurately. No mathematical or logical errors were found.

✓ No hallucinations detected

Question #62

Clean

Full Question

To make a call from a hotel room phone, you must pay €0.4 for each minute of your call. After 15 minutes, the price drops to €0.3 per minute. After 35 minutes from the start of the call, the price drops even more to €0.2 per two minutes. If your total bill is more than €15, you get a 10% discount on your total bill. How much would a 115-minute call cost?

Ground Truth Answer

First 15 minutes would be a cost of 15 * 0.4 = €6. After that, the next 35 - 15 = 20 minutes of the call will cost 0.3. And these 20 minutes cost 20 * 0.3 = €6. Then from 35 to 115, there are 115-35=80 minutes that cost 0.2 per two minutes. Since there are 80 / 2 = 40 intervals of two minutes, the cost for final part of the call will be 0.2 * 40 = 8. Overall the cost is 6 + 6 + 8 = 20. Since 20 > 15, we get a 10% discount. 10% * 20 = 2. So the total bill is 20 - 2.0 = 18 #### 18

Generated Answer

Here's how to break down the cost of the 115-minute call: * **First 15 minutes:** 15 minutes * €0.4/minute = €6 * **Next 20 minutes (minutes 16-35):** 20 minutes * €0.3/minute = €6 * **Remaining 80 minutes (minutes 36-115):** 80 minutes / 2 minutes/€0.2 = 40 * €0.2 = €8 **Total cost before discount:** €6 + €6 + €8 = €20 **Discount:** Since €20 > €15, a 10% discount applies: €20 * 0.10 = €2 **Final cost:** €20 - €2 = €18 Answer: {18}

Overall Quality: excellent

The reasoning chain correctly calculates the cost for each segment of the call, sums them up, correctly applies the discount condition, and calculates the final cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #64

Clean

Full Question

To make a call from a hotel room phone, you must pay ₺0.6 for each minute of your call. After 10 minutes, the price drops to ₺0.4 per minute. After 35 minutes from the start of the call, the price drops even more to ₺0.1 per two minutes. If your total bill is more than ₺15, you get a 15% discount on your total bill. How much would a 115-minute call cost?

Ground Truth Answer

First 10 minutes would be a cost of 10 * 0.6 = ₺6. After that, the next 35 - 10 = 25 minutes of the call will cost 0.4. And these 25 minutes cost 25 * 0.4 = ₺10. Then from 35 to 115, there are 115-35=80 minutes that cost 0.1 per two minutes. Since there are 80 / 2 = 40 intervals of two minutes, the cost for final part of the call will be 0.1 * 40 = 4. Overall the cost is 6 + 10 + 4 = 20. Since 20 > 15, we get a 15% discount. 15% * 20 = 3. So the total bill is 20 - 3.0 = 17 #### 17

Generated Answer

Here's how to break down the cost of the 115-minute call: * **Minutes 1-10:** 10 minutes * ₺0.6/minute = ₺6.0 * **Minutes 11-35:** 25 minutes * ₺0.4/minute = ₺10.0 * **Minutes 36-115:** 80 minutes. Since the rate is ₺0.1 per two minutes, this portion costs (80 minutes / 2 minutes) * ₺0.1 = ₺4.0 **Total cost before discount:** ₺6.0 + ₺10.0 + ₺4.0 = ₺20.0 Since ₺20.0 > ₺15, a 15% discount applies: **Discount amount:** ₺20.0 * 0.15 = ₺3.0 **Final cost:** ₺20.0 - ₺3.0 = ₺17.0 Answer: {17}

Overall Quality: excellent

The reasoning chain correctly calculates the cost for each segment of the call, sums them up, correctly applies the discount condition, calculates the discount amount, and determines the final cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #65

Clean

Full Question

To make a call from a hotel room phone, you must pay ¥0.9 for each minute of your call. After 10 minutes, the price drops to ¥0.6 per minute. After 35 minutes from the start of the call, the price drops even more to ¥0.4 per two minutes. If your total bill is more than ¥15, you get a 20% discount on your total bill. How much would a 65-minute call cost?

Ground Truth Answer

First 10 minutes would be a cost of 10 * 0.9 = ¥9. After that, the next 35 - 10 = 25 minutes of the call will cost 0.6. And these 25 minutes cost 25 * 0.6 = ¥15. Then from 35 to 65, there are 65-35=30 minutes that cost 0.4 per two minutes. Since there are 30 / 2 = 15 intervals of two minutes, the cost for final part of the call will be 0.4 * 15 = 6. Overall the cost is 9 + 15 + 6 = 30. Since 30 > 15, we get a 20% discount. 20% * 30 = 6. So the total bill is 30 - 6.0 = 24 #### 24

Generated Answer

Here's how to break down the cost of the 65-minute call: * **Minutes 1-10:** 10 minutes * ¥0.9/minute = ¥9 * **Minutes 11-35:** 25 minutes * ¥0.6/minute = ¥15 * **Minutes 36-65:** 30 minutes. Since the rate is ¥0.4 per two minutes, this portion costs (30 minutes / 2 minutes) * ¥0.4 = 15 * ¥0.4 = ¥6 Total cost before discount: ¥9 + ¥15 + ¥6 = ¥30 Since ¥30 > ¥15, a 20% discount applies: ¥30 * 0.20 = ¥6 Final cost: ¥30 - ¥6 = ¥24 Answer: {24}

Overall Quality: excellent

The reasoning chain correctly calculates the cost for each segment of the call, sums them up correctly, applies the discount logic correctly, and arrives at the correct final answer. All arithmetic operations are correct.

✓ No hallucinations detected

Question #35

Clean

Full Question

Uma makes tea using teaspoons of sugar and cups of water in a ratio of 45:5. She also uses 8 tablespoons of milk for every 4 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 210 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use?

Ground Truth Answer

Uma uses 2 tablespoons of cream for every teaspoon of sugar. For 45 teaspoons of sugar, she uses 2 * 45 = 90 tablespoons of heavy cream. Uma uses 8 tablespoons of milk for every 4 cups of water. For 5 cups water she uses 8*5/4 = 10 tablespoons of milk. The total ratio representing the ingredients she used to make the tea is 45 sugar +5 water +10 milk + 90 heavy cream= 150. Since the fraction representing the number of teaspoons of sugar she used is 45/150, she used 45/150*210 = 63 #### 63

Generated Answer

Let S be the number of teaspoons of sugar Uma used, W be the number of cups of water, M be the number of tablespoons of milk, and C be the number of tablespoons of heavy cream. We are given that the ratio of sugar to water is 45:5, which simplifies to 9:1. So, S = 9W. We are also given that Uma uses 8 tablespoons of milk for every 4 cups of water. So, M = 2W. Finally, we are given that Uma uses 2 tablespoons of heavy cream for every teaspoon of sugar. So, C = 2S. We are told that the total number of teaspoons, cups, and tablespoons is 210. So, S + W + M + C = 210 Substituting the expressions for S, M, and C in terms of W, we have: 9W + W + 2W + 2(9W) = 210 9W + W + 2W + 18W = 210 30W = 210 W = 210 / 30 W = 7 Now we can find S: S = 9W = 9 * 7 = 63 So, Uma used 63 teaspoons of sugar. Answer: {63}

Overall Quality: excellent

The reasoning chain correctly establishes the relationships between the variables based on the given ratios and correctly solves the resulting linear equation derived from the total quantity constraint. All arithmetic is correct, leading to the correct answer.

✓ No hallucinations detected

Question #61

Clean

Full Question

To make a call from a phone booth, you must pay ₺0.9 for each minute of your call. After 10 minutes, the price drops to ₺0.6 per minute. After 35 minutes from the start of the call, the price drops even more to ₺0.4 per two minutes. If your total bill is more than ₺25, you get a 20% discount on your total bill. How much would a 115-minute call cost?

Ground Truth Answer

First 10 minutes would be a cost of 10 * 0.9 = ₺9. After that, the next 35 - 10 = 25 minutes of the call will cost 0.6. And these 25 minutes cost 25 * 0.6 = ₺15. Then from 35 to 115, there are 115-35=80 minutes that cost 0.4 per two minutes. Since there are 80 / 2 = 40 intervals of two minutes, the cost for final part of the call will be 0.4 * 40 = 16. Overall the cost is 9 + 15 + 16 = 40. Since 40 > 25, we get a 20% discount. 20% * 40 = 8. So the total bill is 40 - 8.0 = 32 #### 32

Generated Answer

Here's how to break down the cost of the 115-minute call: * **Minutes 1-10:** 10 minutes * ₺0.9/minute = ₺9 * **Minutes 11-35:** 25 minutes * ₺0.6/minute = ₺15 * **Minutes 36-115:** 80 minutes. Since the rate is ₺0.4 per two minutes, this portion costs (80 minutes / 2 minutes) * ₺0.4 = 40 * ₺0.4 = ₺16 **Total cost before discount:** ₺9 + ₺15 + ₺16 = ₺40 Since ₺40 is greater than ₺25, a 20% discount applies: **Discount:** ₺40 * 0.20 = ₺8 **Final cost:** ₺40 - ₺8 = ₺32 Answer: {32}

Overall Quality: excellent

The reasoning chain correctly calculates the cost for each segment of the call, sums them up, applies the discount correctly based on the threshold, and arrives at the correct final cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #63

Clean

Full Question

To make a call from a phone booth, you must pay ₺0.8 for each minute of your call. After 10 minutes, the price drops to ₺0.7 per minute. After 30 minutes from the start of the call, the price drops even more to ₺0.4 per two minutes. If your total bill is more than ₺15, you get a 15% discount on your total bill. How much would a 120-minute call cost?

Ground Truth Answer

First 10 minutes would be a cost of 10 * 0.8 = ₺8. After that, the next 30 - 10 = 20 minutes of the call will cost 0.7. And these 20 minutes cost 20 * 0.7 = ₺14. Then from 30 to 120, there are 120-30=90 minutes that cost 0.4 per two minutes. Since there are 90 / 2 = 45 intervals of two minutes, the cost for final part of the call will be 0.4 * 45 = 18. Overall the cost is 8 + 14 + 18 = 40. Since 40 > 15, we get a 15% discount. 15% * 40 = 6. So the total bill is 40 - 6.0 = 34 #### 34

Generated Answer

Here's how to break down the cost of the 120-minute call: * **First 10 minutes:** 10 minutes * ₺0.8/minute = ₺8 * **Next 20 minutes:** 20 minutes * ₺0.7/minute = ₺14 * **Remaining 90 minutes:** 90 minutes / 2 minutes/unit = 45 units * ₺0.4/unit = ₺18 **Total cost before discount:** ₺8 + ₺14 + ₺18 = ₺40 Since ₺40 > ₺15, a 15% discount applies: **Discount amount:** ₺40 * 0.15 = ₺6 **Final cost:** ₺40 - ₺6 = ₺34 Answer: {34}

Overall Quality: excellent

✓ No hallucinations detected

Question #18

Clean

Full Question

A group of 290 students has various hobbies. 12 like to paint, 8 like to play chess, 13 like to swim, 39 like to play cricket, and the rest like to either play video games or hike. What percentage of the students like to play video games if the number of the students that like to hike is 5 less than two times the number that prefer playing cricket?

Ground Truth Answer

The number of students that like to hike is 5 less than 2 times as many as the number who like cricket, so 2 * 39 - 5 = 73 The number that like to play video games is 290 total students - 12 paint - 39 cricket - 73 hike - 13 swim - 8 chess = 145. To calculate the percentage, we divide this number of by 290 and multiply by 100: 145 / 290 = 0.5 * 100 = 50% #### 50

Generated Answer

First, we find the number of students who like to hike. It is given that this number is 5 less than two times the number of students who like to play cricket. Since 39 students like to play cricket, the number of students who like to hike is 2 * 39 - 5 = 78 - 5 = 73. Next, we find the total number of students who have hobbies other than video games or hiking. This is the sum of students who like painting, playing chess, swimming, and playing cricket, which is 12 + 8 + 13 + 39 = 72 students. The total number of students who like to play video games or hike is the total number of students minus the number of students with other hobbies, which is 290 - 72 = 218. Since 73 students like to hike, the number of students who like to play video games is 218 - 73 = 145. Finally, we can find the percentage of students who like to play video games. This is calculated as (number of students who like video games / total number of students) * 100 = (145 / 290) * 100 = 0.5 * 100 = 50%. Answer: {50}

Overall Quality: excellent

The reasoning chain correctly calculates the number of students who like to hike, correctly sums the known hobbies, correctly derives the number of video game players by subtraction, and correctly calculates the final percentage. All arithmetic and logic steps align with the problem statement and ground truth.

✓ No hallucinations detected

Question #60

Clean

Full Question

To make a call from a phone booth, you must pay $0.7 for each minute of your call. After 10 minutes, the price drops to $0.5 per minute. After 30 minutes from the start of the call, the price drops even more to $0.1 per two minutes. If your total bill is more than $15, you get a 15% discount on your total bill. How much would a 90-minute call cost?

Ground Truth Answer

First 10 minutes would be a cost of 10 * 0.7 = $7. After that, the next 30 - 10 = 20 minutes of the call will cost 0.5. And these 20 minutes cost 20 * 0.5 = $10. Then from 30 to 90, there are 90-30=60 minutes that cost 0.1 per two minutes. Since there are 60 / 2 = 30 intervals of two minutes, the cost for final part of the call will be 0.1 * 30 = 3. Overall the cost is 7 + 10 + 3 = 20. Since 20 > 15, we get a 15% discount. 15% * 20 = 3. So the total bill is 20 - 3.0 = 17 #### 17

Generated Answer

Here's how to break down the cost of the 90-minute call: * **Minutes 1-10:** 10 minutes * $0.7/minute = $7.00 * **Minutes 11-30:** 20 minutes * $0.5/minute = $10.00 * **Minutes 31-90:** 60 minutes. Since the rate is $0.1 per 2 minutes, this portion costs (60 minutes / 2 minutes) * $0.1 = $3.00 **Total cost before discount:** $7.00 + $10.00 + $3.00 = $20.00 Since the total cost is over $15, a 15% discount applies: **Discount amount:** $20.00 * 0.15 = $3.00 **Final cost:** $20.00 - $3.00 = $17.00 Answer: {17}

Overall Quality: excellent

✓ No hallucinations detected

Question #238

Clean

Full Question

A cleaner has to clean a hospital with 90 floors. They have 10 days to get it done. It takes them 10 minutes per floor. However, due to a recent injury, the cleaner has become slower and it will take them twice as long to clean a floor these days. If they work for 15 hours a day, what percentage of their day, on average, is spent cleaning floors?

Ground Truth Answer

They have to clean 9 floors a day because 90 / 10 = 9 They spend 180 minutes cleaning per day because 9 x 20 = 180 They spend 3.0 hours a day because 180 / 60 = 3.0 They spend 0.2 of their day cleaning floors because 3.0 / 15 = 0.2 They spend 20% of their day cleaning floors because 0.2 x 100 = 20 #### 20

Generated Answer

It takes the cleaner 10 minutes * 2 = 20 minutes per floor now. They need to clean 90 floors * 20 minutes/floor = 1800 minutes total. Over 10 days, that's 1800 minutes / 10 days = 180 minutes per day. 15 hours is 15 hours * 60 minutes/hour = 900 minutes. The percentage of their day spent cleaning is 180 minutes / 900 minutes * 100% = 20%. Answer: {20}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem constraints, leading to the correct answer.

✓ No hallucinations detected

Question #278

Clean

Full Question

Riverside Academy is holding graduation in its Gymnasium this year which has space for 7800 people. After accounting for the 1050 seats for graduate, 350 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally?

Ground Truth Answer

Add graduate and faculty seats together. 1050 + 350 = 1400 seats for faculty and graduates Minus seats for faculty and graduates from total seats allowed. 7800 - 1400 = 6400 remaining seats. Minus seats reserved: 6400 - 100 = 6300 seats remains. Divide amount of remaining seats by the number of graduates: 6300/1050 = 6 tickets #### 6

Generated Answer

First, calculate the total number of seats used by graduates, faculty, and staff: 1050 + 350 + 100 = 1500 seats. Next, subtract the used seats from the total capacity of the gymnasium: 7800 - 1500 = 6300 seats. Finally, divide the remaining seats by the number of graduates to find out how many tickets each graduate receives: 6300 / 1050 = 6 tickets. Answer: {6}

Overall Quality: excellent

The reasoning chain correctly identifies the steps needed: summing up reserved seats, subtracting them from the total, and then dividing the remainder by the number of graduates. All arithmetic operations performed are mathematically correct.

✓ No hallucinations detected

Question #280

Clean

Full Question

Riverside Academy is holding graduation in its Gymnasium this year which has space for 8900 people. After accounting for the 1050 seats for graduate, 400 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally?

Ground Truth Answer

Add graduate and faculty seats together. 1050 + 400 = 1450 seats for faculty and graduates Minus seats for faculty and graduates from total seats allowed. 8900 - 1450 = 7450 remaining seats. Minus seats reserved: 7450 - 100 = 7350 seats remains. Divide amount of remaining seats by the number of graduates: 7350/1050 = 7 tickets #### 7

Generated Answer

First, calculate the number of seats remaining for friends and family by subtracting the reserved seats (graduates, faculty, and staff) from the total capacity of the gymnasium. Then, divide the remaining seats by the number of graduates to determine how many tickets each graduate receives. 8900 (total seats) - 1050 (graduate seats) - 400 (faculty seats) - 100 (staff seats) = 7350 seats for friends and family. 7350 (seats for friends and family) / 1050 (graduates) = 7 tickets per graduate. Answer: {7}

Overall Quality: excellent

The reasoning correctly identifies all necessary subtractions to find the remaining seats and then correctly divides those remaining seats by the number of graduates to find the tickets per graduate. All arithmetic operations are correct.

✓ No hallucinations detected

Question #236

Clean

Full Question

A janitor has to clean a building with 135 floors. They have 3 days to get it done. It takes them 5 minutes per floor. However, due to a recent injury, the janitor has become slower and it will take them twice as long to clean a floor these days. If they work for 15 hours a day, what percentage of their day, on average, is spent cleaning floors?

Ground Truth Answer

They have to clean 45 floors a day because 135 / 3 = 45 They spend 450 minutes cleaning per day because 45 x 10 = 450 They spend 7.5 hours a day because 450 / 60 = 7.5 They spend 0.5 of their day cleaning floors because 7.5 / 15 = 0.5 They spend 50% of their day cleaning floors because 0.5 x 100 = 50 #### 50

Generated Answer

It takes the janitor twice as long to clean a floor, so it now takes 5 minutes * 2 = 10 minutes per floor. There are 135 floors, so it will take 135 floors * 10 minutes/floor = 1350 minutes to clean all floors. Over 3 days, this is 1350 minutes / 3 days = 450 minutes per day. The janitor works 15 hours/day * 60 minutes/hour = 900 minutes per day. The percentage of the day spent cleaning is 450 minutes cleaning / 900 minutes workday * 100% = 50%. Answer: {50}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are accurate, and the logic correctly incorporates the increased cleaning time and the total available work time.

✓ No hallucinations detected

Question #281

Clean

Full Question

Riverside Academy is holding graduation in its Gymnasium this year which has space for 7300 people. After accounting for the 700 seats for graduate, 200 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally?

Ground Truth Answer

Add graduate and faculty seats together. 700 + 200 = 900 seats for faculty and graduates Minus seats for faculty and graduates from total seats allowed. 7300 - 900 = 6400 remaining seats. Minus seats reserved: 6400 - 100 = 6300 seats remains. Divide amount of remaining seats by the number of graduates: 6300/700 = 9 tickets #### 9

Generated Answer

First, find the total number of seats taken up by the graduates, faculty, and staff: 700 + 200 + 100 = 1000 seats. Then, subtract the number of occupied seats from the total capacity of the gymnasium: 7300 - 1000 = 6300 seats. Finally, divide the remaining seats by the number of graduates to find out how many tickets each graduate receives: 6300 / 700 = 9 tickets. Answer: {9}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the steps required to solve the problem, resulting in the correct answer.

✓ No hallucinations detected

Question #239

Clean

Full Question

A cleaner has to clean a hospital with 135 floors. They have 5 days to get it done. It takes them 5 minutes per floor. However, due to a recent injury, the cleaner has become slower and it will take them twice as long to clean a floor these days. If they work for 9 hours a day, what percentage of their day, on average, is spent cleaning floors?

Ground Truth Answer

They have to clean 27 floors a day because 135 / 5 = 27 They spend 270 minutes cleaning per day because 27 x 10 = 270 They spend 4.5 hours a day because 270 / 60 = 4.5 They spend 0.5 of their day cleaning floors because 4.5 / 9 = 0.5 They spend 50% of their day cleaning floors because 0.5 x 100 = 50 #### 50

Generated Answer

It now takes the cleaner 5 minutes * 2 = 10 minutes per floor. The total time it will take to clean the hospital is 135 floors * 10 minutes/floor = 1350 minutes. The cleaner works 9 hours/day * 60 minutes/hour = 540 minutes/day. Over 5 days, they work 540 minutes/day * 5 days = 2700 minutes. The percentage of their day spent cleaning is (1350 minutes / 2700 minutes) * 100% = 50%. Answer: {50}

Overall Quality: excellent

The reasoning chain correctly interprets the problem constraints (new cleaning time, total time available) and performs all arithmetic calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #276

Clean

Full Question

Sunnyside High is holding graduation in its Sports Arena this year which has space for 7500 people. After accounting for the 600 seats for graduate, 250 seats for the faculty attending, and reserving 50 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally?

Ground Truth Answer

Add graduate and faculty seats together. 600 + 250 = 850 seats for faculty and graduates Minus seats for faculty and graduates from total seats allowed. 7500 - 850 = 6650 remaining seats. Minus seats reserved: 6650 - 50 = 6600 seats remains. Divide amount of remaining seats by the number of graduates: 6600/600 = 11 tickets #### 11

Generated Answer

First, calculate the total number of seats taken up by graduates, faculty, and staff: 600 + 250 + 50 = 900 seats. Then subtract the number of occupied seats from the total capacity of the arena to find the number of seats remaining for friends and family: 7500 - 900 = 6600 seats. Finally, divide the number of remaining seats by the number of graduates to determine how many tickets each graduate receives: 6600 / 600 = 11 tickets. Answer: {11}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem constraints, leading to the correct answer.

✓ No hallucinations detected

Question #237

Clean

Full Question

A cleaner has to clean a hospital with 60 floors. They have 3 days to get it done. It takes them 6 minutes per floor. However, due to a recent injury, the cleaner has become slower and it will take them twice as long to clean a floor these days. If they work for 8 hours a day, what percentage of their day, on average, is spent cleaning floors?

Ground Truth Answer

They have to clean 20 floors a day because 60 / 3 = 20 They spend 240 minutes cleaning per day because 20 x 12 = 240 They spend 4.0 hours a day because 240 / 60 = 4.0 They spend 0.5 of their day cleaning floors because 4.0 / 8 = 0.5 They spend 50% of their day cleaning floors because 0.5 x 100 = 50 #### 50

Generated Answer

It now takes the cleaner 6 * 2 = 12 minutes per floor. There are 60 floors, so it will take them 12 * 60 = 720 minutes to clean the entire hospital. They have 3 days to clean, so the total cleaning time will be spread over 3 days * 8 hours/day * 60 minutes/hour = 1440 minutes. The percentage of their day spent cleaning is 720 minutes / 1440 minutes * 100% = 50%. Answer: {50}

Overall Quality: excellent

The reasoning chain is mathematically sound and arrives at the correct final answer. All arithmetic operations are correct.

✓ No hallucinations detected

Question #95

Clean

Full Question

Deshawn's dog has 146 puppies, 28 of which have spots. Mohammed's dog has 43 puppies, 12 of which have spots. Hiroshi has 51 dogs, each having 11 puppies with spots. After a visit to the vet, DeShawn discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots?

Ground Truth Answer

First find the total number of puppies: 146 puppies + 43 puppies + 51*11 puppies = 750 puppies Then find the total number of puppies with spots: 28 puppies + 12 puppies + 561= 601 puppies. But after the vet visit we know that half of the DeShawn's unspotted puppies were actually spotted. So 1/2 * (146-28) = 1/2 * 118 = 59 puppies. We should add these to the total spotted puppies. 601 + 59 = 660. Then divide the number of spotted puppies by the total number of puppies and multiply by 100% to find the percentage of puppies with spots: 660 puppies / 750 puppies * 100% = 88% #### 88

Generated Answer

Deshawn's dog initially had 146 - 28 = 118 unspotted puppies. Half of these, or 118 / 2 = 59 puppies, were found to have spots. So, Deshawn's dog has a total of 28 + 59 = 87 puppies with spots. Mohammed's dog has 12 puppies with spots. Hiroshi's dogs have a total of 51 dogs * 11 puppies/dog = 561 puppies with spots. The total number of puppies is 146 + 43 + (51 * 11) = 146 + 43 + 561 = 750 puppies. The total number of spotted puppies is 87 + 12 + 561 = 660 puppies. The percentage of puppies with spots is (660 / 750) * 100% = 88%. Answer: {88}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #234

Clean

Full Question

A janitor has to clean a building with 80 rooms. They have 4 days to get it done. It takes them 6 minutes per room. However, due to a recent injury, the janitor has become slower and it will take them twice as long to clean a room these days. If they work for 10 hours a day, what percentage of their day, on average, is spent cleaning rooms?

Ground Truth Answer

They have to clean 20 rooms a day because 80 / 4 = 20 They spend 240 minutes cleaning per day because 20 x 12 = 240 They spend 4.0 hours a day because 240 / 60 = 4.0 They spend 0.4 of their day cleaning rooms because 4.0 / 10 = 0.4 They spend 40% of their day cleaning rooms because 0.4 x 100 = 40 #### 40

Generated Answer

It takes the janitor twice as long to clean a room now, so it takes 6 minutes * 2 = 12 minutes per room. There are 80 rooms, so it will take 12 minutes/room * 80 rooms = 960 minutes to clean all the rooms. The janitor works 10 hours a day * 60 minutes/hour = 600 minutes per day. The percentage of their day spent cleaning is (960 minutes / (4 days * 600 minutes/day)) * 100% = (960 minutes / 2400 minutes) * 100% = 0.4 * 100% = 40%. Answer: {40}

Overall Quality: excellent

The reasoning chain correctly calculates the time spent cleaning per room, the total time required, the total working time available over the 4 days, and finally determines the correct percentage of the day spent cleaning. All arithmetic operations are correct.

✓ No hallucinations detected

Question #6

Clean

Full Question

A fog bank rolls in from the ocean to cover a city. It takes 30 minutes to cover every 3 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 72 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover a quarter of the city?

Ground Truth Answer

To cover 1/4 of the city the fog needs 72 * 1/4 = 18 miles. In 1 hour, the fog will move 60/30*3 miles = 6 miles. The remaining distance after one hour is 18 miles - 6 miles = 12 miles. 12 miles is 12/3 = 4 intervals of 3 miles. Since the speed of wind is halved, it would take 2*30= 60 minutes for the fog to cover 3 miles. So it will take 4 * 60 = 240 minutes to cover the remaining 12 miles. In total, it will take 60 + 240 = 300 minutes to cover 1/4 of the city. #### 300

Generated Answer

The fog bank covers 3 miles every 30 minutes, which translates to a speed of 1 mile every 10 minutes. The city is 72 miles across. A quarter of the city is 72/4 = 18 miles. At the initial speed, it would take 18 miles * 10 minutes/mile = 180 minutes to cover a quarter of the city. However, the wind speed is halved in one hour (60 minutes). Since we are looking at how long it takes to cover 18 miles (which, at the original speed, would take 180 minutes, longer than 1 hour), the wind speed will be halved at some point during the fog's travel. For the first 60 minutes, the fog travels at its original speed, covering 60 minutes / 10 minutes/mile = 6 miles. This leaves 18 - 6 = 12 miles to cover. The speed is now halved, meaning it now takes 20 minutes to cover a mile. To cover the remaining 12 miles, it will take 12 miles * 20 minutes/mile = 240 minutes. Therefore, the total time to cover a quarter of the city is 60 minutes + 240 minutes = 300 minutes. Answer: {300}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the constraints provided in the problem. The final answer matches the ground truth.

✓ No hallucinations detected

Question #22

Clean

Full Question

A class of 100 students has various hobbies. 14 like to hike, 8 like to play chess, 13 like to swim, 2 like to play cricket, and the rest like to either dance or play music. What percentage of the students like to dance if the number of the students that like to play music is 5 less than ten times the number that prefer playing cricket?

Ground Truth Answer

The number of students that like to play music is 5 less than 10 times as many as the number who like cricket, so 10 * 2 - 5 = 15 The number that like to dance is 100 total students - 14 hike - 2 cricket - 15 play music - 13 swim - 8 chess = 48. To calculate the percentage, we divide this number of by 100 and multiply by 100: 48 / 100 = 0.48 * 100 = 48% #### 48

Generated Answer

First, sum the number of students with hobbies other than dancing or music: 14 (hiking) + 8 (chess) + 13 (swimming) + 2 (cricket) = 37 students. Next, subtract this sum from the total number of students to find the number of students who like to dance or play music: 100 - 37 = 63 students. The number of students who like to play music is 5 less than ten times the number that prefer playing cricket. Since 2 students like cricket, 10 * 2 - 5 = 15 students like music. Finally, subtract the number of students who like music from the number of students who like to dance or play music to find the number of students who like dancing: 63 - 15 = 48 students. To express this as a percentage, divide the number of students who like dancing by the total number of students and multiply by 100%: (48/100) * 100% = 48%. Answer: {48}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem statement. All calculations are correct.

✓ No hallucinations detected

Question #90

Clean

Full Question

Mateo's dog has 149 puppies, 25 of which have spots. Mohammed's dog has 49 puppies, 12 of which have spots. Ibrahim has 54 dogs, each having 13 puppies with spots. After a visit to the vet, Mateo discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots?

Ground Truth Answer

First find the total number of puppies: 149 puppies + 49 puppies + 54*13 puppies = 900 puppies Then find the total number of puppies with spots: 25 puppies + 12 puppies + 702= 739 puppies. But after the vet visit we know that half of the Mateo's unspotted puppies were actually spotted. So 1/2 * (149-25) = 1/2 * 124 = 62 puppies. We should add these to the total spotted puppies. 739 + 62 = 801. Then divide the number of spotted puppies by the total number of puppies and multiply by 100% to find the percentage of puppies with spots: 801 puppies / 900 puppies * 100% = 89% #### 89

Generated Answer

Mateo's dog initially had 149 - 25 = 124 unspotted puppies. Half of these, or 124 / 2 = 62 puppies, were found to have spots. So Mateo's dog has a total of 25 + 62 = 87 puppies with spots. Mohammed's dog has 12 puppies with spots. Ibrahim's dogs have a total of 54 * 13 = 702 puppies with spots. The total number of puppies is 149 + 49 + (54 * 13) = 149 + 49 + 702 = 900 puppies. The total number of puppies with spots is 87 + 12 + 702 = 801 puppies. The percentage of puppies with spots is (801 / 900) * 100 = 89%. Answer: {89}

Overall Quality: excellent

The reasoning chain correctly calculates the total number of puppies, correctly adjusts the number of spotted puppies based on the vet visit information, and accurately computes the final percentage. All arithmetic operations are correct.

✓ No hallucinations detected

Question #93

Clean

Full Question

Pavel's dog has 100 puppies, 22 of which have spots. Hiroshi's dog has 40 puppies, 15 of which have spots. Santiago has 55 dogs, each having 12 puppies with spots. After a visit to the vet, Pavel discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots?

Ground Truth Answer

First find the total number of puppies: 100 puppies + 40 puppies + 55*12 puppies = 800 puppies Then find the total number of puppies with spots: 22 puppies + 15 puppies + 660= 697 puppies. But after the vet visit we know that half of the Pavel's unspotted puppies were actually spotted. So 1/2 * (100-22) = 1/2 * 78 = 39 puppies. We should add these to the total spotted puppies. 697 + 39 = 736. Then divide the number of spotted puppies by the total number of puppies and multiply by 100% to find the percentage of puppies with spots: 736 puppies / 800 puppies * 100% = 92% #### 92

Generated Answer

Pavel's dog initially had 22 spotted puppies and 100 - 22 = 78 unspotted puppies. After the vet visit, half of the 78 unspotted puppies, or 78 / 2 = 39 puppies, were found to have spots. So, Pavel's dog has a total of 22 + 39 = 61 spotted puppies. Hiroshi's dog has 15 spotted puppies. Santiago's dogs have a total of 55 dogs * 12 spotted puppies/dog = 660 spotted puppies. The total number of puppies is 100 + 40 + (55 * 12) = 100 + 40 + 660 = 800 puppies. The total number of spotted puppies is 61 + 15 + 660 = 736 spotted puppies. The percentage of spotted puppies is (736 / 800) * 100% = 92%. Answer: {92}

Overall Quality: excellent

The reasoning chain correctly calculates the total number of puppies, correctly adjusts the number of spotted puppies for Pavel's litter based on the vet visit information, and accurately computes the final percentage. All arithmetic operations are correct.

✓ No hallucinations detected

Question #291

Clean

Full Question

Ava can peel 5 zucchinis a minute and saute 20 zucchinis in 6 minutes. How many minutes will it take her to peel and saute 140 zucchinis if it takes 24 seconds to wash each zucchini before peeling it? Note that Ava can't work in parallel and needs to take a 15-minute break after peeling the zucchinis before she can start sautéing them.

Ground Truth Answer

First find how long it takes Ava to peel the zucchini: 140 zucchini / 5 zucchini/minute = 28 minutes Then find how many batches of zucchini she needs to cook: 140 zucchini / 20 zucchini/batch = 7 batches Then multiply the number of batches by the time per batch to find the total cook time: 7 batches * 6 minutes/batch = 42 minutes Then add the peeling time to find the total time Ava spends: 42 minutes + 28 minutes = 70 minutes. We also should add 56 minutes time for washing. Also we should add 15 minutes for the break. So the total is 70 + 56 + 15 = 141. #### 141

Generated Answer

First, we calculate the time it takes to peel 140 zucchinis: 140 zucchinis / 5 zucchinis/minute = 28 minutes. Next, we calculate the time it takes to wash 140 zucchinis: 140 zucchinis * 24 seconds/zucchini = 3360 seconds. Convert this to minutes: 3360 seconds / 60 seconds/minute = 56 minutes. Then, we calculate the time it takes to saute 140 zucchinis: 140 zucchinis / 20 zucchinis = 7 sets of 20 zucchinis. Each set takes 6 minutes to saute, so it will take 7 sets * 6 minutes/set = 42 minutes to saute all the zucchinis. Finally, we add up the times for each step, including the 15-minute break: 56 minutes (washing) + 28 minutes (peeling) + 15 minutes (break) + 42 minutes (sauteing) = 141 minutes. Answer: {141}

Overall Quality: excellent

The reasoning chain correctly calculates all required times (peeling, washing, sauteing) and correctly sums them up, including the break time, matching the ground truth result.

✓ No hallucinations detected

Question #11

Clean

Full Question

A fog bank rolls in from the ocean to cover a city. It takes 90 minutes to cover every 3 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 78 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover a third of the city?

Ground Truth Answer

To cover 1/3 of the city the fog needs 78 * 1/3 = 26 miles. In 1 hour, the fog will move 60/90*3 miles = 2 miles. The remaining distance after one hour is 26 miles - 2 miles = 24 miles. 24 miles is 24/3 = 8 intervals of 3 miles. Since the speed of wind is halved, it would take 2*90= 180 minutes for the fog to cover 3 miles. So it will take 8 * 180 = 1440 minutes to cover the remaining 24 miles. In total, it will take 60 + 1440 = 1500 minutes to cover 1/3 of the city. #### 1500

Generated Answer

The fog covers 3 miles in 90 minutes, so its speed is 3 miles / 90 minutes = 1/30 mile per minute. The wind speed is halved in one hour (60 minutes), so the new speed will be (1/30)/2 = 1/60 mile per minute. A third of the city is 78 miles / 3 = 26 miles. Since the wind speed changes after 60 minutes, we need to calculate how far the fog travels in the first 60 minutes. At the initial speed of 1/30 mile per minute, the fog travels (1/30) * 60 = 2 miles in the first hour. The remaining distance to cover a third of the city is 26 miles - 2 miles = 24 miles. At the new speed of 1/60 mile per minute, the fog will take 24 miles / (1/60 mile/minute) = 24 * 60 = 1440 minutes to cover the remaining distance. Therefore, the total time it takes for the fog to cover a third of the city is 60 minutes (initial speed) + 1440 minutes (reduced speed) = 1500 minutes. Answer: {1500}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints of the problem, leading to the correct answer.

✓ No hallucinations detected

Question #37

Clean

Full Question

Oliver has 15 hectares of grape field. There are 15 grapes per 1/3 of a hectare. Oliver can harvest his grapes every 4 months. In addition, Oliver owns a 9-hectare apple field that produces 16 apples per hectare. The apples can be harvested every 4 months. In the span of two years, how many more grapes does Oliver harvest than apples?

Ground Truth Answer

Oliver has 15 x 15= 225 grapes on 1/3 of his field. In total Oliver can get, 1÷1/3 = 3 times more, meaning 225*3=675. Oliver can harvest his grape 12 ÷ 4 = 3 times per year Therefore Oliver can harvest 675 x 3 = 2025 grapes per year. There are 16 apples per hectare of the second field. In total, there are 9*16 = 144 apples. Since Oliver can harvest his apples 12 ÷ 4 = 3 times a year, he can harvest 144 * 3 = 432 apples in a year. Each year, Oliver harvests 2025 grapes - 432 apples = 1593 more grapes. So in two years, Oliver will produce 2 * 1593 = 3186 more. #### 3186

Generated Answer

First, calculate the number of grapes per hectare: 15 grapes / (1/3 hectare) = 45 grapes/hectare. Then, calculate the total number of grapes harvested from the 15-hectare field: 45 grapes/hectare * 15 hectares = 675 grapes. Since Oliver can harvest grapes every 4 months, and there are 12 months in a year, he harvests grapes 12 months/year / 4 months/harvest = 3 times a year. Over two years, he harvests grapes 3 harvests/year * 2 years = 6 times. So, in two years, Oliver harvests a total of 675 grapes/harvest * 6 harvests = 4050 grapes. Next, calculate the total number of apples harvested from the 9-hectare field: 16 apples/hectare * 9 hectares = 144 apples. Since Oliver can harvest apples every 4 months, similar to the grapes, he harvests apples 3 times a year. Over two years, he harvests apples 3 harvests/year * 2 years = 6 times. So, in two years, Oliver harvests a total of 144 apples/harvest * 6 harvests = 864 apples. Finally, find the difference between the number of grapes and apples harvested: 4050 grapes - 864 apples = 3186. Answer: {3186}

Overall Quality: excellent

The reasoning chain correctly interprets the problem and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #7

Clean

Full Question

A fog bank rolls in from the ocean to cover a city. It takes 75 minutes to cover every 10 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 72 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/4 of the city?

Ground Truth Answer

To cover 1/4 of the city the fog needs 72 * 1/4 = 18 miles. In 1 hour, the fog will move 60/75*10 miles = 8 miles. The remaining distance after one hour is 18 miles - 8 miles = 10 miles. 10 miles is 10/10 = 1 intervals of 10 miles. Since the speed of wind is halved, it would take 2*75= 150 minutes for the fog to cover 10 miles. So it will take 1 * 150 = 150 minutes to cover the remaining 10 miles. In total, it will take 60 + 150 = 210 minutes to cover 1/4 of the city. #### 210

Generated Answer

The fog bank covers 10 miles in 75 minutes. This translates to a speed of 10/75 = 2/15 miles per minute. In one hour, the wind speed is halved. Since the fog moves due to wind, its speed is also halved. The new speed will be (2/15)/2 = 1/15 miles per minute. 1/4 of the city is (1/4) * 72 miles = 18 miles. Since the wind speed changes after 1 hour (60 minutes), we need to calculate how far the fog has traveled in the first hour. Distance covered in the first hour = (2/15 miles/minute) * 60 minutes = 8 miles. The remaining distance to cover 1/4 of the city is 18 miles - 8 miles = 10 miles. At the new speed, the time to cover the remaining 10 miles is distance/speed = 10 miles / (1/15 miles/minute) = 150 minutes. The total time taken for the fog to cover 1/4 of the city is 60 minutes (first hour) + 150 minutes = 210 minutes. Answer: {210}

Overall Quality: excellent

The reasoning chain correctly interprets the problem constraints, calculates the required distance, correctly determines the speed change after one hour, calculates the distance covered in the first hour, and accurately sums the time components to reach the correct total time.

✓ No hallucinations detected

Question #8

Clean

Full Question

A fog bank rolls in from the ocean to cover a city. It takes 60 minutes to cover every 3 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 54 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/3 of the city?

Ground Truth Answer

To cover 1/3 of the city the fog needs 54 * 1/3 = 18 miles. In 1 hour, the fog will move 60/60*3 miles = 3 miles. The remaining distance after one hour is 18 miles - 3 miles = 15 miles. 15 miles is 15/3 = 5 intervals of 3 miles. Since the speed of wind is halved, it would take 2*60= 120 minutes for the fog to cover 3 miles. So it will take 5 * 120 = 600 minutes to cover the remaining 15 miles. In total, it will take 60 + 600 = 660 minutes to cover 1/3 of the city. #### 660

Generated Answer

The fog bank covers 3 miles every 60 minutes, meaning it moves at a speed of 3 miles / 60 minutes = 1/20 miles per minute. One-third of the city is (1/3) * 54 miles = 18 miles. Since the speed is constant for the first hour, the time it takes to cover the first 18 miles is 18 miles / (1/20 mile/minute) = 360 minutes. Answer: {360}

Overall Quality: poor

The reasoning chain fails to correctly model the time constraint imposed by the wind speed halving after one hour. It incorrectly calculates the time to cover 18 miles using the initial speed for the entire duration, ignoring the fact that only 3 miles are covered in the first 60 minutes.

✓ No hallucinations detected

Question #9

Clean

Full Question

A fog bank rolls in from the ocean to cover a city. It takes 60 minutes to cover every 6 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 72 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/3 of the city?

Ground Truth Answer

To cover 1/3 of the city the fog needs 72 * 1/3 = 24 miles. In 1 hour, the fog will move 60/60*6 miles = 6 miles. The remaining distance after one hour is 24 miles - 6 miles = 18 miles. 18 miles is 18/6 = 3 intervals of 6 miles. Since the speed of wind is halved, it would take 2*60= 120 minutes for the fog to cover 6 miles. So it will take 3 * 120 = 360 minutes to cover the remaining 18 miles. In total, it will take 60 + 360 = 420 minutes to cover 1/3 of the city. #### 420

Generated Answer

Here's how to solve this problem: 1. **Initial fog speed:** The fog covers 6 miles in 60 minutes, so its speed is 6 miles / 60 minutes = 0.1 miles per minute. 2. **Wind speed halving:** The wind speed halving means the fog's speed will also be halved. So, the new speed will be 0.1 miles/minute / 2 = 0.05 miles/minute. 3. **Distance to cover:** 1/3 of the city is (1/3) * 72 miles = 24 miles. 4. **Time to cover 1/3 of the city:** Since the fog travels the first 6 miles at the original speed and the remaining distance at the reduced speed, we need to calculate the time for each part. * **Time for the first 6 miles:** 6 miles / 0.1 mile/minute = 60 minutes * **Remaining distance:** 24 miles - 6 miles = 18 miles * **Time for the remaining distance:** 18 miles / 0.05 mile/minute = 360 minutes 5. **Total time:** 60 minutes + 360 minutes = 420 minutes Answer: {420}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the constraints of the problem, correctly calculating the time taken for the first 6 miles at the initial speed and the remaining distance at the halved speed.

✓ No hallucinations detected

Question #10

Clean

Full Question

A fog bank rolls in from the ocean to cover a city. It takes 25 minutes to cover every 5 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 54 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/2 of the city?

Ground Truth Answer

To cover 1/2 of the city the fog needs 54 * 1/2 = 27 miles. In 1 hour, the fog will move 60/25*5 miles = 12 miles. The remaining distance after one hour is 27 miles - 12 miles = 15 miles. 15 miles is 15/5 = 3 intervals of 5 miles. Since the speed of wind is halved, it would take 2*25= 50 minutes for the fog to cover 5 miles. So it will take 3 * 50 = 150 minutes to cover the remaining 15 miles. In total, it will take 60 + 150 = 210 minutes to cover 1/2 of the city. #### 210

Generated Answer

The fog bank covers 5 miles in 25 minutes. This means its speed is 5 miles / 25 minutes = 1/5 mile per minute. The city is 54 miles across, and we want to know how long it takes for the fog bank to cover half of the city, which is 54/2 = 27 miles. However, the wind speed is halved in one hour (60 minutes). We need to determine if the fog bank reaches the halfway point before or after the wind speed change. At the initial speed, it would take 27 miles / (1/5 mile/minute) = 27 * 5 = 135 minutes to cover half the city. Since 135 minutes is longer than 60 minutes (1 hour), the wind speed will change before the fog bank covers half the city. So, the fog bank travels at the initial speed for 60 minutes, covering a distance of (1/5 mile/minute) * 60 minutes = 12 miles. The remaining distance to the halfway point is 27 miles - 12 miles = 15 miles. The new speed is half the original speed: (1/5 mile/minute) / 2 = 1/10 mile/minute. The time it takes to cover the remaining 15 miles at the new speed is 15 miles / (1/10 mile/minute) = 15 * 10 = 150 minutes. The total time to cover half the city is the initial 60 minutes plus the additional 150 minutes, which equals 60 + 150 = 210 minutes. Answer: {210}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the constraints of the problem correctly, leading to the correct final answer.

✓ No hallucinations detected

Questions Analyzed

200

With Issues

11.5% of questions

Total Issues Found

0.16 per question

Issue Type Distribution

logical_error: 19calculation_error: 13

Question Analysis

Question #199

3 issues

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Daphne and Olivia are sisters from Cairo who love collecting signatures from movie stars. During their spring break from school, the sisters spend every afternoon collecting signatures. After 3 weeks, Daphne has 17 signatures in her book, and Olivia has 31. The sisters have 3 more weeks of spring break, and they decide they want to reach 120 signatures between them by the end of the break. However, during the remaining 3 weeks, Daphne is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Olivia decides to increase her weekly collection. How many signatures will Olivia need to collect per week to make sure they reach their goal? **Answer:** First, we determine Daphne's weekly collection rate during the first three weeks: 17 signatures / 3 weeks = 5.67 signatures/week (approximately). Next, we calculate Daphne's reduced weekly collection rate: 5.67 signatures/week - 5 signatures/week = 0.67 signatures/week (approximately). Now we find how many signatures Daphne will collect in the next 3 weeks: 0.67 signatures/week * 3 weeks = 2 signatures (approximately). Then we calculate the total number of signatures Daphne will have: 17 signatures + 2 signatures = 19 signatures. We subtract Daphne's total expected signatures from the sisters' goal: 120 signatures - 19 signatures = 101 signatures. This is the number of signatures Olivia needs to collect. Since Olivia already has 31 signatures, we subtract that from the number she still needs to collect: 101 signatures - 31 signatures = 70 signatures. Finally, we divide the number of signatures Olivia needs by the remaining 3 weeks to find her weekly collection rate: 70 signatures / 3 weeks = 23.33 signatures/week (approximately). Therefore, Olivia will need to collect approximately \boxed{23} signatures per week to ensure they reach their goal of 120 signatures.

Overall Quality: poor

The reasoning chain contains multiple calculation errors stemming from an initial logical misinterpretation of how to determine Daphne's future collection rate. The model incorrectly calculates the subtraction in the second step and the multiplication in the third step based on its own intermediate results.

Detected Issues (3)

logical_error medium

Statement

First, we determine Daphne's weekly collection rate during the first three weeks: 17 signatures / 3 weeks = 5.67 signatures/week (approximately).

Explanation

The problem states Daphne collected 17 signatures in the first 3 weeks. It then states that during the *remaining* 3 weeks, her weekly collection is reduced by 5 per week. This implies we need to know her *original* weekly rate to calculate the reduction. However, the problem does not explicitly state her original weekly rate, only the total collected (17). The ground truth suggests that the information about the initial 3 weeks (17 signatures) is only used to establish the starting total, and the reduction of 5 per week applies to some assumed baseline rate, or perhaps the problem implies the reduction is relative to the *average* rate achieved in the first 3 weeks, which is what the model calculated. However, the ground truth calculation implies that the reduction of 5 per week is applied to an *unspecified* baseline rate, and the model's attempt to derive this baseline rate from the initial 17 signatures is flawed because the problem structure suggests the reduction applies to a fixed rate that Daphne *would have* maintained, not necessarily the average of the first 3 weeks. Crucially, the ground truth uses the information that Daphne collects 5 per week (from the ground truth analysis, which seems to be derived from the context that 5 is the reduction amount, implying her *original* rate was 5 per week, or that the reduction is applied to a known rate). Let's re-read the prompt: 'Daphne is only able to collect signatures on weekends, reducing her weekly collection by 5 per week'. This implies we need her original weekly rate. Since the problem doesn't state her original rate, we must rely on the ground truth interpretation: Daphne's original rate was 5 per week, and she reduces it by 5, meaning she collects 0 per week, OR the ground truth implies Daphne's original rate was X, and the reduction means her new rate is X-5. The ground truth calculation states: 'Since Daphne collects 5 per week, she'll collect 3 * 5 = 15.' This implies the ground truth *assumes* Daphne's original rate was 5 per week, and the reduction of 5 means her new rate is 0. But the ground truth then calculates 3 * 5 = 15 collected in the next 3 weeks, which contradicts the reduction logic if her original rate was 5. Let's follow the ground truth logic: If Daphne collects 5 per week (original rate), and she reduces it by 5, her new rate is 0. If she collects 15 in 3 weeks, her new rate is 5/week. This suggests the phrase 'reducing her weekly collection by 5 per week' is misinterpreted or the problem is poorly phrased relative to the ground truth. The ground truth calculation *uses* 5 signatures per week for Daphne's collection in the remaining 3 weeks (3 * 5 = 15). This means the ground truth interprets the constraint as: Daphne collects 5 signatures per week during the remaining 3 weeks, ignoring the 'reducing by 5' clause, or assuming the reduction brought her rate *to* 5. Given the ambiguity, the model's approach of deriving a rate from the first 3 weeks is logically unsound because the initial 17 signatures might not reflect a consistent weekly rate, and the reduction applies to an unknown baseline. The ground truth implies Daphne collects 5/week for the remaining 3 weeks, leading to 15 signatures total. The model's derivation is an unnecessary and flawed step.

Reference/Question Span:

reducing her weekly collection by 5 per week

calculation_error medium

Statement

Next, we calculate Daphne's reduced weekly collection rate: 0.67 signatures/week - 5 signatures/week = 0.67 signatures/week (approximately).

Explanation

The arithmetic operation is incorrect. 0.67 - 5 should equal -4.33, not 0.67.

Answer Span:

0.67 signatures/week - 5 signatures/week = 0.67 signatures/week (approximately)

calculation_error medium

Statement

Now we find how many signatures Daphne will collect in the next 3 weeks: 0.67 signatures/week * 3 weeks = 2 signatures (approximately).

Explanation

The arithmetic operation is incorrect. 0.67 * 3 should equal 2.01, not 2 (though rounding might be intended, the previous step already introduced significant error based on the flawed logic). More importantly, if we use the result from the previous (incorrect) step (0.67), then 0.67 * 3 = 2.01. If we use the correct result from the previous step (-4.33), the result would be -12.99. Since the model is following its own flawed chain, 0.67 * 3 = 2 is mathematically incorrect (it should be 2.01).

Answer Span:

0.67 signatures/week * 3 weeks = 2 signatures (approximately)

Question #201

1 issue

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Mei and Haruka are sisters from Singapore who love collecting signatures from politicians. During their summer break from school, the sisters spend every afternoon collecting signatures. After 5 weeks, Mei has 24 signatures in her book, and Haruka has 51. The sisters have 3 more weeks of summer break, and they decide they want to reach 135 signatures between them by the end of the break. However, during the remaining 3 weeks, Mei is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Haruka decides to increase her weekly collection. How many signatures will Haruka need to collect per week to make sure they reach their goal? Answer: Mei's initial weekly collection rate is 24 signatures / 5 weeks = 4.8 signatures per week. Due to only collecting signatures on weekends, Mei's new weekly collection rate is 4.8 - 5 = -0.2 signatures per week. This actually means she won't be collecting any new signatures; in fact, this doesn't even logically make sense in the context of the problem. However, we'll proceed with the calculated number since that's what's mathematically implied. Over the next 3 weeks, Mei will collect -0.2 signatures/week * 3 weeks = -0.6 signatures. Again, we'll treat this as 0 since negative signatures don't make sense. So, Mei's total signatures by the end of the summer will be 24 + 0 = 24 signatures. To reach their goal of 135 signatures, Haruka needs to collect 135 - 24 = 111 signatures in total. Since Haruka already has 51 signatures, she needs to collect an additional 111 - 51 = 60 signatures over the next 3 weeks. Therefore, Haruka needs to collect 60 signatures / 3 weeks = 20 signatures per week. Final Answer: The final answer is $\boxed{20}$

Overall Quality: poor

The reasoning chain contains significant logical errors in interpreting the initial conditions regarding Mei's collection rate. It incorrectly calculates an initial average rate and then incorrectly applies the reduction, leading to a negative rate. Although the model attempts to correct this by setting the total collected to 0, the entire premise of calculating Mei's future collection based on the initial 5 weeks is flawed and unnecessary, as shown by the ground truth approach.

Detected Issues (1)

logical_error high

Statement

Mei's initial weekly collection rate is 24 signatures / 5 weeks = 4.8 signatures per week.

Explanation

The problem does not state that Mei collected 24 signatures evenly over 5 weeks. It states that *after* 5 weeks, Mei *has* 24 signatures. We do not know her initial weekly rate, nor is it necessary to calculate it to solve the problem, as the remaining collection depends only on the current total and the future collection rate.

Answer Span:

Mei's initial weekly collection rate is 24 signatures / 5 weeks = 4.8 signatures per week.

Reference/Question Span:

After 5 weeks, Mei and Haruka compare their autograph books, counting up the number of signatures each sister has collected. Mei has 24 signatures in her book

Question #198

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Uma and Zahra are sisters from Marrakech who love collecting signatures from politicians. During their spring break from school, the sisters spend every afternoon collecting signatures. After 6 weeks, Uma has 29 signatures in her book, and Zahra has 37 signatures. The sisters have 4 more weeks of spring break, and they decide they want to reach 130 signatures between them by the end of the break. However, during the remaining 4 weeks, Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Zahra decides to increase her weekly collection. How many signatures will Zahra need to collect per week to make sure they reach their goal? **Answer:** 1. **Uma's average weekly collection (first 6 weeks):** 29 signatures / 6 weeks = 4.83 signatures/week (approximately). 2. **Zahra's average weekly collection (first 6 weeks):** 37 signatures / 6 weeks = 6.17 signatures/week (approximately). 3. **Uma's reduced weekly collection (next 4 weeks):** 4.83 signatures/week - 5 signatures/week = -0.17 signatures/week. Since she can't collect negative signatures, we assume she collects 0 signatures per week during this period. 4. **Uma's total signatures in the next 4 weeks:** 0 signatures/week * 4 weeks = 0 signatures. 5. **Uma's total signatures by the end of spring break:** 29 signatures + 0 signatures = 29 signatures. 6. **Signatures needed from Zahra to reach the goal:** 130 signatures - 29 signatures = 101 signatures. 7. **Signatures Zahra already has:** 37 signatures. 8. **Signatures Zahra needs to collect in the next 4 weeks:** 101 signatures - 37 signatures = 64 signatures. 9. **Signatures Zahra needs to collect per week:** 64 signatures / 4 weeks = 16 signatures/week. Therefore, Zahra needs to collect $\boxed{16}$ signatures per week to make sure they reach their goal.

Overall Quality: poor

The reasoning chain incorrectly interprets how to use the information about Uma's reduced collection rate. It calculates an average rate for the first 6 weeks, subtracts 5, and incorrectly concludes Uma collects 0 signatures in the remaining 4 weeks. This leads to an incorrect final answer (16 instead of 11).

Detected Issues (1)

logical_error high

Statement

Uma's average weekly collection (first 6 weeks): 29 signatures / 6 weeks = 4.83 signatures/week (approximately).

Explanation

The problem states Uma has 29 signatures after 6 weeks. The subsequent steps rely on calculating her *future* collection rate based on a reduction of 5 signatures per week from her *past* rate. However, the problem states: 'Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week'. This implies a fixed reduction from an *implied* previous rate, not necessarily her average rate over the first 6 weeks. More critically, the ground truth calculation shows that the initial average rate calculation is unnecessary and leads to flawed subsequent steps. The core logical error is assuming the reduction applies to the average rate calculated from the first 6 weeks, rather than using the information provided in the ground truth approach, which focuses on the total remaining need.

Answer Span:

Uma's average weekly collection (first 6 weeks): 29 signatures / 6 weeks = 4.83 signatures/week (approximately).

Reference/Question Span:

Uma has 29 signatures in her book, and Zahra has 37. The sisters have 4 more weeks of spring break, and they decide they want to reach 130 signatures between them by the end of the break. However, during the remaining 4 weeks, Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

Question #203

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Chen and Tara are sisters from Lisbon who love collecting signatures from politicians. During their winter break from school, the sisters spend every afternoon collecting signatures. After 5 weeks, Chen has 36 signatures in her book, and Tara has 32. The sisters have 4 more weeks of winter break, and they decide they want to reach 140 signatures between them by the end of the break. However, during the remaining 4 weeks, Chen is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Tara decides to increase her weekly collection. How many signatures will Tara need to collect per week to make sure they reach their goal? **Answer:** Chen collected 36 signatures in 5 weeks, so she was collecting 36/5 = 7.2 signatures per week. Chen's rate: 7.2/week Due to only collecting on weekends, Chen will now collect 7.2 - 5 = 2.2 signatures per week for the next 4 weeks. Chen's new rate: 2.2/week Over the next 4 weeks, Chen will collect 2.2 * 4 = 8.8 signatures. Chen's next 4 weeks collection: 8.8 signatures Adding this to her existing 36 signatures, Chen will have 36 + 8.8 = 44.8 signatures. Chen's total after 9 weeks: 44.8 signatures They want 140 signatures total, and with Chen's projected 44.8, Tara needs to collect 140 - 44.8 = 95.2 signatures. Tara's target in next 4 weeks: 95.2 signatures Tara currently has 32 signatures. To reach the remaining 95.2 signatures in the next 4 weeks, she needs to collect an additional 95.2 - 32 = 63.2 signatures. Additional signatures Tara needs: 63.2 To collect 63.2 signatures over 4 weeks, Tara needs to collect 63.2/4 = 15.8 signatures per week. Tara's required rate: 15.8/week Therefore, Tara needs to collect $\boxed{15.8}$ signatures per week.

Overall Quality: poor

The model attempts to calculate Chen's past rate and subtract 5 from it, leading to an incorrect projection for Chen's future collection. This deviates significantly from the logic required to reach the ground truth answer, which implies Chen collects 5 signatures per week for the remaining 4 weeks (totaling 20 signatures).

Detected Issues (1)

logical_error high

Statement

Due to only collecting on weekends, Chen will now collect 7.2 - 5 = 2.2 signatures per week for the next 4 weeks.

Explanation

The problem states: 'Chen is only able to collect signatures on weekends, reducing her weekly collection by 5 per week'. This implies her *new* rate is 5 less than her *old* rate. However, the problem does not state what her old rate was, only that she collected 36 in 5 weeks (7.2/week). The ground truth solution bypasses this ambiguity by using the information provided in the ground truth derivation which implies Chen collects 5 signatures per week in the remaining 4 weeks (4 * 5 = 20 total), suggesting the 'reducing her weekly collection by 5 per week' might be interpreted differently or that the problem intends for Chen to collect a fixed amount (5/week) during the remaining time, or that the reduction applies to some baseline not explicitly stated. Given the ground truth result (which implies Chen collects 4*5=20 total), the model's interpretation of subtracting 5 from the calculated average rate (7.2 - 5 = 2.2) is a flawed interpretation of the constraint 'reducing her weekly collection by 5 per week' when applied to an average rate derived from past performance.

Answer Span:

Due to only collecting on weekends, Chen will now collect 7.2 - 5 = 2.2 signatures per week for the next 4 weeks.

Reference/Question Span:

Chen is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

Question #200

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ava and Quinn are sisters from Helsinki who love collecting signatures from authors. During their spring break from school, the sisters spend every afternoon collecting signatures. After 3 weeks, Ava has 30 signatures in her book, and Quinn has 37. The sisters have 2 more weeks of spring break, and they decide they want to reach 135 signatures between them by the end of the break. However, during the remaining 2 weeks, Ava is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Quinn decides to increase her weekly collection. How many signatures will Quinn need to collect per week to make sure they reach their goal? **Answer:** First, we determine Ava's weekly collection rate during the first 3 weeks: 30 signatures / 3 weeks = 10 signatures/week. Next, we calculate Ava's reduced weekly collection rate for the remaining 2 weeks: 10 signatures/week - 5 signatures/week = 5 signatures/week. Then, we find the total number of signatures Ava will collect in the remaining 2 weeks: 5 signatures/week * 2 weeks = 10 signatures. Now, we calculate the total number of signatures Ava will have at the end of spring break: 30 signatures + 10 signatures = 40 signatures. Since they want to reach 135 signatures together, we can determine how many signatures Quinn needs to collect in total: 135 signatures - 40 signatures = 95 signatures. Quinn already has 37 signatures, so we figure out how many more signatures she needs: 95 signatures - 37 signatures = 58 signatures. Finally, we calculate how many signatures Quinn needs to collect per week for the remaining 2 weeks: 58 signatures / 2 weeks = 29 signatures/week. The answer is $\boxed{29}$.

Overall Quality: excellent

The reasoning chain correctly interprets the problem constraints and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #202

3 issues

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Uma and Olga are sisters from Lisbon who love collecting signatures from politicians. During their summer break from school, the sisters spend every afternoon collecting signatures. After 3 weeks, Uma has 25 signatures in her book, and Olga has 59. The sisters have 2 more weeks of summer break, and they decide they want to reach 140 signatures between them by the end of the break. However, during the remaining 2 weeks, Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week, while Olga decides to increase her weekly collection. How many signatures will Olga need to collect per week to make sure they reach their goal? Answer: Uma collected 25 signatures in 3 weeks, so she was collecting 25/3 ≈ 8.33 signatures per week. With her collection reduced by 5 signatures per week, Uma will collect 8.33 - 5 = 3.33 signatures per week for the next two weeks. This means she'll collect 3.33 * 2 ≈ 6.66 signatures, which we can round up to 7 additional signatures since she can't collect fractions of signatures. Uma will therefore have a total of 25 + 7 = 32 signatures. They want to reach 140 signatures total, and with Uma having 32 signatures, Olga will need to collect 140 - 32 = 108 signatures total. Olga already has 59 signatures, so she needs 108 - 59 = 49 more signatures in the remaining 2 weeks. Therefore, Olga needs to collect 49/2 = 24.5 signatures per week. Since we can assume she can't collect half a signature, she needs to collect at least 25. Final Answer: The final answer is $\boxed{25}$

Overall Quality: poor

The model makes several logical errors by calculating a past average rate (25/3) and applying the reduction to it, leading to premature rounding (6.66 to 7). This deviates significantly from the logic required to reach the ground truth answer, which implies Uma collects exactly 10 signatures over the next two weeks (2 weeks * 5 signatures/week, suggesting the reduction means she collects 5/week, not 3.33/week).

Detected Issues (3)

logical_error medium

Statement

Uma collected 25 signatures in 3 weeks, so she was collecting 25/3 ≈ 8.33 signatures per week.

Explanation

The problem states Uma has 25 signatures after 3 weeks. It does not state that her collection rate was constant over those 3 weeks, nor does it state that the rate reduction applies to her *past* rate. The ground truth implies that the initial 25 signatures are a fixed amount already collected, and the reduction applies to her *future* collection rate based on an assumed baseline rate derived from the past 3 weeks. However, the problem statement is ambiguous about the baseline rate. The ground truth calculation bypasses this ambiguity entirely by focusing only on the remaining signatures needed and how Uma's *future* collection contributes, which is a more robust interpretation given the constraints on Olga's future rate. The model's attempt to calculate a past rate (25/3) and then reduce it by 5 is an unnecessary and potentially flawed step based on how these problems are usually structured, especially since the ground truth calculation doesn't rely on this past rate calculation.

Answer Span:

Uma collected 25 signatures in 3 weeks, so she was collecting 25/3 ≈ 8.33 signatures per week.

Reference/Question Span:

Uma has 25 signatures in her book... during the remaining 2 weeks, Uma is only able to collect signatures on weekends, reducing her weekly collection by 5 per week

calculation_error low

Statement

With her collection reduced by 5 signatures per week, Uma will collect 8.33 - 5 = 3.33 signatures per week for the next two weeks.

Explanation

The calculation 8.33 - 5 = 3.33 is mathematically correct based on the preceding (flawed) premise, but the subsequent step uses rounding that leads away from the precise calculation needed for the final answer, which is based on the ground truth logic.

Answer Span:

8.33 - 5 = 3.33

logical_error high

Statement

This means she'll collect 3.33 * 2 ≄ 6.66 signatures, which we can round up to 7 additional signatures since she can't collect fractions of signatures.

Explanation

The ground truth calculation (which leads to the correct answer 23) implies that the remaining signatures needed (56) are distributed precisely, suggesting that fractional signatures must be accounted for in the intermediate steps to determine the exact required rate for Olga. Rounding Uma's contribution prematurely (6.66 to 7) leads to an incorrect final requirement for Olga (24.5, rounded to 25). The ground truth calculation uses the exact remaining amount needed (56) and subtracts Uma's exact future contribution (10) to find Olga's exact need (46).

Answer Span:

which we can round up to 7 additional signatures since she can't collect fractions of signatures.

Reference/Question Span:

How many signatures will Olga need to collect per week to make sure they reach their goal?

Question #47

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: A farmer is buying feed for his alpacas. He buys a variety of apples, wheat, cucumbers and hay. Since hay are a rare treat, he only buys six 3-pound boxes of them. He only wants enough cucumbers to feed the alpacas while the vegetables are fresh, so he buys fifteen 8-pound bags. Apples are the main diet of his alpacas, so he buys thirty four 43-pound packs. Wheat are a staple to supplement the apples, so he buys eighteen 15-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 170 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items? Answer: Hay: six 3-pound boxes total 6 * 3 = 18 pounds. Cucumbers: fifteen 8-pound bags total 15 * 8 = 120 pounds. Apples: thirty four 43-pound packs total 34 * 43 = 1462 pounds. Wheat: eighteen 15-pound sacks total 18 * 15 = 270 pounds. The total weight of alpaca feed is 18 + 120 + 1462 + 270 = 1870 pounds. Adding the groceries (43 pounds), tools (27 pounds), and wood (100 pounds), the total weight of all items is 1870 + 43 + 27 + 100 = 2040 pounds. With three trucks carrying 170 pounds each, the combined capacity per trip is 3 * 170 = 510 pounds. The number of trips needed is 2040 / 510 = 4. Therefore, the farmer needs $\boxed{4}$ trips.

Overall Quality: fair

The reasoning chain contains two calculation errors flagged based on the structure mismatch with the ground truth, but upon strict re-evaluation of the arithmetic operations presented in the chain, all individual arithmetic steps are mathematically correct (6*3=18, 15*8=120, 34*43=1462, 18*15=270, sums are correct, 2040/510=4). The final answer matches the ground truth (4). The initial error flagging was based on misinterpreting the structure relative to the ground truth's calculation order, but the actual arithmetic performed in the chain is sound. Since the final answer matches and all arithmetic is correct, I must retract the calculation errors as they are not mathematically false operations. The logical step regarding truck capacity (dividing total weight by capacity per truck) is correct, and the final division by 3 trucks is also correctly integrated into the capacity calculation (170 * 3 = 510). Therefore, there are no mathematical or logical errors in the provided reasoning chain leading to the correct answer.

✓ No hallucinations detected

Question #46

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: A farmer is buying feed for his sheep. He buys a variety of apples, wheat, carrots and oats. Since oats are a rare treat, he only buys eight 7-pound boxes of them for the whole stable. He only wants enough carrots to feed the sheep while the vegetables are fresh, so he buys twelve 6-pound bags. Apples are the main diet of his sheep, so he buys thirty two 43-pound packs. Wheat are a staple to supplement the apples, so he buys eighteen 17-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 110 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items? Answer: The farmer bought 8 boxes of oats at 7 pounds each, for a total of 8 * 7 = 56 pounds of oats. He bought 12 bags of carrots at 6 pounds each, for a total of 12 * 6 = 72 pounds of carrots. He bought 32 packs of apples at 43 pounds each, for a total of 32 * 43 = 1376 pounds of apples. He bought 18 sacks of wheat at 17 pounds each, for a total of 18 * 17 = 306 pounds of wheat. He also bought 43 pounds of groceries, 27 pounds of tools, and 100 pounds of wood. The total weight of all items is 56 + 72 + 1376 + 306 + 43 + 27 + 100 = 1980 pounds. Since the farmer has three trucks and each truck can carry 110 pounds, the total carrying capacity per trip is 3 * 110 = 330 pounds. The number of trips needed is 1980 / 330 = 6 trips. Final Answer: The final answer is $\boxed{6}$

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item, sums them up, correctly determines the total carrying capacity per trip (3 trucks * 110 lbs/truck = 330 lbs), and correctly calculates the required number of trips (1980 / 330 = 6). The final answer matches the ground truth.

✓ No hallucinations detected

Question #42

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: A farmer is buying feed for his cows. He buys a variety of apples, hay, cucumbers and corn. Since corn are a rare treat, he only buys four 6-pound boxes of them for the whole stable. He only wants enough cucumbers to feed the cows while the vegetables are fresh, so he buys fourteen 8-pound bags. Apples are the main diet of his cows, so he buys thirty five 42-pound packs. Hay are a staple to supplement the apples, so he buys eighteen 18-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 140 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items? Answer: Corn: four 6-pound boxes total 4 * 6 = 24 pounds. Cucumbers: fourteen 8-pound bags total 14 * 8 = 112 pounds. Apples: thirty five 42-pound packs total 35 * 42 = 1470 pounds. Hay: eighteen 18-pound sacks total 18 * 18 = 324 pounds. The total weight of animal feed is 24 + 112 + 1470 + 324 = 1930 pounds. Other items: The total weight of the other items is 43 + 27 + 100 = 170 pounds. Total weight of all items: 1930 + 170 = 2100 pounds. Carrying capacity per trip: Since the farmer has three trucks and each truck can carry 140 pounds, the total carrying capacity per trip is 3 * 140 = 420 pounds. Number of trips: The total number of trips required is 2100 / 420 = 5. Final Answer: The final answer is $\boxed{5}$

Overall Quality: fair

The model made a mistake in identifying which item was which weight calculation compared to the ground truth structure, but the arithmetic itself appears correct based on the inputs it used (18*18=324). However, upon re-examining the ground truth structure vs the model's structure, the model swapped the calculation for Apples and Hay compared to the ground truth's listed order, but the actual arithmetic results are correct for the items listed in the problem description. Let's re-evaluate the model's arithmetic against the ground truth's arithmetic: Model Corn: 4 * 6 = 24 (Correct) Model Cucumbers: 14 * 8 = 112 (Correct) Model Apples: 35 * 42 = 1470 (Correct) Model Hay: 18 * 18 = 324 (Correct) Model Sum Feed: 24 + 112 + 1470 + 324 = 1930 (Correct: 24+112=136; 136+1470=1606; 1606+324=1930) Model Other: 43 + 27 + 100 = 170 (Correct) Model Total: 1930 + 170 = 2100 (Correct) Model Trips (Single Truck): 2100 / 140 = 15 (This step is missing in the model's final output but implied by the ground truth structure, though the model calculates the final answer directly using 3 trucks). Model Trips (3 Trucks): 2100 / (3 * 140) = 2100 / 420 = 5 (Correct) Wait, the model's final calculation step is: Carrying capacity per trip: Since the farmer has three trucks and each truck can carry 140 pounds, the total carrying capacity per trip is 3 * 140 = 420 pounds. Number of trips: The total number of trips required is 2100 / 420 = 5. This logic is sound and the arithmetic is correct. The final answer matches the ground truth (5). Why did I flag an error? I flagged an error because the model listed Hay as 18*18=324, while the ground truth listed Apples as 18*18=324 and Hay as 14*8=112 (Wait, no, the ground truth lists Hay as 18*18=324 and Apples as 35*42=1470). Let's check the problem statement vs the model's assignment: Corn: 4 * 6 = 24 (Model: Correct) Cucumbers: 14 * 8 = 112 (Model: Correct) Apples: 35 * 42 = 1470 (Model: Correct) Hay: 18 * 18 = 324 (Model: Correct) All calculations performed by the model are mathematically correct based on the numbers it used, and the final logic (dividing total weight by combined capacity of 3 trucks) is correct and leads to the correct answer (5). Therefore, there are NO calculation errors or logical errors in the provided reasoning chain, despite the initial confusion regarding the structure matching the ground truth's internal steps (which is irrelevant if the model's steps are mathematically sound and lead to the correct result). Revising error count to 0.

✓ No hallucinations detected

Question #45

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: A farmer is buying feed for his cows. He buys a variety of hay, wheat, carrots and apples. Since apples are a rare treat, he only buys five 7-pound boxes of them for the whole stable. He only wants enough carrots to feed the cows while the vegetables are fresh, so he buys fourteen 5-pound bags. Hay are the main diet of his cows, so he buys thirty five 44-pound packs. Wheat are a staple to supplement the hay, so he buys nineteen 15-pound sacks. Finally, he buys 43 pounds of groceries, and 27 pounds of tools, and 100 pounds of wood. A farm truck can carry 100 pounds at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items? Answer: First, let's calculate the total weight of the apples: five boxes * 7 pounds/box = 35 pounds of apples. Next, the total weight of carrots is: fourteen bags * 5 pounds/bag = 70 pounds of carrots. The total weight of hay is: thirty five packs * 44 pounds/pack = 1540 pounds of hay. The total weight of wheat is: nineteen sacks * 15 pounds/sack = 285 pounds of wheat. The total weight of all the feed is 35 + 70 + 1540 + 285 = 1930 pounds. Adding the groceries, tools, and wood, the total weight of all items is 1930 + 43 + 27 + 100 = 2100 pounds. Since each truck can carry 100 pounds, and the farmer has three trucks, they can carry a total of 100 * 3 = 300 pounds per trip. The number of trips required is the total weight divided by the weight capacity per trip: 2100 / 300 = 7 trips. Final Answer: The final answer is $\boxed{7}$

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item, sums them up, correctly determines the total carrying capacity per trip (3 trucks * 100 lbs/truck = 300 lbs/trip), and accurately calculates the required number of trips (2100 / 300 = 7). All arithmetic and logic align with the ground truth.

✓ No hallucinations detected

Question #26

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Oliver is popping popcorn for a snack. As the skillet of kernels heats up, the kernels start popping faster. 60 pop in the first 22 seconds of cooking, then 3 times that amount in the next 22 seconds. The kernels increase to 4 times the initial popping rate in the next 22 seconds. In the final 22 seconds, the popping slows down to half the rate as the past 22 seconds. After Oliver takes the skillet off the heat, a quarter of the number of kernels that popped in the final 22 seconds of cooking also pop from the residual heat. Oliver gives one-tenth of the made popcorn to his brother Thiago. How many more pieces of popcorn does Oliver have to eat than his brother? **Answer:** * In the first 22 seconds, 60 kernels popped. * In the next 22 seconds, 3 * 60 = 180 kernels popped. * In the next 22 seconds, 4 * 60 = 240 kernels popped. * In the final 22 seconds, 240 / 2 = 120 kernels popped. * From residual heat, 120 / 4 = 30 kernels popped. * The total number of popped kernels is 60 + 180 + 240 + 120 + 30 = 630. * Oliver gave Thiago 630 / 10 = 63 pieces of popcorn. * Oliver has 630 - 63 = 567 pieces left. * Oliver has 567 - 63 = \boxed{504} more pieces than Thiago.

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem. All arithmetic calculations are correct, and the final step correctly calculates the difference between Oliver's share and Thiago's share.

✓ No hallucinations detected

Question #27

Clean

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**Reformatted Question:** Thiago is popping popcorn for a snack. As the skillet of kernels heats up, the kernels start popping faster. 40 pop in the first 26 seconds of cooking, then 3 times that amount in the next 26 seconds. The kernels increase to 4 times the initial popping rate in the next 26 seconds. In the final 26 seconds, the popping slows down to half the rate as the past 26 seconds. After Thiago takes the skillet off the heat, a quarter of the number of kernels that popped in the final 26 seconds of cooking also pop from the residual heat. Thiago gives 1/10 of the made popcorn to his brother Sanjay. How many more pieces of popcorn does Thiago have to eat than his brother? **Answer:** * In the first 26 seconds, 40 kernels popped. * In the next 26 seconds, 3 * 40 = 120 kernels popped. * In the next 26 seconds, the popping rate increased to 4 times the initial rate, meaning 4 * 40 = 160 kernels popped. * In the final 26 seconds, the rate was half of the previous rate, so 160 / 2 = 80 kernels popped. * From residual heat, 80 / 4 = 20 kernels popped. The total number of popped kernels is 40 + 120 + 160 + 80 + 20 = 420 kernels. Thiago gave 1/10 * 420 = 42 kernels to Sanjay. Thiago has 420 - 42 = 378 kernels left. Thiago has 378 - 42 = 336 more kernels than Sanjay. Final Answer: The final answer is $\boxed{336}$

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final result matches the ground truth.

✓ No hallucinations detected

Question #25

Clean

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Generated Answer

**Reformatted Question:** Benjamin is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. 80 pop in the first 26 seconds of cooking, then 2 times that amount in the next 26 seconds. The kernels increase to 3 times the initial popping rate in the next 26 seconds. In the final 26 seconds, the popping slows down to half the rate as the past 26 seconds. After Benjamin takes the pan off the heat, a quarter of the number of kernels that popped in the final 26 seconds of cooking also pop from the residual heat. Benjamin gives 1/7 of the made popcorn to his brother Yusuf. How many more pieces of popcorn does Benjamin have to eat than his brother? **Answer:** * In the first 26 seconds, 80 kernels popped. * In the next 26 seconds, 2 * 80 = 160 kernels popped. * In the next 26 seconds, 3 * 80 = 240 kernels popped. * In the final 26 seconds, 240 / 2 = 120 kernels popped. * From residual heat, an additional 120 / 4 = 30 kernels popped. The total number of popped kernels is 80 + 160 + 240 + 120 + 30 = 630. Total Kernels = 630 Benjamin gave 1/7 * 630 = 90 kernels to Yusuf. Kernels to Yusuf = 90 This leaves Benjamin with 630 - 90 = 540 kernels. Kernels for Benjamin = 540 Therefore, Benjamin has 540 - 90 = 450 more pieces of popcorn than Yusuf. Difference = 450 Final Answer: \boxed{450}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #44

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Reformatted Question: A farmer is buying feed for his cows. He buys a variety of wheat, oats, carrots and corn. Since corn are a rare treat, he only buys seven 5-kg boxes of them for the whole stable. He only wants enough carrots to feed the cows while the vegetables are fresh, so he buys eleven 7-kg bags. Wheat are the main diet of his cows, so he buys thirty four 39-kg packs. Oats are a staple to supplement the wheat, so he buys nineteen 18-kg sacks. Finally, he buys 43 kgs of groceries, and 27 kgs of tools, and 100 kgs of wood. A farm truck can carry 130 kgs at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items? Answer: The farmer buys seven 5-kg boxes of corn, so the total weight of corn is 7 * 5 = 35 kg. He buys eleven 7-kg bags of carrots, so the total weight of carrots is 11 * 7 = 77 kg. He buys thirty four 39-kg packs of wheat, so the total weight of wheat is 34 * 39 = 1326 kg. He buys nineteen 18-kg sacks of oats, so the total weight of oats is 19 * 18 = 342 kg. The total weight of animal feed is 35 + 77 + 1326 + 342 = 1780 kg. He also buys 43 kg of groceries, 27 kg of tools, and 100 kg of wood. The total weight of these items is 43 + 27 + 100 = 170 kg. The total weight of all purchased items is 1780 + 170 = 1950 kg. Each truck can carry 130 kg, and the farmer has three trucks, so in one trip they can carry 130 * 3 = 390 kg. The number of trips needed is 1950 / 390 = 5 trips. Final Answer: The final answer is $\boxed{5}$

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item, sums them up, correctly determines the carrying capacity per trip using all three trucks, and accurately calculates the total number of trips required. All arithmetic operations are correct.

✓ No hallucinations detected

Question #29

Clean

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Generated Answer

**Reformatted Question:** Oscar is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. 80 pop in the first 16 seconds of cooking, then 3 times that amount in the next 16 seconds. The kernels increase to 5 times the initial popping rate in the next 16 seconds. In the final 16 seconds, the popping slows down to half the rate as the past 16 seconds. After Oscar takes the pan off the heat, a quarter of the number of kernels that popped in the final 16 seconds of cooking also pop from the residual heat. Oscar gives two-fifths of the made popcorn to his brother Benjamin. How many more pieces of popcorn does Oscar have to eat than his brother? **Answer:** * In the first 16 seconds, 80 kernels popped. * In the next 16 seconds, 3 * 80 = 240 kernels popped. * In the next 16 seconds, 5 * 80 = 400 kernels popped. * In the final 16 seconds, 400 / 2 = 200 kernels popped. * From residual heat, an additional 200 / 4 = 50 kernels popped. The total number of popped kernels is 80 + 240 + 400 + 200 + 50 = 970 kernels. Oscar gave 2/5 * 970 = 388 kernels to Benjamin. Oscar has 970 - 388 = 582 kernels left. Oscar has 582 - 388 = 194 more kernels than Benjamin. Final Answer: The final answer is $\boxed{194}$

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #43

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Reformatted Question: A farmer is buying feed for his sheep. He buys a variety of wheat, corn, beets and oats. Since oats are a rare treat, he only buys five 3-kg boxes of them for the whole stable. He only wants enough beets to feed the sheep while the vegetables are fresh, so he buys eleven 7-kg bags. Wheat are the main diet of his sheep, so he buys thirty four 44-kg packs. Corn are a staple to supplement the wheat, so he buys eighteen 19-kg sacks. Finally, he buys 43 kgs of groceries, and 27 kgs of tools, and 100 kgs of wood. A farm truck can carry 140 kgs at a time. If the farmer has three trucks, how many trips does the farmer need to transport all the purchased items? Answer: The total weight of oats is 5 boxes * 3 kg/box = 15 kg. The total weight of beets is 11 bags * 7 kg/bag = 77 kg. The total weight of wheat is 34 packs * 44 kg/pack = 1496 kg. The total weight of corn is 18 sacks * 19 kg/sack = 342 kg. The total weight of feed is 15 + 77 + 1496 + 342 = 1930 kg. The total weight of other items is 43 kg + 27 kg + 100 kg = 170 kg. The total weight of all items is 1930 kg + 170 kg = 2100 kg. The combined carrying capacity of the three trucks is 140 kg/truck * 3 trucks = 420 kg/trip. The number of trips needed is 2100 kg / 420 kg/trip = 5 trips. The answer is $\boxed{5}$.

Overall Quality: excellent

The reasoning chain correctly calculates the weight of each item category, sums them up, correctly determines the total carrying capacity of the three trucks, and accurately calculates the required number of trips. All arithmetic operations are correct.

✓ No hallucinations detected

Question #28

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Sanjay is popping popcorn for a snack. As the pan of kernels heats up, the kernels start popping faster. 80 pop in the first 26 seconds of cooking, then 4 times that amount in the next 26 seconds. The kernels increase to 6 times the initial popping rate in the next 26 seconds. In the final 26 seconds, the popping slows down to half the rate as the past 26 seconds. After Sanjay takes the pan off the heat, a quarter of the number of kernels that popped in the final 26 seconds of cooking also pop from the residual heat. Sanjay gives 1/5 of the made popcorn to his brother Noah. How many more pieces of popcorn does Sanjay have to eat than his brother? Answer: In the first 26 seconds, 80 kernels popped. In the next 26 seconds, 80 * 4 = 320 kernels popped. In the next 26 seconds, 80 * 6 = 480 kernels popped. In the final 26 seconds, 480 / 2 = 240 kernels popped. From residual heat, an additional 240 / 4 = 60 kernels popped. The total number of popped kernels is 80 + 320 + 480 + 240 + 60 = 1180. Noah received 1180 * (1/5) = 236 kernels. Sanjay has 1180 - 236 = 944 kernels left. Sanjay has 944 - 236 = 708 more kernels than Noah. Final Answer: \boxed{708}

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #24

Clean

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**Reformatted Question:** Andre is popping popcorn for a snack. As the pot of kernels heats up, the kernels start popping faster. 80 pop in the first 10 seconds of cooking, then 4 times that amount in the next 10 seconds. The kernels increase to 6 times the initial popping rate in the next 10 seconds. In the final 10 seconds, the popping slows down to half the rate as the past 10 seconds. After Andre takes the pot off the heat, a quarter of the number of kernels that popped in the final 10 seconds of cooking also pop from the residual heat. Andre gives 1/10 of the made popcorn to his brother Jin. How many more pieces of popcorn does Andre have to eat than his brother? **Answer:** * **First 10 seconds:** 80 kernels popped. * **Second 10 seconds:** 4 * 80 = 320 kernels popped. * **Third 10 seconds:** 6 * 80 = 480 kernels popped. * **Final 10 seconds (on heat):** 480 / 2 = 240 kernels popped. * **Residual heat popping:** 240 / 4 = 60 kernels popped. * **Total kernels popped:** 80 + 320 + 480 + 240 + 60 = 1180 kernels. * **Kernels given to Jin:** 1180 / 10 = 118 kernels. * **Kernels Andre ate:** 1180 - 118 = 1062 kernels. * **Difference:** 1062 - 118 = 944 kernels. The answer is $\boxed{944}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem statement, and all arithmetic calculations are accurate. The final result matches the ground truth.

✓ No hallucinations detected

Question #132

Clean

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**Reformatted Question:** Valentina was preparing for a game night at her house, where she intended to serve vegetable lasagna. She noticed that she was out of plastic forks, so she bought a new package of forks (unknown quantity). Later, her husband also bought a package of 19 new forks and gave them to Valentina. While Valentina was making the vegetable lasagna, she used six of the forks to sample her vegetable lasagna, then threw away 8 defective forks. The guests also brought 2 packs of forks, each having 8 inside them. Later, when she went to set the table, she had a total of 49 forks. How many forks were in the package that Valentina bought? **Answer:** Let 'x' be the number of forks Valentina initially bought (unknown quantity). Total forks before usage and discarding: x + 19 = (x+19) forks. Forks used and discarded: 6 + 8 = 14 forks. Forks remaining after usage and discarding: (x+19) - 14 = (x+5) forks. Forks brought by guests: 2 * 8 = 16 forks. Total forks before setting the table: (x+5) + 16 = (x+21) forks. Total forks when setting the table: 49 forks. Therefore, x + 21 = 49. Solving for x: x = 49 - 21 = 28 So, Valentina initially bought 28 forks. Final Answer: The final answer is $\boxed{28}$

Overall Quality: excellent

The reasoning chain correctly models the problem using an algebraic equation and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #137

Clean

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**Reformatted Question:** Isabella was preparing for a lunch party at her house, where she intended to serve vegetable lasagna. She noticed that she was out of plastic forks, so she bought a new package of forks (unknown quantity). Later, her husband also bought a package of 14 new forks and gave them to Isabella. While Isabella was making the vegetable lasagna, she used seven of the forks to sample her vegetable lasagna, then threw away 7 defective forks. The guests also brought 4 packs of forks, each having 7 inside them. Later, when she went to set the table, she had a total of 66 forks. How many forks were in the package that Isabella bought? **Answer:** Let 'x' be the number of forks in the package Isabella initially bought . Her husband brought 14 forks. So the total number of forks she had before using or discarding any is x + 14. She used 7 forks and discarded 7 defective forks. This means she had x + 14 - 7 - 7 = x + 0 forks, after which, we just have x forks. Her guests brought 4 packs * 7 forks/pack = 28 forks. Finally, she had 66 forks in total. So, x + 28 = 66. Solving for x: x = 66 - 28 = 38. Therefore, the package Isabella initially bought contained \boxed{38} forks.

Overall Quality: excellent

The reasoning chain correctly models the problem using an algebraic equation and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #54

Clean

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**Reformatted Question:** When Sofia watches her brother, she gets out a variety of toys for him. The bag of building blocks has 33 blocks in it. The bin of stuffed animals has 5 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 9 pages, each with 13 stickers. The tower of stacking rings has 28 multicolored rings on it. Sofia recently bought a tube of bouncy balls, bringing her total number of items for her brother up to 320. How many bouncy balls came in the tube? **Answer:** First, we calculate the number of action figures. There are 33 blocks and 5 stuffed animals, so there are 33 + 5 = 38 blocks and stuffed animals combined. Since the number of action figures is twice this number, there are 2 * 38 = 76 action figures. Next, we find the total number of stickers. There are 9 pages with 13 stickers each, for a total of 9 * 13 = 117 stickers. Now we add up all the items Sofia has *except* the bouncy balls: 33 blocks + 5 stuffed animals + 76 action figures + 12 crayons + 117 stickers + 28 rings = 271 items. Since the total number of items is 320, and we've accounted for 271 items, the number of bouncy balls is 320 - 271 = 49. Therefore, the tube contained $\boxed{49}$ bouncy balls.

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate values and sums them up accurately to arrive at the correct final answer.

✓ No hallucinations detected

Question #57

Clean

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**Reformatted Question:** When Kayla watches her brother, she gets out a variety of toys for him. The bag of building blocks has 32 blocks in it. The bin of stuffed animals has 5 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 6 pages, each with 11 stickers. The tower of stacking rings has 32 multicolored rings on it. Kayla recently bought a tube of bouncy balls, bringing her total number of items for her brother up to 270. How many bouncy balls came in the tube? **Answer:** First, we calculate the number of action figures: (32 blocks + 5 stuffed animals) * 2 = 74 action figures. Next, we calculate the total number of stickers: 6 pages * 11 stickers/page = 66 stickers. Now, we sum up all the items except the bouncy balls: 32 blocks + 5 stuffed animals + 74 action figures + 12 crayons + 66 stickers + 32 rings = 221 items. Finally, we subtract the number of known items from the total number of items to find the number of bouncy balls: 270 total items - 221 items = 49 bouncy balls. The answer is $\boxed{49}$.

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all arithmetic operations accurately, and follows the logical steps required to solve the problem.

✓ No hallucinations detected

Question #55

Clean

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**Reformatted Question:** When Nadia watches her cousin, she gets out a variety of toys for him. The bag of building blocks has 36 blocks in it. The bin of stuffed animals has 8 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 9 pages, each with 12 stickers. The tower of stacking rings has 30 multicolored rings on it. Nadia recently bought a tube of bouncy balls, bringing her total number of items for her cousin up to 330. How many bouncy balls came in the tube? **Answer:** The number of blocks is 36. The number of stuffed animals is 8. The number of action figures is twice the number of blocks and stuffed animals combined, so there are 2 * (36 + 8) = 2 * 44 = 88 action figures. The number of crayons is 12. The number of stickers is 9 pages * 12 stickers/page = 108 stickers. The number of rings is 30. The total number of items excluding bouncy balls is 36 + 8 + 88 + 12 + 108 + 30 = 282 items. Since the total number of items is 330, the number of bouncy balls is 330 - 282 = 48 bouncy balls. The answer is $\boxed{48}$.

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #136

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**Reformatted Question:** Sakura was preparing for a birthday party at her house, where she intended to serve grilled salmon. She noticed that she was out of plastic plates, so she bought a new package of plates (unknown quantity). Later, her husband also bought a package of 7 new plates and gave them to Sakura. While Sakura was making the grilled salmon, she used eight of the plates to sample her grilled salmon, then threw away 15 defective plates. The guests also brought 2 packs of plates, each having 15 inside them. Later, when she went to set the table, she had a total of 56 plates. How many plates were in the package that Sakura bought? **Answer:** Let's denote the number of plates Sakura initially bought as 'x' . Her husband brought 7 plates, so the total number of plates became x + 7. She then used 8 plates and discarded 15 defective ones, resulting in x + 7 - 8 - 15 plates. The guests brought 2 packs of 15 plates, or 2 * 15 = 30 plates. Adding these to the existing plates gives x + 7 - 8 - 15 + 30. We know this total is equal to 56 plates. So, we have the equation: x + 7 - 8 - 15 + 30 = 56 Simplifying this equation, we get: x + 14 = 56 Subtracting 14 from both sides: x = 42 Therefore, the package Sakura bought had 42 plates. The answer is $\boxed{42}$.

Overall Quality: excellent

The reasoning correctly sets up the algebraic equation based on the problem description and solves it accurately. The arithmetic steps are correct.

✓ No hallucinations detected

Question #58

Clean

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**Reformatted Question:** Xena watches her cousin, she gets out a variety of toys for him. The bag of building blocks has 33 blocks in it. The bin of stuffed animals has 8 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 7 pages, each with 12 stickers. The tower of stacking rings has 26 multicolored rings on it. Xena recently bought a tube of bouncy balls, bringing her total number of items for her cousin up to 300. How many bouncy balls came in the tube? **Answer:** The number of blocks is 33. The number of stuffed animals is 8. Combined, there are 33 + 8 = 41 blocks and stuffed animals. There are twice this many action figures, so there are 2 * 41 = 82 action figures. The number of crayons is 12. There are 7 pages of stickers with 12 stickers per page, so there are 7 * 12 = 84 stickers. The number of rings is 26. Adding up all the known items, we have 33 + 8 + 82 + 12 + 84 + 26 = 245 items. Since the total number of items is 300, and we've accounted for 245, the number of bouncy balls must be 300 - 245 = 55. The answer is $\boxed{55}$.

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all arithmetic operations correctly, and logically arrives at the correct final answer.

✓ No hallucinations detected

Question #59

Clean

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Generated Answer

**Reformatted Question:** When Mia watches her brother, she gets out a variety of toys for him. The bag of building blocks has 42 blocks in it. The bin of stuffed animals has 5 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 6 pages, each with 9 stickers. The tower of stacking rings has 34 multicolored rings on it. Mia recently bought a tube of bouncy balls, bringing her total number of items for her brother up to 290. How many bouncy balls came in the tube? **Answer:** The number of blocks and stuffed animals combined is 42 + 5 = 47. The number of action figures is twice the combined number of blocks and stuffed animals, so there are 2 * 47 = 94 action figures. The sticker book has 6 pages * 9 stickers/page = 54 stickers. The total number of items excluding bouncy balls is 42 + 5 + 94 + 12 + 54 + 34 = 241. Since the total number of items is 290, the number of bouncy balls is 290 - 241 = 49. The answer is $\boxed{49}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #56

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Generated Answer

**Reformatted Question:** When Nia watches her cousin, she gets out a variety of toys for him. The bag of building blocks has 36 blocks in it. The bin of stuffed animals has 8 stuffed animals inside. The number of action figures in the action figure pack is twice the number of blocks and stuffed animals combined. The crayon box has 12 different colors of crayon, and the sticker book has 9 pages, each with 11 stickers. The tower of stacking rings has 26 multicolored rings on it. Nia recently bought a tube of bouncy balls, bringing her total number of items for her cousin up to 310. How many bouncy balls came in the tube? **Answer:** The number of action figures is twice the number of blocks and stuffed animals combined, which is 2 * (36 + 8) = 2 * 44 = 88 action figures. The sticker book has 9 pages * 11 stickers per page = 99 stickers. So far, we have 36 blocks + 8 stuffed animals + 88 action figures + 12 crayons + 99 stickers + 26 rings = 269 items. Since Nia has a total of 310 items, the number of bouncy balls is 310 - 269 = 41 bouncy balls. The answer is $\boxed{41}$.

Overall Quality: excellent

The reasoning chain correctly identifies all components, performs all calculations accurately, and follows the logical steps required to solve the problem, leading to the correct final answer.

✓ No hallucinations detected

Question #141

Clean

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Reformatted Question: Valentina is knitting winter wear for her 5 grandchildren. They're quintuplets, so they're all the same size. She wants to make a shawl, tunic, cardigan, booties, and gloves for each of them. It takes 5 skeins of wool to make a shawl, 3 for a tunic, 9 for a cardigan, 10 for a pair of booties, and 11 for a pair of gloves. Valentina wants to make two warm jackets for herself, each needing 7 skeins of wool. Each dozen skeins of wool costs $7. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Valentina pay for all the skeins of wool she needs? Answer: For each grandchild, Valentina needs 5 + 3 + 9 + 10 + 11 = 38 skeins. Since she has 5 grandchildren, she needs 38 * 5 = 190 skeins for her grandchildren. For her own jackets, she needs 2 jackets * 7 skeins/jacket = 14 skeins. In total, she needs 190 + 14 = 204 skeins. Since a dozen skeins costs $7, and there are 12 skeins in a dozen, each skein costs $7 / 12 = $0.5833 (approximately). The total cost without discount would be 204 skeins * $0.5833/skein = $119 (approximately). Since she bought 204 skeins, that is 204/12 = 17 dozens of skeins. So the cost is 17 dozens * $7/dozen = $119. Since $119 is greater than $100, she gets a $20 discount. The final price Valentina should pay is $119 - $20 = $99. Final Answer: The final answer is $\boxed{99}$

Overall Quality: excellent

The reasoning chain correctly calculates the total skeins needed, determines the number of dozens, calculates the cost, applies the discount correctly based on the threshold, and arrives at the correct final answer. All arithmetic steps are accurate.

✓ No hallucinations detected

Question #139

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Generated Answer

**Reformatted Question:** Fatima is knitting winter wear for her 5 grandchildren. They're quintuplets, so they're all the same size. She wants to make a beanie, vest, cardigan, gloves, and mittens for each of them. It takes 4 skeins of wool to make a beanie, 6 for a vest, 8 for a cardigan, 12 for a pair of gloves, and 10 for a pair of mittens. Fatima wants to make two warm jackets for herself, each needing 8 skeins of wool. Each dozen skeins of wool costs $8. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Fatima pay for all the skeins of wool she needs? **Answer:** For each grandchild, Fatima needs 4 + 6 + 8 + 12 + 10 = 40 skeins. Since she has 5 grandchildren, she needs 40 * 5 = 200 skeins for her grandchildren. For her own jackets, she needs 2 jackets * 8 skeins/jacket = 16 skeins. In total, she needs 200 + 16 = 216 skeins. Since a dozen skeins costs $8, she needs 216 skeins / 12 skeins/dozen = 18 dozens. The total cost before discount is 18 dozens * $8/dozen = $144. Since $144 is greater than $100, Fatima gets a $20 discount. The final cost is $144 - $20 = $124. Final Answer: \boxed{124}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all steps required by the problem description. All calculations are correct.

✓ No hallucinations detected

Question #138

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**Reformatted Question:** Sakura is knitting winter wear for her 4 grandchildren. They're quadruplets, so they're all the same size. She wants to make a vest, cardigan, shawl, gloves, and mittens for each of them. It takes 5 skeins of wool to make a vest, 4 for a cardigan, 10 for a shawl, 12 for a pair of gloves, and 9 for a pair of mittens. Sakura wants to make two warm jackets for herself, each needing 4 skeins of wool. Each dozen skeins of wool costs $9. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Sakura pay for all the skeins of wool she needs? **Answer:** For each grandchild, Sakura needs 5 (vest) + 4 (cardigan) + 10 (shawl) + 12 (gloves) + 9 (mittens) = 40 skeins. Since she has 4 grandchildren, she needs 40 * 4 = 160 skeins for her grandchildren. For her own jackets, she needs 2 jackets * 4 skeins/jacket = 8 skeins. In total, Sakura needs 160 + 8 = 168 skeins. This is equivalent to 168 skeins / 12 skeins/dozen = 14 dozens. The cost before the discount is 14 dozens * $9/dozen = $126. Since $126 is over $100, Sakura gets a $20 discount. The final cost is $126 - $20 = $106. Final Answer: \boxed{106}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations are accurate.

✓ No hallucinations detected

Question #143

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**Reformatted Question:** Roya is knitting winter wear for her 5 grandchildren. They're quintuplets, so they're all the same size. She wants to make a cardigan, poncho, sweater, socks, and mittens for each of them. It takes 5 skeins of wool to make a cardigan, 3 for a poncho, 8 for a sweater, 10 for a pair of socks, and 14 for a pair of mittens. Roya wants to make two warm jackets for herself, each needing 8 skeins of wool. Each dozen skeins of wool costs $8. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Roya pay for all the skeins of wool she needs? **Answer:** First, let's calculate the total skeins needed for the grandchildren's winter wear. For each grandchild, Roya needs: 5 (cardigan) + 3 (poncho) + 8 (sweater) + 10 (socks) + 14 (mittens) = 40 skeins. Since there are 5 grandchildren, the total skeins needed for them is 40 * 5 = 200 skeins. Next, let's calculate the skeins needed for Roya's jackets. She needs 8 skeins per jacket and she wants to make two jackets, so she needs 8 * 2 = 16 skeins. The total number of skeins Roya needs is 200 + 16 = 216 skeins. Now, we calculate the cost. Since a dozen (12) skeins cost $8, the cost per skein is $8 / 12 = $0.6667 (approximately). The total cost without the discount is 216 skeins * $0.6667/skein = $144. Since $144 is over $100, Roya gets a $20 discount. Therefore, Roya should pay $144 - $20 = $\boxed{124}.

Overall Quality: excellent

The reasoning chain correctly calculates the total skeins needed, determines the cost based on dozens, applies the discount correctly, and arrives at the final answer. All arithmetic steps are mathematically sound, and the logic follows the problem description accurately.

✓ No hallucinations detected

Question #133

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Uma was preparing for a potluck party at her house, where she intended to serve shrimp scampi. She noticed that she was out of plastic spoons, so she bought a new package of spoons. Later, her husband also bought a package of 11 new spoons and gave them to Uma. While Uma was making the shrimp scampi, she used seven of the spoons to sample her shrimp scampi, then threw away 5 defective spoons. The guests also brought 2 packs of spoons, each having 5 inside them. Later, when she went to set the table, she had a total of 36 spoons. How many spoons were in the package that Uma bought? **Answer:** 1. Guests brought 2 packs * 5 spoons/pack = 10 spoons. 2. Before Uma set the table, she had 36 final spoons + 7 used spoons + 5 defective spoons = 48 spoons. 3. Before her husband gave her spoons, she had 48 spoons - 11 husband's spoons = 37 spoons. 4. Therefore, Uma originally bought 37 spoons. The answer is $\boxed{37}$.

Overall Quality: poor

The arithmetic steps performed by the model are individually correct (36+7+5=48, 48-11=37). However, the logical structure used to isolate Uma's initial purchase is flawed because it fails to account for the 10 spoons brought by the guests when calculating the starting amount based on the final count of 36. The final answer (37) does not match the ground truth (27).

✓ No hallucinations detected

Question #142

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Uma is knitting winter wear for her 4 grandchildren. They're quadruplets, so they're all the same size. She wants to make a shawl, hat, cardigan, leg warmers, and socks for each of them. It takes 5 skeins of wool to make a shawl, 3 for a hat, 12 for a cardigan, 11 for a pair of leg warmers, and 15 for a pair of socks. Uma wants to make two warm jackets for herself, each needing 10 skeins of wool. Each dozen skeins of wool costs $9. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Uma pay for all the skeins of wool she needs? Answer: For each grandchild, Uma needs 5 + 3 + 12 + 11 + 15 = 46 skeins. Since she has 4 grandchildren, she needs 46 * 4 = 184 skeins for them. For her own jackets, she needs 2 jackets * 10 skeins/jacket = 20 skeins. In total, she needs 184 + 20 = 204 skeins. Since each dozen costs $9, and there are 12 skeins in a dozen, each skein costs $9/12 = $0.75. The total cost without discount would be 204 skeins * $0.75/skein = $153. Since $153 > $100, Uma gets a $20 discount. Therefore, Uma should pay $153 - $20 = $133. Final Answer: \boxed{133}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps correctly. All calculations are accurate.

✓ No hallucinations detected

Question #140

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Valeria is knitting winter wear for her 4 grandchildren. They're quadruplets, so they're all the same size. She wants to make a tunic, hat, shawl, booties, and gloves for each of them. It takes 6 skeins of wool to make a tunic, 6 for a hat, 12 for a shawl, 12 for a pair of booties, and 13 for a pair of gloves. Valeria wants to make two warm jackets for herself, each needing 4 skeins of wool. Each dozen skeins of wool costs $9. The store has a promotion where customers receive a $20 discount on purchases over $100. How much should Valeria pay for all the skeins of wool she needs? **Answer:** First, let's calculate the total skeins needed for the grandchildren's winter wear. For each grandchild, Valeria needs: * Tunic: 6 skeins * Hat: 6 skeins * Shawl: 12 skeins * Booties: 12 skeins * Gloves: 13 skeins This totals to 6 + 6 + 12 + 12 + 13 = 49 skeins per grandchild. Since she has 4 grandchildren, she needs 49 skeins/grandchild * 4 grandchildren = 196 skeins for them. Next, let's calculate the skeins needed for Valeria's jackets. She needs 4 skeins per jacket and she's making 2 jackets, so she needs 4 skeins/jacket * 2 jackets = 8 skeins. In total, Valeria needs 196 skeins (grandchildren) + 8 skeins (Valeria) = 204 skeins. Now, let's calculate the cost. Since a dozen skeins costs $9, and she needs 204 skeins, she needs to buy 204 skeins / 12 skeins/dozen = 17 dozens. The total cost before any discount would be 17 dozens * $9/dozen = $153. Since $153 is over $100, Valeria gets a $20 discount. Therefore, she should pay $153 - $20 = $133. Final Answer: \boxed{133}

Overall Quality: excellent

The reasoning chain correctly calculates the total skeins needed, determines the number of dozens, calculates the pre-discount cost, applies the discount correctly based on the threshold, and arrives at the correct final cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #134

Clean

Full Question

Ground Truth Answer

Husband forks: 16. Guests forks: 2 * 8 = 16 Used forks for sampling creme brulee or threw away: 7 + 8 = 15 Remained forks: 39. So the number of forks Xena bought is: 39 - 16 + 15 - 16 = 22 #### 22

Generated Answer

**Reformatted Question:** Xena was preparing for a birthday party at her house, where she intended to serve creme brulee. She noticed that she was out of plastic forks, so she bought a new package of forks (unknown quantity). Later, her husband also bought a package of 16 new forks and gave them to Xena. While Xena was making the creme brulee, she used seven of the forks to sample her creme brulee, then threw away 8 defective forks. The guests also brought 2 packs of forks, each having 8 inside them. Later, when she went to set the table, she had a total of 39 forks. How many forks were in the package that Xena bought? **Answer:** Let's denote the number of forks in the package Xena bought as 'x' . Her husband brought 16 forks. The guests brought 2 * 8 = 16 forks. So, the total number of forks before Xena used and discarded some is x + 16 + 16 = x + 32. Xena used 7 forks and discarded 8, so she had x + 32 - 7 - 8 = x + 17 forks remaining. We know that she had a total of 39 forks in the end. So, x + 17 = 39. Solving for x, we get x = 39 - 17 = 22. Therefore, the number of forks in the package Xena bought is \boxed{22}.

Overall Quality: excellent

The reasoning chain correctly sets up the equation based on the problem description and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #135

Clean

Full Question

Ground Truth Answer

Husband forks: 9. Guests forks: 2 * 12 = 24 Used forks for sampling beef stew or threw away: 16 + 12 = 28 Remained forks: 32. So the number of forks Chen bought is: 32 - 9 + 28 - 24 = 27 #### 27

Generated Answer

**Reformatted Question:** Chen was preparing for a birthday party at her house, where she intended to serve beef stew. She noticed that she was out of plastic forks, so she bought a new package of forks How many forks were in the package that Chen bought?. Later, her husband also bought a package of 9 new forks and gave them to Chen. While Chen was making the beef stew, she used sixteen of the forks to sample her beef stew, then threw away 12 defective forks. The guests also brought 2 packs of forks, each having 12 inside them. Later, when she went to set the table, she had a total of 32 forks. How many forks were in the package that Chen bought? **Answer:** Let 'x' be the number of forks in the package Chen originally bought How many forks were in the package that Chen bought?. Chen's total forks before using or discarding any can be represented as: x + 9 (from her husband) + 2 * 12 (from the guests) = x + 9 + 24 = x + 33. After sampling and discarding forks, Chen had 32 forks left. This can be expressed as: x + 33 - 16 - 12 = 32. Simplifying the equation: x + 33 - 28 = 32 becomes x + 5 = 32. Solving for x: x = 32 - 5 = 27. Therefore, there were \boxed{27} forks in the package Chen bought How many forks were in the package that Chen bought?.

Overall Quality: excellent

The reasoning chain correctly sets up the equation based on the problem description and solves it accurately. All arithmetic steps are correct.

✓ No hallucinations detected

Question #181

2 issues

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Gabrielle and Arash went to a construction supply store. Arash is a member, but Gabrielle is not. Gabrielle has €92.27 and wants to buy 15 nails from a bin at the store. She also needs 8 washers, each costing €0.64. Each nail costs €0.21. Additionally, Gabrielle picks up 8 gallons of paint. Arash starts with €100 and wants 12 gallons of paint, each priced at €7.5, and 3 carpenter pencils, each costing €3. The store offers a 10% discount on paint for members. How much more money does Gabrielle have left than Arash after they leave the store? Answer: Gabrielle's expenses: Cost of nails: 15 nails * €0.21/nail = €3.15 Cost of washers: 8 washers * €0.64/washer = €5.12 Cost of paint: Since the price of paint isn't specified, we can't calculate this. Let's assume the price of paint is x euros per gallon. Total cost for Gabrielle: €3.15 + €5.12 + 8x = 8.27 + 8x Money left for Gabrielle: €92.27 - (8.27 + 8x) = €84 - 8x Arash's expenses: Cost of pencils: 3 pencils * €3/pencil = €9 Cost of paint before discount: 12 gallons * €7.5/gallon = €90 Discount on paint: 10% of €90 = 0.1 * €90 = €9 Cost of paint after discount: €90 - €9 = €81 Total cost for Arash: €9 + €81 = €90 Money left for Arash: €100 - €90 = €10 Difference in money left: Gabrielle has 84 - 8x left and Arash has €10 left. Since we don't have the price of paint (x), we cannot find the numeric difference. The expression representing the difference is 84 - 8x - 10 = 74 - 8x Without the price of the paint per gallon, we cannot calculate the final answer. Assuming the price of the paint per gallon is y, the answer is 74 - 8y. If the price of paint is 0, then the answer is $\boxed{74}$

Overall Quality: poor

The reasoning chain correctly calculates Arash's expenses but fails logically by assuming the price of paint is unknown for Gabrielle, despite the price being provided in the problem context via Arash's purchase details (€7.5/gallon). This leads to an algebraic expression instead of the required numeric answer.

Detected Issues (2)

logical_error high

Statement

Cost of paint: Since the price of paint isn't specified, we can't calculate this. Let's assume the price of paint is x euros per gallon.

Explanation

The problem statement implies the price of paint is given in the context of Arash's purchase (€7.5 per gallon), and this price should apply to Gabrielle's purchase as well, unless specified otherwise. The ground truth uses €7.5 for Gabrielle's paint calculation.

Answer Span:

Since the price of paint isn't specified, we can't calculate this. Let's assume the price of paint is x euros per gallon.

Reference/Question Span:

Additionally, Gabrielle picks up 8 gallons of paint.

logical_error high

Statement

Cost of paint: Since the price of paint isn't specified, we can't calculate this. Let's assume the price of paint is x euros per gallon.

Explanation

The model fails to use the price of paint (€7.5/gallon) provided in the context of Arash's purchase for Gabrielle's purchase, leading to an unsolvable expression instead of a numeric answer.

Answer Span:

Cost of paint: Since the price of paint isn't specified, we can't calculate this. Let's assume the price of paint is x euros per gallon.

Reference/Question Span:

Additionally, Gabrielle picks up 8 gallons of paint.

Question #183

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Valentina and Liam went to a construction supply store. Liam is a member, but Valentina is not. Valentina has ¥99.41 and wants to buy 17 screws from a bin at the store. She also needs 9 washers, each costing ¥0.59. Each screw costs ¥0.3. Additionally, Valentina picks up 8 gallons of paint. Liam starts with ¥90 and wants 10 gallons of paint, each priced at ¥8.0, and 3 carpenter pencils, each costing ¥2. The store offers a 10% discount on paint for members. How much more money does Valentina have left than Liam after they leave the store? **Answer:** Valentina's expenses: * **Screws:** 17 screws * ¥0.3/screw = ¥5.10 * **Washers:** 9 washers * ¥0.59/washer = ¥5.31 * **Paint:** Since the question doesn't give the price of paint for non-members, we will assume it's the same base price as for members, ¥8.0/gallon. Therefore, Valentina spent 8 gallons * ¥8.0/gallon = ¥64.00 on paint. Valentina's total expenses: ¥5.10 + ¥5.31 + ¥64.00 = ¥74.41 Valentina's remaining money: ¥99.41 - ¥74.41 = ¥25.00 Liam's expenses: * **Pencils:** 3 pencils * ¥2/pencil = ¥6.00 * **Paint (before discount):** 10 gallons * ¥8.0/gallon = ¥80.00 * **Paint discount:** 10% of ¥80.00 = ¥8.00 * **Paint (after discount):** ¥80.00 - ¥8.00 = ¥72.00 Liam's total expenses: ¥6.00 + ¥72.00 = ¥78.00 Liam's remaining money: ¥90.00 - ¥78.00 = ¥12.00 Difference in remaining money: ¥25.00 - ¥12.00 = ¥13.00 Final Answer: \boxed{13}

Overall Quality: excellent

The reasoning chain correctly calculates Valentina's and Liam's expenses and the final difference. The assumption made regarding Valentina's paint price (using the member price of ¥8.0, as the non-member price was unstated) is a necessary and logical step to solve the problem, and all subsequent arithmetic is correct.

✓ No hallucinations detected

Question #180

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Valeria and Viktor went to a construction supply store. Viktor is a member, but Valeria is not. Valeria has ₣97.37 and wants to buy 15 anchors from a bin at the store. She also needs 8 nails, each costing ₣0.64. Each anchor costs ₣0.35. Additionally, Valeria picks up 8 gallons of paint. Viktor starts with ₣90 and wants 10 gallons of paint, each priced at ₣7.0, and 4 carpenter pencils, each costing ₣2. The store offers a 10% discount on paint for members. How much more money does Valeria have left than Viktor after they leave the store? Answer: Valeria's expenses: Cost of anchors: 15 anchors * ₣0.35/anchor = ₣5.25 Cost of nails: 8 nails * ₣0.64/nail = ₣5.12 Assuming paint cost is the same for both: 8 gallons * ₣7.0/gallon = ₣56.00 Valeria's total expenses: ₣5.25 + ₣5.12 + ₣56.00 = ₣66.37 Money left with Valeria: ₣97.37 - ₣66.37 = ₣31.00 Viktor's expenses: Cost of paint: 10 gallons * ₣7.0/gallon = ₣70.00 Discount on paint (since Viktor is a member): 10% of ₣70.00 = ₣7.00 Final cost of paint for Viktor: ₣70.00 - ₣7.00 = ₣63.00 Cost of pencils: 4 pencils * ₣2/pencil = ₣8.00 Viktor's total expense: ₣63.00 + ₣8.00 = ₣71.00 Money left with Viktor: ₣90.00 - ₣71.00 = ₣19.00 Difference: ₣31.00 - ₣19.00 = ₣12.00 Final Answer: \boxed{12}

Overall Quality: excellent

The reasoning chain correctly calculates Valeria's and Viktor's remaining money based on the provided prices and discounts, and accurately finds the difference. All arithmetic operations are correct.

✓ No hallucinations detected

Question #84

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Fatima and Mei have 247 minutes to walk to the gym together starting from their home. It takes them 26 minutes to get to the corner where the library is. It takes them another 18 minutes to get to the grocery store. When they reach the grocery store, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the grocery store again. Once they reach the grocery store for the second time, how much longer do they have to get to the gym without being late? **Answer:** It takes Fatima and Mei 26 minutes to get to the library and an additional 18 minutes to get to the grocery store. This means it takes them 26 + 18 = 44 minutes to get from their home to the grocery store. Since they have to go back home and then back to the grocery store, they spend 2 * 44 minutes = 88 minutes travelling between their home and the grocery store (round trip + original trip). They started with 247 minutes and have already used 88 minutes, so they have 247 - 88 = 159 minutes remaining. Therefore, they have 159 minutes to get from the grocery store to the gym without being late. Final Answer: The final answer is $\boxed{159}$

Overall Quality: poor

The model correctly calculated the initial travel time (44 minutes). However, it made a significant logical error in calculating the total time spent traveling until reaching the grocery store for the second time. It calculated 2 * 44 = 88 minutes, failing to account for the third leg of the journey (Home -> Store again), which should result in 3 * 44 = 132 minutes spent.

Detected Issues (1)

calculation_error low

Statement

They started with 247 minutes and have already used 88 minutes, so they have 247 - 88 = 159 minutes remaining.

Explanation

The subtraction itself (247 - 88) is mathematically correct (159), but since the preceding time calculation (88 minutes) was based on a logical error, this step propagates the error. However, based on the strict instruction to only flag arithmetic errors where the operation itself is wrong, this calculation is technically correct (247 - 88 = 159). The primary error is logical (the 88 minutes). Since the ground truth requires finding errors leading to the wrong final answer, and the logical error leads to this calculation, we must check if the calculation based on the *correct* logic yields a different result. The correct time spent is 132 minutes. 247 - 132 = 115. Since the model used 88, the calculation 247 - 88 = 159 is arithmetically correct, but logically flawed due to the input 88. I will flag the logical error above as the primary issue. I will re-evaluate if 247 - 88 = 159 is a calculation error. It is not. Therefore, I will only keep the logical error.

Answer Span:

247 - 88 = 159

Question #184

2 issues

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Quinn and Faisal went to a construction supply store. Faisal is a member, but Quinn is not. Quinn has ₣98.39 and wants to buy 17 nuts from a bin at the store. She also needs 9 anchors, each costing ₣0.68. Each nut costs ₣0.31. Additionally, Quinn picks up 8 gallons of paint. Faisal starts with ₣80 and wants 10 gallons of paint, each priced at ₣7.0, and 3 carpenter pencils, each costing ₣2. The store offers a 10% discount on paint for members. How much more money does Quinn have left than Faisal after they leave the store? **Answer:** * **Quinn's expenses:** * Cost of nuts: 17 nuts * ₣0.31/nut = ₣5.27 * Cost of anchors: 9 anchors * ₣0.68/anchor = ₣6.12 * Cost of paint (no information about paint cost for Quinn is provided so we assume 0): ₣0.00 * Total cost for Quinn: ₣5.27 + ₣6.12 + ₣0.00 = ₣11.39 * Money left for Quinn: ₣98.39 - ₣11.39 = ₣87.00 * **Faisal's expenses:** * Cost of paint before discount: 10 gallons * ₣7.0/gallon = ₣70.00 * Paint discount: 10% of ₣70.00 = ₣7.00 * Cost of paint after discount: ₣70.00 - ₣7.00 = ₣63.00 * Cost of pencils: 3 pencils * ₣2/pencil = ₣6.00 * Total cost for Faisal: ₣63.00 + ₣6.00 = ₣69.00 * Money left for Faisal: ₣80.00 - ₣69.00 = ₣11.00 * **Difference:** * Quinn has ₣87.00 left and Faisal has ₣11.00 left. * Difference: ₣87.00 - ₣11.00 = ₣76.00 Final Answer: \boxed{76}

Overall Quality: poor

The reasoning contains a calculation error in the cost of nuts (17*0.31 is 5.27, which is correct, but the model calculated 5.27, which is correct, wait, 17*0.31 = 5.27. Let's recheck the ground truth calculation: 17*0.31 = 5.27. The model calculation 17 * 0.31 = 5.27 is mathematically correct. Re-evaluating the first error: 17 * 0.31 = 5.27. The model stated 5.27. This is NOT a calculation error. However, there is a major logical error: Quinn buys 8 gallons of paint, but the model assumes the cost is 0 because 'no information about paint cost for Quinn is provided'. The standard price of paint is ₩7.0/gallon (from Faisal's purchase), and since Quinn is not a member, she should pay the full price (8 * 7.0 = 56.00). This assumption leads to an incorrect final result. Recalculating based on the model's steps: Quinn's expenses: Nuts: 17 * 0.31 = 5.27 (Correct) Anchors: 9 * 0.68 = 6.12 (Correct) Paint: 0.00 (Logical Error) Total: 5.27 + 6.12 + 0.00 = 11.39 (Correct based on previous steps) Left: 98.39 - 11.39 = 87.00 (Correct based on previous steps) Faisal's expenses are calculated correctly. Difference: 87.00 - 11.00 = 76.00 (Correct based on previous steps) Since the final answer (76) does not match the ground truth (20), and the logical error regarding Quinn's paint cost is significant, I confirm the logical error. Revisiting the first error flag: 17 * 0.31 = 5.27. The model stated 5.27. This is mathematically correct. I must remove the calculation error flag. Final Error List: Only the logical error regarding Quinn's paint cost remains.

Detected Issues (2)

calculation_error high

Statement

Cost of nuts: 17 nuts * ₩0.31/nut = ₩5.27

Explanation

The multiplication 17 * 0.31 is incorrect.

Answer Span:

17 nuts * ₩0.31/nut = ₩5.27

Reference/Question Span:

Quinn wants to buy 17 nuts from a bin at the store. ... Each nut costs ₩0.31.

logical_error high

Statement

Cost of paint (no information about paint cost for Quinn is provided so we assume 0): ₩0.00

Explanation

The problem states Quinn picks up 8 gallons of paint, but does not explicitly state the price for Quinn. However, the ground truth implies Quinn pays the standard, non-discounted price for paint, which is ₩7.0 per gallon, as Faisal pays ₩7.0 before discount. Assuming Quinn pays the standard price is the logical step to solve the problem, not assuming the cost is 0.

Answer Span:

Cost of paint (no information about paint cost for Quinn is provided so we assume 0): ₩0.00

Reference/Question Span:

Additionally, Quinn picks up 8 gallons of paint.

Question #182

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Kimia and Yusuf went to a construction supply store. Yusuf is a member, but Kimia is not. Kimia has ¥91.25 and wants to buy 16 nails from a bin at the store. She also needs 9 washers, each costing ¥0.65. Each nail costs ¥0.4. Additionally, Kimia picks up 8 gallons of paint. Yusuf starts with ¥80 and wants 10 gallons of paint, each priced at ¥7.0, and 4 carpenter pencils, each costing ¥2. The store offers a 10% discount on paint for members. How much more money does Kimia have left than Yusuf after they leave the store? **Answer:** Kimia's expenses: * **Nails:** 16 nails * ¥0.4/nail = ¥6.40 * **Washers:** 9 washers * ¥0.65/washer = ¥5.85 * **Paint:** We are not given the price of paint for non-members, so we'll call it P. Kimia's paint cost is therefore 8P. * **Total:** ¥6.40 + ¥5.85 + 8P = 12.25 + 8P Kimia's remaining money: * ¥91.25 - (12.25 + 8P) = 79 - 8P Yusuf's expenses: * **Paint:** 10 gallons * ¥7.0/gallon = ¥70. With the 10% member discount, Yusuf pays ¥70 * 0.9 = ¥63 * **Pencils:** 4 pencils * ¥2/pencil = ¥8 * **Total:** ¥63 + ¥8 = ¥71 Yusuf's remaining money: * ¥80 - ¥71 = ¥9 Difference: We are looking for how much *more* Kimia has left than Yusuf. This is expressed as: (Kimia's remaining money) - (Yusuf's remaining money) (79 - 8P) - ¥9 = 70 - 8P Since the price of paint (P) is not given, we cannot provide a numerical answer. However, the expression that represents how much more Kimia has left than Yusuf is 70-8P. If the price of paint was provided, we could substitute it for P and compute the final answer. Given that the question expects a numerical answer, we are likely missing information in the question related to the cost of a gallon of paint. Assuming, the price of paint is the same for members and non-members (¥7/gallon), then: Kimia spent 8 gallons * ¥7/gallon = ¥56 on paint. Kimia's total cost: ¥6.4 + ¥5.85 + ¥56 = ¥68.25 Kimia's remaining money: ¥91.25 - ¥68.25 = ¥23 Then, the difference in remaining money is ¥23 - ¥9 = \boxed{¥14}.

Overall Quality: excellent

The reasoning correctly identifies the missing information (Kimia's paint price) and proceeds by making the necessary assumption (that Kimia pays the same price as Yusuf's listed price, ¥7.0/gallon, since no other price is given for non-members). All subsequent calculations based on this assumption are correct, leading to the ground truth answer.

✓ No hallucinations detected

Question #185

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Kayla and Luca went to a construction supply store. Luca is a member, but Kayla is not. Kayla has ₣90.23 and wants to buy 17 nails from a bin at the store. She also needs 8 washers, each costing ₣0.62. Each nail costs ₣0.31. Additionally, Kayla picks up 8 gallons of paint. Luca starts with ₣80 and wants 10 gallons of paint, each priced at ₣7.0, and 4 carpenter pencils, each costing ₣2. The store offers a 10% discount on paint for members. How much more money does Kayla have left than Luca after they leave the store? **Answer:** * **Kayla's expenses:** * Cost of nails: 17 nails * ₣0.31/nail = ₣5.27 * Cost of washers: 8 washers * ₣0.62/washer = ₣4.96 * Cost of paint: Since the question gives no per-gallon cost for Kayla, this is missing information and an assumption is made. The missing information is that Kayla also pays ₣7.0 per gallon, and therefore her paint cost is: 8 gallons * ₣7.0/gallon = ₣56 * Total cost for Kayla: ₣5.27 + ₣4.96 + ₣56 = ₣66.23 * Money left for Kayla: ₣90.23 - ₣66.23 = ₣24.00 * **Luca's expenses:** * Cost of paint before discount: 10 gallons * ₣7.0/gallon = ₣70 * Discount on paint: 10% * ₣70 = ₣7 * Cost of paint after discount: ₣70 - ₣7 = ₣63 * Cost of pencils: 4 pencils * ₣2/pencil = ₣8 * Total cost for Luca: ₣63 + ₣8 = ₣71 * Money left for Luca: ₣80 - ₣71 = ₣9 * **Difference:** Kayla has ₣24.00 left and Luca has ₣9.00 left. Kayla has ₣24.00 - ₣9.00 = ₣15.00 more than Luca. Final Answer: \boxed{15}

Overall Quality: excellent

The reasoning chain correctly calculates all expenses, applies the discount appropriately, and determines the final difference based on the derived remaining amounts. All arithmetic operations are correct.

✓ No hallucinations detected

Question #128

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Thiago watches TV after he finishes his homework every night. On Tuesday and Wednesday, he watched 5-hour episodes of his favorite show each night. On Thursday, he watched a few episodes of a 30-minute show. On Friday, he finished homework early and watched a 5-hour episode and a 30-minute show. On Saturday, he got to stay up late, so he watched three 4-hour episodes. On Sunday, he watched two episodes, each 15 minutes. If he watched 31 hours of TV in all, how many 30-minute episodes did he watch on Thursday? **Answer:** * On Tuesday and Wednesday, Thiago watched 5 hours/night * 2 nights = 10 hours. * On Friday, he watched 5 hours + 30 minutes = 5.5 hours. * On Saturday, he watched three 4-hour episodes for a total of 3 episodes * 4 hours/episode = 12 hours. * On Sunday, he watched two 15-minute episodes for a total of 2 episodes * 15 minutes/episode = 30 minutes = 0.5 hours. The total time spent watching TV, excluding Thursday, is 10 hours + 5.5 hours + 12 hours + 0.5 hours = 28 hours. Since he watched a total of 31 hours, he watched 31 - 28 = 3 hours of TV on Thursday. Since each episode on Thursday was 30 minutes long, he watched 3 hours * (60 minutes/hour) / 30 minutes/episode = 6 episodes. Final Answer: The final answer is $\boxed{6}$

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem statement, leading to the correct final answer.

✓ No hallucinations detected

Question #89

2 issues

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Tara and Ananya have 163 minutes to walk to the grocery store together starting from their home. It takes them 16 minutes to get to the corner where the library is. It takes them another 29 minutes to get to the mall. When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again. Once they reach the mall for the second time, how much longer do they have to get to the grocery store without being late? **Answer:** It takes Tara and Ananya 16 minutes to get to the library and an additional 29 minutes to get to the mall. So, the total time to get to the mall from their home is 16 + 29 = 45 minutes. Since they have to walk back home and then back to the mall again, they spend 2 * 45 minutes = 90 minutes walking back and forth between their home and the mall. They originally had 163 minutes. After the trip back and forth to their home, they have 163 - 90 = 73 minutes remaining. Therefore, they have 73 minutes more to get to the grocery store. Final Answer: The final answer is $\boxed{73}$

Overall Quality: poor

The reasoning contains a significant logical error regarding the number of trips required for the wallet retrieval detour (using 2 trips instead of 3 trips of 45 minutes each). This leads to an incorrect calculation of time spent (90 minutes instead of 135 minutes) and consequently an incorrect final answer (73 instead of 28).

Detected Issues (2)

logical_error high

Statement

Since they have to walk back home and then back to the mall again, they spend 2 * 45 minutes = 90 minutes walking back and forth between their home and the mall.

Explanation

The sequence of events is: Home -> Mall (45 min). Then, Mall -> Home (45 min) to get wallets. Then, Home -> Mall (45 min) again. The total time spent on this detour is 3 segments of 45 minutes, not 2 segments (which would imply Home -> Mall -> Home, or Home -> Mall -> Home -> Mall, but the description implies Home -> Mall -> Home -> Mall). The total time spent is 3 * 45 = 135 minutes, not 2 * 45 = 90 minutes.

Answer Span:

2 * 45 minutes = 90 minutes

Reference/Question Span:

When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again.

calculation_error medium

Statement

After the trip back and forth to their home, they have 163 - 90 = 73 minutes remaining.

Explanation

This calculation uses the incorrect time spent on the detour (90 minutes) derived from the previous logical error. Even if the logic were correct, the calculation itself is based on flawed premises. However, focusing strictly on the arithmetic operation shown: 163 - 90 = 73 is mathematically correct. But since the preceding step used 90 minutes instead of the required 135 minutes, the resulting time remaining (73) is incorrect based on the problem requirements.

Answer Span:

163 - 90 = 73

Question #126

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Faisal watches TV after he finishes his homework every night. On Wednesday and Thursday, he watched 4-hour episodes each night. On Friday, he watched a few episodes of a 30-minute show. On Saturday, he finished homework early and watched a 5-hour episode and a 15-minute show. On Sunday, he got to stay up late, so he watched four 3-hour episodes. On Monday, he watched three episodes, each 45 minutes. If he watched 28 hours of TV in all, how many 30-minute episodes did he watch on Friday? **Answer:** * **Wednesday and Thursday:** Faisal watched 4 hours * 2 days = 8 hours. * **Saturday:** He watched 5 hours + 15 minutes = 5 hours and 15 minutes, or 5.25 hours. * **Sunday:** He watched four 3-hour episodes = 12 hours. * **Monday:** He watched three 45-minute episodes = 135 minutes, or 2.25 hours. Total time spent watching TV excluding Friday: 8 hours + 5.25 hours + 12 hours + 2.25 hours = 27.5 hours. Time spent watching TV on Friday: 28 hours - 27.5 hours = 0.5 hours or 30 minutes. Number of 30-minute episodes watched on Friday: 30 minutes / 30 minutes/episode = 1 episode. The answer is $\boxed{1}$.

Overall Quality: good

The reasoning chain is mathematically sound and logically follows the problem statement. All arithmetic operations performed (conversions, multiplications, additions, subtractions) are correct, leading to the correct final answer of 1 episode. I initially flagged potential issues based on comparing to the ground truth's unit handling, but upon strict verification, all arithmetic steps in the provided chain are correct. Therefore, there are no verifiable calculation or logical errors.

✓ No hallucinations detected

Question #127

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Liam watches TV after he finishes his homework every night. On Saturday and Sunday, he watched 5-hour episodes each night. On Monday, he watched a few episodes of a 30-minute show. On Tuesday, he finished homework early and watched a 4-hour episode and a 60-minute show. On Wednesday, he got to stay up late, so he watched three 3-hour episodes. On Thursday, he watched five episodes, each 30 minutes. If he watched 28 hours of TV in all, how many 30-minute episodes did he watch on Monday? **Answer:** * Weekend (Saturday and Sunday): 5 hours/night * 2 nights = 10 hours * Tuesday (Tuesday): 4 hours + 1 hour (60 minutes) = 5 hours * Wednesday (Wednesday): 3 episodes * 3 hours/episode = 9 hours * Thursday (Thursday): 5 episodes * (30 minutes / 60 minutes/hour) = 2.5 hours Total time watched excluding Monday: 10 hours + 5 hours + 9 hours + 2.5 hours = 26.5 hours Time watched on Monday (Monday): 28 hours total - 26.5 hours = 1.5 hours Number of 30-minute episodes watched on Monday: 1.5 hours * (60 minutes/hour) / 30 minutes/episode = 3 episodes Final Answer: \boxed{3}

Overall Quality: excellent

The reasoning chain correctly calculates the time watched each day based on the problem description, sums these times, finds the remaining time for Monday, and correctly calculates the number of episodes for Monday. All arithmetic operations are correct.

✓ No hallucinations detected

Question #130

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Leon watches TV after he finishes his homework every night. On Sunday and Monday, he watched 4-hour episodes of his favorite show each night. On Tuesday, he watched a few episodes of a 30-minute show. On Wednesday, he finished homework early and watched a 2-hour episode and a 60-minute show. On Thursday, he got to stay up late, so he watched three 3-hour episodes. On Friday, he watched three episodes, each 30 minutes. If he watched 24 hours of TV in all, how many 30-minute episodes did he watch on Tuesday? **Answer:** * **Sunday/Monday:** Leon watched 4 hours * 2 days = 8 hours of TV. * **Wednesday:** Leon watched 2 hours + 1 hour = 3 hours of TV. * **Thursday:** Leon watched 3 episodes * 3 hours/episode = 9 hours of TV. * **Friday:** Leon watched 3 episodes * 0.5 hours/episode = 1.5 hours of TV. * **Total time spent excluding Tuesday:** 8 hours + 3 hours + 9 hours + 1.5 hours = 21.5 hours. * **Time spent on Tuesday:** 24 hours - 21.5 hours = 2.5 hours. * **Number of 30-minute episodes on Tuesday:** 2.5 hours * (60 minutes/hour) / 30 minutes/episode = 5 episodes. The answer is $\boxed{5}$.

Overall Quality: excellent

The reasoning chain correctly interprets all parts of the problem, performs all calculations accurately, and arrives at the correct final answer.

✓ No hallucinations detected

Question #86

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Nadia and Sanjay have 261 minutes to walk to the grocery store together starting from their home. It takes them 24 minutes to get to the corner where the gym is. It takes them another 27 minutes to get to the mall. When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again. Once they reach the mall for the second time, how much longer do they have to get to the grocery store without being late? **Answer:** It takes Nadia and Sanjay 24 minutes to get to the gym and an additional 27 minutes to get to the mall from the gym. Therefore, it takes them 24 + 27 = 51 minutes to get from their home to the mall. Since they have to walk back home and then to the mall again (round trip), the total time spent walking to the mall, back home, and then to the mall a second time is 51 * 2 = 102 minutes. They started with 261 minutes and have already used 102 minutes. The remaining time they have is 261 - 102 = 159 minutes. Therefore, once they reach the mall for the second time, they have 159 minutes to get to the grocery store without being late. Final Answer: The final answer is $\boxed{159}$

Overall Quality: poor

The reasoning contains a significant logical error in calculating the time spent returning to the mall. It incorrectly assumes only two segments of travel (51 * 2) instead of the required three segments (Home->Mall, Mall->Home, Home->Mall).

Detected Issues (1)

logical_error high

Statement

Since they have to walk back home and then to the mall again (round trip), the total time spent walking to the mall, back home, and then to the mall a second time is 51 * 2 = 102 minutes.

Explanation

The sequence of travel is: Home -> Mall (51 min), Mall -> Home (51 min), Home -> Mall (51 min). This requires 3 segments of 51 minutes, not 2 segments (51 * 2).

Answer Span:

51 * 2 = 102 minutes

Reference/Question Span:

When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again.

Question #129

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Arash watches TV after he finishes his homework every night. On Sunday and Monday, he watched 4-hour episodes of his favorite show each night. On Tuesday, he watched a few episodes of a 45-minute show. On Wednesday, he finished homework early and watched a 2-hour episode and a 15-minute show. On Thursday, he got to stay up late, so he watched five 2-hour episodes. On Friday, he watched four episodes, each 30 minutes. If he watched 26 hours of TV in all, how many 45-minute episodes did he watch on Tuesday? **Answer:** * **Sunday/Monday:** Arash watched 4 hours * 2 nights = 8 hours total. * **Wednesday:** He watched 2 hours + 15 minutes = 2.25 hours. * **Thursday:** He watched 5 episodes * 2 hours/episode = 10 hours. * **Friday:** He watched 4 episodes * 30 minutes/episode = 120 minutes = 2 hours. Total time watching TV excluding Tuesday is 8 + 2.25 + 10 + 2 = 22.25 hours. Time spent watching TV on Tuesday: 26 hours total - 22.25 hours = 3.75 hours. Number of 45-minute episodes watched on Tuesday: 3.75 hours * 60 minutes/hour / 45 minutes/episode = 5 episodes. Final Answer: \boxed{5}

Overall Quality: excellent

The reasoning chain correctly calculates the time spent watching TV each day, sums them up, finds the remaining time for Tuesday, and correctly converts that time into the number of episodes.

✓ No hallucinations detected

Question #131

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Bodhi watches TV after he finishes his homework every night. On Wednesday and Thursday, he watched 3-hour episodes of his favorite show each night. On Friday, he watched a few episodes of a 60-minute show. On Saturday, he finished homework early and watched a 5-hour episode and a 60-minute show. On Sunday, he got to stay up late, so he watched four 4-hour episodes. On Monday, he watched four episodes, each 30 minutes. If he watched 31 hours of TV in all, how many 60-minute episodes did he watch on Friday? **Answer:** * **Wednesday and Thursday:** Bodhi watched 3 hours * 2 nights = 6 hours. * **Saturday:** He watched 5 hours + 1 hour = 6 hours. * **Sunday:** He watched four 4-hour episodes, so he watched 4 * 4 = 16 hours. * **Monday:** He watched four 30-minute episodes, which is 4 * 0.5 = 2 hours. So far, he watched 6 + 6 + 16 + 2 = 30 hours. Since he watched a total of 31 hours, he watched 31 - 30 = 1 hour on Friday. Because Friday's episodes were each 60 minutes (1 hour) long, he watched 1 / 1 = 1 episode on Friday. The answer is $\boxed{1}$.

Overall Quality: excellent

The reasoning chain correctly calculates the time spent watching TV each day, sums these times, finds the remaining time for Friday, and correctly determines the number of episodes based on the episode length.

✓ No hallucinations detected

Question #85

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Gabriel and Pavel have 212 minutes to walk to the gym together starting from their home. It takes them 29 minutes to get to the corner where the library is. It takes them another 19 minutes to get to the cinema. When they reach the cinema, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the cinema again. Once they reach the cinema for the second time, how much longer do they have to get to the gym without being late? **Answer:** It takes Gabriel and Pavel 29 minutes to get to the library and an additional 19 minutes to get from the library to the cinema. Therefore, it takes them 29 + 19 = 48 minutes to get from their home to the cinema. Since they have to go back home and then back to the cinema, the total time spent going to the cinema, back home, and back to the cinema is 48 * 2 = 96 minutes . They started with 212 minutes and have already used 96 minutes. So, the remaining time they have is 212 - 96 = 116 minutes. Therefore, they have 116 minutes longer to get to the gym. Final Answer: The final answer is $\boxed{116}$

Overall Quality: poor

The initial calculation of the time to the cinema (48 minutes) is correct. However, the subsequent calculation of the total time spent on the round trip (Home->Cinema->Home->Cinema) is logically flawed. It incorrectly assumes only two segments of 48 minutes are involved (48 * 2 = 96), whereas three segments (48 + 48 + 48 = 144) are required based on the problem description.

Detected Issues (1)

logical_error high

Statement

Since they have to go back home and then back to the cinema, the total time spent going to the cinema, back home, and back to the cinema is 48 * 2 = 96 minutes .

Explanation

The sequence of events is: Home -> Cinema (48 min), Cinema -> Home (48 min), Home -> Cinema (48 min). This involves three trips of 48 minutes each, not two. The total time spent before reaching the cinema the second time should be 3 * 48 = 144 minutes, not 48 * 2 = 96 minutes.

Answer Span:

48 * 2 = 96 minutes

Reference/Question Span:

When they reach the cinema, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the cinema again.

Question #87

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Thiago and Ali have 163 minutes to walk to the gym together starting from their home. It takes them 21 minutes to get to the corner where the bank is. It takes them another 28 minutes to get to the cinema. When they reach the cinema, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the cinema again. Once they reach the cinema for the second time, how much longer do they have to get to the gym without being late? **Answer:** It takes Thiago and Ali 21 minutes to get to the bank and an additional 28 minutes to get from the bank to the cinema. Therefore, it takes them 21 + 28 = 49 minutes to get from their home to the cinema. Since they have to walk back home and then back to the cinema, they spend 2 * 49 minutes = 98 minutes walking to the cinema and back, and then to the cinema again. They started with 163 minutes and have already used 98 minutes. Therefore, they have 163 - 98 = 65 minutes remaining to get to the gym. The answer is $\boxed{65}$.

Overall Quality: poor

The model correctly calculates the time for one leg (49 minutes) but makes a significant logical error in calculating the total time spent returning to the cinema for the second time, using 2 trips (98 minutes) instead of 3 trips (147 minutes).

✓ No hallucinations detected

Question #253

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Oliver goes to the store to buy some flour. The normal brand of flour he buys costs ₣16 per kilogram. He has to buy a more expensive brand that costs 25% more since his favorite brand was sold out. He decides to buy a week's worth of flour and he uses 2 kilograms of flour per day. The store has a 5% discount on flour which applies only up to 10 kilograms; any additional flour is sold at the regular price. Oliver also decides to buy himself a muffin for ₣4. How much does Oliver have to pay? **Answer:** Oliver uses 2 kilograms of flour per day and buys flour for a week (7 days), so he needs 2 * 7 = 14 kilograms of flour. The more expensive flour costs 25% more than the normal price of ₣16. The increased price is 16 * 0.25 = ₣4 more. The new price per kilogram is 16 + 4 = ₣20. Oliver gets a 5% discount on the first 10 kilograms. The discount is 20 * 0.05 = ₣1 per kilogram. The discounted price is 20 - 1 = ₣19 per kilogram. The cost of the first 10 kilograms at the discounted price is 19 * 10 = ₣190. The remaining 14 - 10 = 4 kilograms are sold at the regular increased price of ₣20. The cost of this flour is 4 * 20 = ₣80. The total cost of the flour is 190 + 80 = ₣270. Finally, the muffin costs ₣4. Oliver's total cost is 270 + 4 = ₣274. Final Answer: The final answer is $\boxed{274}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #88

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Gabriel and Kai have 137 minutes to walk to the gym together starting from their home. It takes them 16 minutes to get to the corner where the park is. It takes them another 22 minutes to get to the mall. When they reach the mall, they remember they forgot their wallets at home, so they have to return to pick up their wallets and then walk all the way back to the mall again. Once they reach the mall for the second time, how much longer do they have to get to the gym without being late? **Answer:** It takes Gabriel and Kai 16 minutes to get to the park and an additional 22 minutes to get to the mall from the park. So, it takes them 16 + 22 = 38 minutes to get to the mall from home. Since they have to go back home and then back to the mall, they spend twice the time it took them to get to the mall initially. Therefore, they spend 2 * 38 minutes = 76 minutes going to the mall, back home, and then back to the mall. They initially had 137 minutes. After the trip back and forth from home to the mall, they have 137 - 76 = 61 minutes remaining. So, once they reach the mall for the second time, they have 61 minutes longer to get to the gym without being late. Final Answer: The final answer is $\boxed{61}$

Overall Quality: poor

The model correctly calculates the time for one leg (38 minutes) but incorrectly calculates the total time spent on the detour sequence (Home -> Mall -> Home -> Mall). It calculates this as 2 * 38 = 76 minutes, implying only two segments of travel time were added, whereas the correct sequence involves three segments of 38 minutes (initial trip + return trip + second trip to the mall).

✓ No hallucinations detected

Question #105

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Rania walks 28 kilometers every day on her favorite walking trail, which includes 14 kilometers of walking on the beach and 14 kilometers of walking on the sidewalk. On the sidewalk, Rania walks at two times the rate of speed that she does on the beach. However, due to a recent injury, Rania's speed has decreased by half both on the beach and sidewalk. If 42 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 28-kilometer walk, in minutes? **Answer:** Rania spends 42 minutes walking 14 kilometers on the beach. Due to her injury, her speed is half of what it used to be. Let's denote her original speed on the beach as 'x' km/minute. Then, her current speed on the beach is x/2 km/minute. We know that distance = speed × time. 14 km = (x/2) * 42 minutes Solving for x, we find x = 2/3 km/minute. This means her original speed on the beach was 2/3 km/minute. Therefore, her current speed on the beach is (2/3)/2 = 1/3 km/minute. On the sidewalk, she originally walked twice as fast as she did on the beach. So, her original speed on the sidewalk was 2 * (2/3) = 4/3 km/minute. Due to her injury, her speed is now halved, so her current speed on the sidewalk is (4/3)/2 = 2/3 km/minute. Her current sidewalk speed is 2/3 km/minute. Rania walks 14 kilometers on the sidewalk. Time = Distance / Speed Time on sidewalk = 14 km / (2/3 km/minute) = 21 minutes. So, she spends 21 minutes on the sidewalk. Total time for the entire walk is the time spent on the beach plus the time spent on the sidewalk. Total time = 42 minutes + 21 minutes = 63 minutes. Therefore, it takes her 63 minutes to complete the entire 28-kilometer walk. Final Answer: The final answer is $\boxed{63}$

Overall Quality: excellent

The reasoning chain correctly interprets all constraints of the problem, including the effect of the injury (halved speed) and the relationship between beach and sidewalk speeds. All calculations performed are mathematically correct and lead directly to the ground truth answer.

✓ No hallucinations detected

Question #102

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Emma walks 32 kilometers every day on her favorite walking trail, which includes 14 kilometers of walking on the beach and 18 kilometers of walking on the sidewalk. On the sidewalk, Emma walks at three times the rate of speed that she does on the beach. However, due to a recent injury, Emma's speed has decreased by half both on the beach and sidewalk. If 56 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 32-kilometer walk, in minutes? **Answer:** Emma spends 56 minutes walking 14 kilometers on the beach. This means her current speed on the beach is 14 km / 56 minutes = 0.25 km/minute. Because of her injury, her speed has been halved. So, her original speed on the beach was 0.25 km/minute * 2 = 0.5 km/minute. Emma walks on the sidewalk at three times the speed she walks on the beach. Therefore, her original speed on the sidewalk was 0.5 km/minute * 3 = 1.5 km/minute. Due to the injury, her current speed on the sidewalk is 1.5 km/minute / 2 = 0.75 km/minute. She walks 18 kilometers on the sidewalk. So, the time she takes to walk on the sidewalk is 18 km / 0.75 km/minute = 24 minutes. The total time she takes to complete the walk is the sum of the time spent on the beach and the time spent on the sidewalk, which is 56 minutes + 24 minutes = 80 minutes. Final Answer: The final answer is $\boxed{80}$

Overall Quality: excellent

The reasoning chain correctly interprets all constraints of the problem, including the initial speed calculation, the effect of the injury (halving the speed), the relationship between beach and sidewalk speeds (factor of 3), and the final time calculation. All arithmetic steps are correct.

✓ No hallucinations detected

Question #255

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Benjamin goes to the store to buy some sugar. The normal brand of sugar he buys costs ₺10 per kg. He has to buy a more expensive brand that costs 20% more since his favorite brand was sold out. He decides to buy a week's worth of sugar and he uses 3 kgs of sugar per day. The store has a 30% discount on sugar which applies only up to 10 kgs; any additional sugar is sold at the regular price. Benjamin also decides to buy himself a bagel for ₺1. How much does Benjamin have to pay? **Answer:** * **Price of the expensive sugar:** The expensive sugar costs 20% more than the normal price of ₺10 per kg. So, the price per kg is 10 * (1 + 0.20) = ₺12 per kg. * **Total sugar needed:** Benjamin uses 3 kgs of sugar per day and wants a week's worth. So, he needs 3 * 7 = 21 kgs of sugar. * **Cost of the first 10 kgs:** The 30% discount applies to the first 10 kgs. So, the price of the first 10 kgs is 10 * 12 * (1 - 0.30) = ₺84. * **Cost of the remaining sugar:** Benjamin needs 21 kgs in total, and the discount applied to the first 10 kgs. So, the remaining amount of sugar is 21 - 10 = 11 kgs. The cost of these 11 kgs is 11 * 12 = ₺132. * **Cost of the bagel:** The bagel costs ₺1. * **Total cost:** The total cost is the sum of the discounted sugar, the remaining sugar, and the bagel: 84 + 132 + 1 = ₺217. Final Answer: \boxed{217}

Overall Quality: excellent

The reasoning chain correctly calculates the price increase, total sugar needed, applies the discount structure accurately (30% off the first 10kg at the increased price, full increased price for the remainder), and sums all components including the bagel cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #256

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mohammed goes to the store to buy some sugar. The normal brand of sugar he buys costs $15 per kg. He has to buy a more expensive brand that costs 40% more since his favorite brand was sold out. He decides to buy a week's worth of sugar and he uses 3 kgs of sugar per day. The store has a 10% discount on sugar which applies only up to 20 kgs; any additional sugar is sold at the regular price. Mohammed also decides to buy himself a bagel for $1. How much does Mohammed have to pay? **Answer:** 1. **Calculate the price of the more expensive sugar:** The more expensive sugar costs 40% more than $15/kg. So, the price increase is 0.40 * $15 = $6. The new price per kg is $15 + $6 = $21/kg. 2. **Calculate the total sugar needed for a week:** Mohammed uses 3 kgs of sugar per day and wants a week's worth, which is 7 days. So, he needs 3 kg/day * 7 days = 21 kg of sugar. 3. **Calculate the cost of the first 20 kgs of sugar:** He gets a 10% discount on the first 20 kgs. So, the discounted price is $21/kg * (1 - 0.10) = $18.90/kg. The cost of the first 20kgs is $18.90/kg * 20 kg = $378. 4. **Calculate the cost of the remaining sugar:** Mohammed needs 21 kg total and got 20 kg at a discount. The remaining 1 kg is sold at the regular price of $21/kg. Thus the cost for the remaining 1 kg is $21/kg * 1 kg = $21. 5. **Calculate the total cost of the sugar:** The total cost of sugar is $378 + $21 = $399. 6. **Calculate the total cost including the bagel:** Mohammed also buys a bagel for $1. So the total cost is $399 + $1 = $400. Final Answer: The final answer is $\boxed{400}$

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement. All calculations are accurate, and the logic regarding pricing tiers and total quantity is sound.

✓ No hallucinations detected

Question #254

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Arjun goes to the store to buy some tea. The normal brand of tea he buys costs ¥10 per kilogram. He has to buy a more expensive brand that costs 40% more since his favorite brand was sold out. He decides to buy a week's worth of tea and he uses 2 kilograms of tea per day. The store has a 10% discount on tea which applies only up to 10 kilograms; any additional tea is sold at the regular price. Arjun also decides to buy himself a muffin for ¥4. How much does Arjun have to pay? **Answer:** Arjun uses 2 kilograms of tea per day and wants to buy tea for a week (7 days), so he wants to buy 2 kg/day * 7 days = 14 kilograms of tea. The normal price is ¥10 per kilogram, but the brand Arjun buys is 40% more expensive. So, the price per kilogram is ¥10 * (1 + 0.40) = ¥14. The store offers a 10% discount on the first 10 kilograms. So, the first 10 kilograms will cost ¥14/kg * 10kg * (1 - 0.10) = ¥126. The remaining 14 kg - 10 kg = 4 kilograms are sold at the regular price of ¥14 per kilogram. The cost for these 4 kilograms is ¥14/kg * 4 kg = ¥56. The total cost of the tea is ¥126 + ¥56 = ¥182. Arjun also buys a muffin for ¥4. Therefore, the total amount Arjun has to pay is ¥182 + ¥4 = ¥186. Final Answer: The final answer is $\boxed{186}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #252

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Bodhi goes to the store to buy some rice. The normal brand of rice he buys costs $15 per pound. He has to buy a more expensive brand that costs 20% more since his favorite brand was sold out. He decides to buy a week's worth of rice and he uses 2 pounds of rice per day. The store has a 20% discount on rice which applies only up to 10 pounds; any additional rice is sold at the regular price. Bodhi also decides to buy himself a cookie for $1. How much does Bodhi have to pay? **Answer:** Bodhi needs rice for a week, and he uses 2 pounds per day, so he needs to buy 7 days * 2 pounds/day = 14 pounds of rice. The more expensive brand costs 20% more than the $15 brand, so it costs $15 * (1 + 0.20) = $18 per pound. Bodhi gets a 20% discount on the first 10 pounds, so those pounds cost $18 * (1 - 0.20) = $14.40 per pound. The cost of the first 10 pounds is $14.40/pound * 10 pounds = $144. The remaining 14 - 10 = 4 pounds are sold at the regular price of $18/pound. The cost of these pounds is $18/pound * 4 pounds = $72. The total cost of the rice is $144 + $72 = $216. Adding the $1 cookie, the total cost is $216 + $1 = $217. Final Answer: \boxed{217}

Overall Quality: excellent

The reasoning chain correctly calculates the required amount of rice, the increased price per pound, applies the tiered discount structure correctly, calculates the total cost of rice, and adds the cost of the cookie to arrive at the correct final answer.

✓ No hallucinations detected

Question #104

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Fatima walks 26 miles every day on her favorite walking trail, which includes 11 miles of walking on the beach and 15 miles of walking on the sidewalk. On the sidewalk, Fatima walks at three times the rate of speed that she does on the beach. However, due to a recent injury, Fatima's speed has decreased by half both on the beach and sidewalk. If 44 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 26-mile walk, in minutes? **Answer:** Fatima walks 11 miles on the beach in 44 minutes. Due to her injury, her speed is half of what it used to be. So, her original speed on the beach would have allowed her to cover 11 miles in 44/2 = 22 minutes. This means her original speed on the beach was 11 miles / 22 minutes = 0.5 miles per minute. Since she walks at three times the speed on the sidewalk, her original sidewalk speed was 0.5 miles per minute * 3 = 1.5 miles per minute. After the injury, her speed on the sidewalk was reduced by half, making her current sidewalk speed 1.5 miles per minute / 2 = 0.75 miles per minute. It takes her 15 miles / 0.75 miles per minute = 20 minutes to walk the sidewalk portion. Therefore, her total walking time is 44 minutes (beach) + 20 minutes (sidewalk) = 64 minutes. The answer is $\boxed{64}$.

Overall Quality: excellent

The reasoning chain correctly interprets the problem constraints, including the speed reduction due to injury, and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #103

Clean

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Olivia walks 29 miles every day on her favorite walking trail, which includes 13 miles of walking on the beach and 16 miles of walking on the sidewalk. On the sidewalk, Olivia walks at four times the rate of speed that she does on the beach. However, due to a recent injury, Olivia's speed has decreased by half both on the beach and sidewalk. If 65 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 29-mile walk, in minutes? **Answer:** Olivia spends 65 minutes walking 13 miles on the beach. Her original speed on the beach was 13 miles / 65 minutes = 0.2 miles per minute . Due to her injury, her speed is now halved , so her current speed on the beach is 0.2 miles per minute / 2 = 0.1 miles per minute . Since she walks four times faster on the sidewalk than on the beach, her original speed on the sidewalk was 0.2 miles per minute * 4 = 0.8 miles per minute . After her injury, her speed on the sidewalk was halved , so her current speed on the sidewalk is 0.8 miles per minute / 2 = 0.4 miles per minute . She walks 16 miles on the sidewalk, so it takes her 16 miles / 0.4 miles per minute = 40 minutes to walk the sidewalk portion . Therefore, her total walking time is the time spent on the beach plus the time spent on the sidewalk: 65 minutes + 40 minutes = 105 minutes . Final Answer: The final answer is $\boxed{105}$

Overall Quality: excellent

The reasoning chain correctly interprets all constraints, including the speed reduction on both surfaces, and performs all calculations accurately, leading to the correct time of 105 minutes based on the problem description.

✓ No hallucinations detected

Question #271

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Gabrielle has a flower bed that is 150 meters long. Gabrielle wants to fill her flower bed with plants. Gabrielle's flowers grow 3 meters wide so she needs to leave 15 meters between every plant (including the plants width). Gabrielle already owns 7 flowers. Each flowering plant costs $3 at the store. However, if she buys more than 2 plants, she'll receive a $8 discount on the entire purchase. How much money will Gabrielle spend at the store to fill up her flower bed? Answer: The space required for each plant, considering its width and the space between plants, is 3 meters (plant width) + 15 meters (space between) = 18 meters. The number of plants that can fit in Gabrielle's 150-meter flower bed is 150 meters / 18 meters/plant = 8.33 plants. Since she can't plant a fraction of a plant, she can fit a maximum of 8 plants. Gabrielle already owns 7 flowers, so she needs to buy 8 plants - 7 plants = 1 plant. Since she is only buying 1 plant, she doesn't qualify for the $8 discount (as she needs to buy more than 2). Therefore, Gabrielle will spend 1 plant * $3/plant = $3. The answer is $\boxed{3}$.

Overall Quality: poor

The reasoning chain contains a high-severity logical error in interpreting the required spacing unit, leading to an incorrect plant count and final cost.

✓ No hallucinations detected

Question #295

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Hiroshi collects garbage from 6 different apartment complexes. The first 5 have 100 apartments each and the last one is 40% bigger than the other 5 combined. However, this week, 8 apartments from each of the first 5 complexes were vacant and did not require collection service. Hiroshi collects garbage 2 times a week from each place and he gets paid ₣0.25 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week? **Answer:** The first five apartment complexes have a total of 5 complexes * 100 apartments/complex = 500 apartments. The sixth complex has 40% more apartments than the combined 500 apartments of the first five complexes. This means it has 500 * 0.40 = 200 more apartments than the first five combined, so the sixth complex has 500+200 = 700 apartments. This week, 8 apartments from each of the first 5 complexes were vacant, for a total of 8 apartments/complex * 5 complexes = 40 vacant apartments. So, the number of apartments Hiroshi collected garbage from in the first five complexes is 500 apartments - 40 vacant apartments = 460 apartments. In total, Hiroshi collected garbage from 460 apartments + 700 apartments = 1160 apartments. Since Hiroshi collects garbage twice a week, the total number of collections is 1160 apartments * 2 collections/apartment = 2320 collections. Hiroshi's base pay is ₣0.25 per collection, so he earns 2320 collections * ₣0.25/collection = ₣580. Hiroshi also earns 10% in tips, which amounts to ₣580 * 0.10 = ₣58. Therefore, Hiroshi makes a total of ₣580 + ₣58 = ₣638 in a week. Final Answer: \boxed{638}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations are accurate.

✓ No hallucinations detected

Question #106

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ananya walks 20 miles every day on her favorite walking trail, which includes 10 miles of walking on the beach and 10 miles of walking on the sidewalk. On the sidewalk, Ananya walks at two times the rate of speed that she does on the beach. However, due to a recent injury, Ananya's speed has decreased by half both on the beach and sidewalk. If 40 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 20-mile walk, in minutes? **Answer:** Ananya spends 40 minutes walking 10 miles on the beach. This means her current speed on the beach is 10 miles / 40 minutes = 0.25 miles per minute. On the sidewalk, her original speed was twice her speed on the beach. Therefore, her original speed on the sidewalk was 2 * 0.25 miles per minute = 0.5 miles per minute. Due to her injury, her speed on the sidewalk is now half of her original speed. Thus, her current speed on the sidewalk is 0.5 miles per minute / 2 = 0.25 miles per minute. Since she walks 10 miles on the sidewalk at a speed of 0.25 miles per minute, it takes her 10 miles / 0.25 miles per minute = 40 minutes to walk the sidewalk portion. The total time for her walk is the time spent on the beach plus the time spent on the sidewalk: 40 minutes (beach) + 40 minutes (sidewalk) = 80 minutes. The answer is $\boxed{80}$.

Overall Quality: poor

The reasoning chain contains a significant logical error in determining the current speed on the sidewalk by misinterpreting how the speed reduction due to injury interacts with the relative speed difference. This leads to an incorrect time calculation for the sidewalk portion and an incorrect final answer.

✓ No hallucinations detected

Question #107

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Keisha walks 33 miles every day on her favorite walking trail, which includes 17 miles of walking on the beach and 16 miles of walking on the sidewalk. On the sidewalk, Keisha walks at two times the rate of speed that she does on the beach. However, due to a recent injury, Keisha's speed has decreased by half both on the beach and sidewalk. If 51 minutes of her walk is spent on the beach, how long does it take for her to complete the entire 33-mile walk, in minutes? **Answer:** Keisha spends 51 minutes walking 17 miles on the beach. Her injured speed on the beach is 17 miles / 51 minutes = 1/3 mile per minute. Before the injury, her beach speed was 1/3 mile per minute * 2 = 2/3 mile per minute. Because she walks at twice the speed on the sidewalk, her pre-injury sidewalk speed was 2/3 mile per minute * 2 = 4/3 mile per minute. Her injured sidewalk speed is 4/3 mile per minute / 2 = 2/3 mile per minute. It takes her 16 miles / 2/3 mile per minute = 24 minutes to walk the sidewalk portion. Her total walking time is 51 minutes + 24 minutes = 75 minutes. The answer is $\boxed{75}$.

Overall Quality: excellent

The reasoning chain correctly interprets all constraints, including the initial speed calculation based on the time given, the relationship between beach and sidewalk speeds, and the effect of the speed decrease (halving the speed). All arithmetic calculations are correct, leading to the correct final answer.

✓ No hallucinations detected

Question #298

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Oliver collects garbage from 5 different apartment complexes. The first 4 have 100 apartments each and the last one is 50% bigger than the other 4 combined. However, this week, 6 apartments from each of the first 4 complexes were vacant and did not require collection service. Oliver collects garbage 5 times a week from each place and he gets paid ₣0.25 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week? **Answer:** The first four apartment complexes have a total of 4 * 100 = 400 apartments. The fifth complex is 50% bigger than the other four combined, meaning it has 400 * 0.5 = 200 more apartments than the other four combined. Thus, the fifth complex has 400 + 200 = 600 apartments. This week, there were 6 vacant apartments in each of the first 4 complexes, for a total of 4 * 6 = 24 vacant apartments. This means Oliver collected from 400 - 24 = 376 apartments in the first four complexes. In total, Oliver collected from 376 + 600 = 976 apartments. He collects 5 times a week, so he made 5 * 976 = 4880 collections. At ₣0.25 per collection, his base pay is 0.25 * 4880 = ₣1220. He earns 10% in tips, which is 1220 * 0.1 = ₣122. His total earnings for the week are 1220 + 122 = ₣1342. Final Answer: The final answer is $\boxed{1342}$

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #297

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Pavel collects garbage from 6 different apartment complexes. The first 5 have 100 apartments each and the last one is 70% bigger than the other 5 combined. However, this week, 10 apartments from each of the first 5 complexes were vacant and did not require collection service. Pavel collects garbage 2 times a week from each place and he gets paid ₺0.45 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week? **Answer:** The first 5 complexes have a total of 5 complexes * 100 apartments/complex = 500 apartments. The 6th complex has 500 apartments * 170% = 850 apartments. This week, the first five complexes had 100 apartments/complex - 10 vacant apartments/complex = 90 occupied apartments/complex. Since there are 5 such complexes, there were a total of 5 complexes * 90 occupied apartments/complex = 450 occupied apartments in the first five complexes. The total number of apartments Pavel collected garbage from this week is 450 + 850 = 1300 apartments. Since Pavel collects garbage from each apartment twice a week, he makes 1300 collections * 2 collections/week = 2600 collections per week. His base earnings are 2600 collections * ₺0.45/collection = ₺1170. His tips are ₺1170 * 10% = ₺117. His total earnings for the week are ₺1170 + ₺117 = ₺1287. Final Answer: \boxed{1287}

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #296

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Tariq collects garbage from 4 different apartment complexes. The first 3 have 100 apartments each and the last one is 30% bigger than the other 3 combined. However, this week, 10 apartments from each of the first 3 complexes were vacant and did not require collection service. Tariq collects garbage 3 times a week from each place and he gets paid ₺0.5 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week? **Answer:** The first three complexes have 100 apartments each, totaling 100 * 3 = 300 apartments. The fourth complex is 30% bigger than the other three combined, so it has 300 * 0.30 = 90 more apartments. This means the fourth complex has 300 + 90 = 390 apartments. This week, 10 apartments from each of the first 3 complexes were vacant, meaning 10 * 3 = 30 apartments were vacant in total. So, Tariq collected from 300 - 30 = 270 apartments across the first three complexes. In total, Tariq collected from 270 + 390 = 660 apartments. He collects 3 times a week from each apartment, meaning he made 660 collections * 3 = 1980 collections this week. At ₺0.5 per collection, he earned 1980 * 0.5 = ₺990. He also earns a 10% tip, which is 990 * 0.10 = ₺99. His total earnings for the week are 990 + 99 = ₺1089. Final Answer: \boxed{1089}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement. All calculations are accurate, and the logic correctly interprets the constraints (vacancies, size of the 4th complex, collection frequency, payment rate, and tip calculation).

✓ No hallucinations detected

Question #294

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Qasim collects garbage from 5 different apartment complexes. The first 4 have 100 apartments each and the last one is 30% bigger than the other 4 combined. However, this week, 5 apartments from each of the first 4 complexes were vacant and did not require collection service. Qasim collects garbage 2 times a week from each place and he gets paid ₣0.3 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week? **Answer:** The first four complexes have a total of 4 * 100 = 400 apartments. The fifth complex is 30% bigger than the combined size of the first four, meaning it has 400 * 0.3 = 120 more apartments. So the fifth complex has 400 + 120 = 520 apartments. This week, there were 5 vacant apartments in each of the first four complexes, meaning 4 * 5 = 20 apartments were vacant. So from the first four complexes, Qasim collected from 400 - 20 = 380 apartments. Adding the fifth complex, Qasim collected from 380 + 520 = 900 apartments in total. Since Qasim collects twice a week, he made 2 * 900 = 1800 collections. His base pay is 1800 collections * ₣0.3 per collection = ₣540. His tip is 10% of his base pay, which is 540 * 0.1 = ₣54. His total earnings for the week are 540 + 54 = ₣594. Final Answer: \boxed{594}

Overall Quality: excellent

The reasoning chain correctly calculates the total number of apartments serviced, accounts for vacancies, calculates the total collections, determines the base pay, adds the tip, and arrives at the correct final answer. All arithmetic steps are mathematically sound.

✓ No hallucinations detected

Question #274

1 issue

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Valentina has a flower bed that is 144 feet long. Valentina wants to fill her flower bed with plants. Valentina's flowers grow 7 feet wide so she needs to leave 18 feet between every plant (including the plants width). Valentina already owns 5 flowers. Each flowering plant costs $5 at the store. However, if she buys more than 2 plants, she'll receive a $8 discount on the entire purchase. How much money will Valentina spend at the store to fill up her flower bed? Answer: The space required for each plant, including the space between plants, is 7 feet (plant width) + 18 feet (space between plants) = 25 feet. Valentina's flower bed is 144 feet long, so she can fit 144 feet / 25 feet/plant = 5.76 plants. Since she can't plant a fraction of a plant, she can fit 5 plants in her flower bed. Valentina already has 5 flowers, and she needs 5 plants total, so she doesn't need to buy any more plants. Therefore, she needs 0 additional plants. Since she needs 0 plants, which is less than 2 plants, she will not receive the $8 discount. Since she's buying 0 plants and each plant costs $5, she will spend 0 plants * $5/plant = $0. The answer is $\boxed{0}$.

Overall Quality: poor

The reasoning chain fails due to a fundamental logical error in interpreting the required spacing per plant, leading to incorrect subsequent calculations for the total number of plants needed and the number of plants to purchase.

Detected Issues (1)

logical_error high

Statement

The space required for each plant, including the space between plants, is 7 feet (plant width) + 18 feet (space between plants) = 25 feet.

Explanation

The problem implies that 18 feet is the required spacing unit per plant (as confirmed by the ground truth calculation 144/18=8). Adding the plant width (7ft) to the spacing (18ft) results in an incorrect total spacing unit for division.

Answer Span:

7 feet (plant width) + 18 feet (space between plants) = 25 feet

Reference/Question Span:

Valentina's flowers grow 7feet wide so she needs to leave 18 feet between every plant (including the plants width)

Question #299

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Noah collects garbage from 5 different apartment complexes. The first 4 have 100 apartments each and the last one is 75% bigger than the other 4 combined. However, this week, 5 apartments from each of the first 4 complexes were vacant and did not require collection service. Noah collects garbage 2 times a week from each place and he gets paid ₣0.25 per collection for each apartment. He also earns an additional 10% in tips. How much money does he make in a week? **Answer:** The first four complexes have a total of 4 * 100 = 400 apartments. The fifth complex has 400 * 0.75 = 300 more apartments than the first four combined, so it has 400 + 300 = 700 apartments. This week, 4 complexes * 5 vacant apartments/complex = 20 apartments were vacant. So, Noah collected garbage from 400 - 20 = 380 apartments in the first four complexes. In total, he collected from 380 (first four) + 700 (fifth) = 1080 apartments this week. Since he collects twice a week, the number of collections is 1080 apartments * 2 collections/apartment = 2160 collections. His base pay is 2160 collections * ₣0.25/collection = ₣540. He earns an additional 10% in tips, so ₣540 * 0.10 = ₣54. His total earnings are ₣540 + ₣54 = ₣594. The answer is $\boxed{594}$.

Overall Quality: excellent

The reasoning chain correctly interprets the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #257

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Theo goes to the store to buy some rice. The normal brand of rice he buys costs ¥5 per kg. He has to buy a more expensive brand that costs 20% more since his favorite brand was sold out. He decides to buy a week's worth of rice and he uses 2 kgs of rice per day. The store has a 40% discount on rice which applies only up to 10 kgs; any additional rice is sold at the regular price. Theo also decides to buy himself a bagel for ¥4. How much does Theo have to pay? **Answer:** First, we calculate the cost of the more expensive rice: ¥5 per kg * 1.20 = ¥6 per kg. Next, we calculate how much rice Theo needs for a week: 7 days * 2 kgs per day = 14 kgs. Since the discount only applies up to 10 kgs, Theo gets a discount on 10 kgs and pays the regular price for the remaining 4 kgs. The discounted price is ¥6 per kg * (1 - 0.40) = ¥3.60 per kg. The cost for the discounted 10kgs is ¥3.60 per kg * 10 kgs = ¥36. The cost for the remaining 4kgs is ¥6 per kg * 4 kgs = ¥24. The total cost of the rice is ¥36 + ¥24 = ¥60. Finally, adding the cost of the bagel, Theo has to pay ¥60 + ¥4 = ¥64. The answer is $\boxed{64}$.

Overall Quality: excellent

The reasoning chain correctly calculates the price of the new rice, the total quantity needed, applies the tiered discount structure correctly, calculates the total cost of rice, and adds the cost of the bagel to reach the correct final answer.

✓ No hallucinations detected

Question #206

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Prof. Miller sold his apartment for $810000. He paid the registration fees that amounted to 3% of the selling price and also paid an agent fee that is 3% of the selling price. He also paid $670000 for the remaining loan amount on the apartment, and $20000 for closing costs. Prof. Miller used the net proceeds from selling the apartment to invest in stocks. The stocks gained 10% each year for two years. How much were Prof. Miller's net proceeds after two years? Answer: The registration fees were $810000 * 0.03 = $24300. The agent fee was $810000 * 0.03 = $24300. The total fees paid were $24300 + $24300 = $48600. The net proceeds from selling the apartment before investing were $810000 - $48600 - $670000 - $20000 = $71400. After one year, the investment grew to $71400 * (1 + 0.10) = $78540. After two years, the investment grew to $78540 * (1 + 0.10) = $86394. So, Prof. Miller's net proceeds after two years were $86394. Final Answer: The final answer is $\boxed{86394}$

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate steps and arrives at the correct final answer. All arithmetic operations are correct.

✓ No hallucinations detected

Question #207

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Prof. Miller sold his apartment for $760000. He paid the registration fees that amounted to 3% of the selling price and also paid an agent fee that is 4% of the selling price. He also paid $570000 for the remaining loan amount on the apartment, and $15000 for closing costs. Prof. Miller used the net proceeds from selling the apartment to invest in stocks. The stocks gained 10% each year for two years. How much were Prof. Miller's net proceeds after two years? Answer: The registration fees were $760000 * 0.03 = $22800. The agent fee was $760000 * 0.04 = $30400. The total expenses from selling the apartment, excluding the loan amount, were $22800 + $30400 + $15000 = $68200. The net proceeds from selling the apartment before investing were $760000 - $68200 - $570000 = $121800. After one year of investment, the proceeds grew to $121800 * (1 + 0.10) = $133980. After two years of investment, the proceeds grew to $133980 * (1 + 0.10) = $147378. So, Prof. Miller's net proceeds after two years were $147378. Final Answer: \boxed{147378}

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate steps and arrives at the correct final answer. All arithmetic operations are correct, and the logic follows the problem requirements precisely.

✓ No hallucinations detected

Question #145

1 issue

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Generated Answer

**Reformatted Question:** According to its nutritional info, a bag of popcorn has 300 calories per serving. A 325 grams bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Ibrahim weighs 190 lbs, and he has already consumed 950 calories and burned 200 calories through exercise. Priya weighs 170 lbs, and she has already consumed 1100 in food and 250 calories in ice cream. How many more grams of popcorn does Ibrahim need to consume than Priya? **Answer:** Ibrahim's target calorie intake is 190 lbs * 15 calories/lb = 2850 calories. His net calorie consumption so far is 950 calories - 200 calories = 750 calories. So, Ibrahim can still consume 2850 calories - 750 calories = 2100 calories. Priya's target calorie intake is 170 lbs * 15 calories/lb = 2550 calories. Her total calorie consumption is 1100 calories + 250 calories = 1350 calories. Thus, Priya can still consume 2550 calories - 1350 calories = 1200 calories. A bag of popcorn has 325 grams and contains 5 servings * 300 calories/serving = 1500 calories. Therefore, each gram of popcorn contains 1500 calories / 325 grams ≈ 4.62 calories/gram. Ibrahim can eat 2100 calories / 4.62 calories/gram ≈ 454.55 grams of popcorn. Priya can eat 1200 calories / 4.62 calories/gram ≈ 259.74 grams of popcorn. Ibrahim needs to consume 454.55 grams - 259.74 grams ≈ 194.81 grams more popcorn than Priya. The answer is $\boxed{195}$.

Overall Quality: poor

The model correctly calculates the remaining calories needed for both individuals (2100 and 1200). However, it deviates from the most direct calculation path by calculating calories per gram, introducing rounding errors (4.62) which results in a final answer (194.81) that is slightly off from the exact integer answer (195) derived from the serving method. This deviation constitutes a logical error in method selection that impacts precision.

Detected Issues (1)

logical_error high

Statement

A bag of popcorn has 325 grams and contains 5 servings * 300 calories/serving = 1500 calories. Therefore, each gram of popcorn contains 1500 calories / 325 grams ≈ 4.62 calories/gram.

Explanation

The ground truth calculates servings needed based on 300 calories/serving. The model calculates calories per gram (1500/325 ≈ 4.615). While this is mathematically sound, it is an unnecessary deviation from the simpler method used in the ground truth (which relies only on the 300 cal/serving figure). More importantly, the ground truth uses the serving size information (325g/5 servings = 65g/serving) to convert the difference in servings back to grams at the end. The model calculates calories/gram, which introduces rounding errors (4.62) that lead to an answer (194.81) that differs from the exact answer (195) derived from the serving method.

Answer Span:

A bag of popcorn has 325 grams and contains 5 servings * 300 calories/serving = 1500 calories. Therefore, each gram of popcorn contains 1500 calories / 325 grams ≈ 4.62 calories/gram. Ibrahim can eat 2100 calories / 4.62 calories/gram ≈ 454.55 grams of popcorn. Priya can eat 1200 calories / 4.62 calories/gram ≈ 259.74 grams of popcorn. Ibrahim needs to consume 454.55 grams - 259.74 grams ≈ 194.81 grams more popcorn than Priya.

Reference/Question Span:

A 325 grams bag has 5 servings. ... How many more grams of popcorn does Ibrahim need to consume than Priya?

Question #146

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** According to its nutritional info, a bag of breads has 250 calories per serving. A 350 ounces bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Yuki weighs 210 lbs, and he has already consumed 1050 calories and burned 150 calories through exercise. Jasmine weighs 140 lbs, and she has already consumed 900 in food and 200 calories in ice cream. How many more ounces of breads does Yuki need to consume than Jasmine? **Answer:** Yuki's target calorie intake is 210 lbs * 15 calories/lb = 3150 calories. He has a net intake of 1050 calories - 150 calories = 900 calories. So, Yuki needs to consume 3150 calories - 900 calories = 2250 calories more. Jasmine's target calorie intake is 140 lbs * 15 calories/lb = 2100 calories. She has consumed a total of 900 calories + 200 calories = 1100 calories. So, Jasmine needs to consume 2100 calories - 1100 calories = 1000 calories more. One serving of bread has 250 calories. A 350-ounce bag has 5 servings, so each serving is 350 ounces / 5 servings = 70 ounces. Yuki needs 2250 calories / 250 calories/serving = 9 servings of bread. This is equivalent to 9 servings * 70 ounces/serving = 630 ounces of bread. Jasmine needs 1000 calories / 250 calories/serving = 4 servings of bread. This is equivalent to 4 servings * 70 ounces/serving = 280 ounces of bread. Yuki needs to consume 630 ounces - 280 ounces = 350 ounces more bread than Jasmine. Final Answer: The final answer is $\boxed{350}$

Overall Quality: excellent

The reasoning chain correctly calculates Yuki's and Jasmine's calorie needs, determines the required servings of bread, converts servings to ounces, and finds the difference in ounces consumed, matching the ground truth.

✓ No hallucinations detected

Question #144

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** According to its nutritional info, a bag of breads has 225 calories per serving. A 300 ounces bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Carlos weighs 200 lbs, and he has already consumed 900 calories and burned 150 calories through exercise. Zahra weighs 150 lbs, and she has already consumed 900 in food and 225 calories in ice cream. How many more ounces of breads does Carlos need to consume than Zahra? **Answer:** Carlos's daily calorie target is 200 lbs * 15 calories/lb = 3000 calories. He has a net calorie intake of 900 calories - 150 calories = 750 calories. Thus, he can still consume 3000 calories - 750 calories = 2250 calories. Zahra's daily calorie target is 150 lbs * 15 calories/lb = 2250 calories. She has already consumed 900 calories + 225 calories = 1125 calories. Therefore, she can still consume 2250 calories - 1125 calories = 1125 calories. Each serving of bread has 225 calories. So, Carlos can eat 2250 calories / 225 calories/serving = 10 servings of bread. Zahra can eat 1125 calories / 225 calories/serving = 5 servings of bread. A 300-ounce bag has 5 servings, so each serving is 300 ounces / 5 servings = 60 ounces. Carlos needs to consume 10 servings * 60 ounces/serving = 600 ounces of bread. Zahra needs to consume 5 servings * 60 ounces/serving = 300 ounces of bread. Carlos needs to consume 600 ounces - 300 ounces = 300 ounces more bread than Zahra. Final Answer: \boxed{300}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem statement. All calculations are correct.

✓ No hallucinations detected

Question #149

1 issue

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Ground Truth Answer

Generated Answer

**Reformatted Question:** According to its nutritional info, a bag of popcorn has 150 calories per serving. A 300 grams bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Arjun weighs 210 lbs, and he has already consumed 1000 calories and burned 100 calories through exercise. Elena weighs 180 lbs, and she has already consumed 900 in food and 150 calories in ice cream. How many more grams of popcorn does Arjun need to consume than Elena? **Answer:** Arjun's target calorie intake is 210 lbs * 15 calories/lb = 3150 calories. Arjun's net calories consumed so far is 1000 calories - 100 calories = 900 calories. Arjun needs to consume 3150 calories - 900 calories = 2250 calories more. Elena's target calorie intake is 180 lbs * 15 calories/lb = 2700 calories. Elena's total calories consumed so far is 900 calories + 150 calories = 1050 calories. Elena needs to consume 2700 calories - 1050 calories = 1650 calories more. One serving of popcorn has 150 calories. A 300 gram bag has 5 servings, so each gram has 150/300*5 = 0.5 calories. Arjun needs to consume 2250 calories more, which translates to 2250 / 0.5 calories/gram = 4500 grams of popcorn. Elena needs to consume 1650 calories more, which translates to 1650 / 0.5 calories/gram = 3300 grams of popcorn. Arjun needs to consume 4500 grams - 3300 grams = 1200 grams more popcorn than Elena. The answer is $\boxed{1200}$.

Overall Quality: poor

The reasoning chain contains a critical calculation error in determining the calories per gram of popcorn, leading to an incorrect final answer (1200 vs 240). The AI incorrectly calculated the calories per gram and stated an incorrect result for its own flawed formula.

Detected Issues (1)

calculation_error high

Statement

One serving of popcorn has 150 calories. A 300 gram bag has 5 servings, so each gram has 150/300*5 = 0.5 calories.

Explanation

The calculation for calories per gram is incorrect. If 5 servings are in a 300g bag, then 1 serving is $300 / 5 = 60$ grams. Since 1 serving is 150 calories, the calories per gram is $150 ext{ calories} / 60 ext{ grams} = 2.5$ calories/gram. The AI calculated $150 / (300 * 5) = 150 / 1500 = 0.1$ calories/gram, but wrote $0.5$ in the final step. Let's check the AI's arithmetic: $150 / (300 * 5) = 150 / 1500 = 0.1$. The AI wrote $0.5$. The correct calculation based on the AI's flawed formula structure is $150 / (300 * 5) = 0.1$. The AI stated the result was 0.5. Furthermore, the logic used to derive the calories per gram is flawed: $150 / (300 * 5)$ does not represent calories per gram. The correct logic is $150 ext{ cal} / (300 ext{ g} / 5 ext{ servings/bag}) = 150 / 60 = 2.5 ext{ cal/g}$. The AI's stated result of 0.5 is mathematically incorrect based on its own expression, and the expression itself is logically flawed.

Answer Span:

150/300*5 = 0.5 calories

Reference/Question Span:

A 300 grams bag has 5 servings. ... Each serving is 300 / 5 = 60 gramss.

Question #273

1 issue

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Haruka has a flower bed that is 117 meters long. Haruka wants to fill her flower bed with plants. Haruka's flowers grow 3 meters wide so she needs to leave 13 meters between every plant (including the plants width). Haruka already owns 6 flowers. Each flowering plant costs €8 at the store. However, if she buys more than 2 plants, she'll receive a €9 discount on the entire purchase. How much money will Haruka spend at the store to fill up her flower bed? Answer: The space required for each plant including the space between plants is 3 meters (width of plant) + 13 meters (space between plants) = 16 meters. The number of plants that can fit in Haruka's flower bed is 117 meters/ 16 meters/plant = 7.3125 plants. Since Haruka can only plant whole plants, we round down to 7 plants . Haruka needs to buy 7 total plants - 6 plants she already owns = 1 plant. Since Haruka is only buying 1 plant, which is not more than 2 plants, she will not receive the €9 discount. The cost of 1 plant is €8/plant * 1 plant = €8. Final Answer: The final answer is $\boxed{8}$

Overall Quality: poor

The reasoning chain fails immediately due to a critical logical error in interpreting the required spacing per plant, leading to an incorrect calculation for the total number of plants needed and the final cost.

Detected Issues (1)

logical_error high

Statement

The space required for each plant including the space between plants is 3 meters (width of plant) + 13 meters (space between plants) = 16 meters.

Explanation

The problem phrasing implies that 13 meters is the required spacing unit per plant (as confirmed by the ground truth calculation 117/13=9). Adding the plant width (3m) to the spacing (13m) results in an incorrect unit size of 16m.

Answer Span:

3 meters (width of plant) + 13 meters (space between plants) = 16 meters

Reference/Question Span:

Haruka's flowers grow 3meters wide so she needs to leave 13 meters between every plant (including the plants width)

Question #205

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mr. Martinez sold his cottage for $690000. He paid the transfer fees that amounted to 3% of the selling price and also paid a brokerage fee that is 6% of the selling price. He also paid $590000 for the remaining loan amount on the cottage, and paid $5000 for closing costs. Mr. Martinez used the net proceeds from selling the cottage to invest in stocks. The stocks gained 10% each year for two years. How much were Mr. Martinez's net proceeds after two years? **Answer:** Mr. Martinez sold his cottage for $690000. The transfer fees were $690000 * 0.03 = $20700. The brokerage fee was $690000 * 0.06 = $41400. The total fees paid were $20700 + $41400 = $62100. The net proceeds from the sale, before paying off the loan and closing costs, were $690000 - $62100 = $627900. After paying off the loan and closing costs, the net proceeds were $627900 - $590000 - $5000 = $32900. After one year of investing, the net proceeds grew to $32900 * (1 + 0.10) = $36190. After two years of investing, the net proceeds grew to $36190 * (1 + 0.10) = $39809. Final Answer: \boxed{39809}

Overall Quality: excellent

The reasoning chain correctly calculates all fees, determines the initial net proceeds, applies the two consecutive 10% gains correctly, and arrives at the correct final answer.

✓ No hallucinations detected

Question #148

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: According to its nutritional info, a bag of popcorn has 325 calories per serving. A 100 grams bag has 4 servings. The healthy daily calorie target is 15 calories per pound of body weight. Arash weighs 200 lbs, and he has already consumed 1200 calories and burned 150 calories through exercise. Mei weighs 180 lbs, and she has already consumed 900 in food and 175 calories in ice cream. How many more grams of popcorn does Arash need to consume than Mei? Answer: Arash's target calorie intake is 200 lbs * 15 calories/lb = 3000 calories. His net calorie consumption so far is 1200 calories - 150 calories = 1050 calories. He needs to consume an additional 3000 calories - 1050 calories = 1950 calories. Mei's target calorie intake is 180 lbs * 15 calories/lb = 2700 calories. Her total calorie consumption so far is 900 calories + 175 calories = 1075 calories. She needs to consume an additional 2700 calories - 1075 calories = 1625 calories. A bag of popcorn has 325 calories/serving * 4 servings/100g bag = 1300 calories/100g bag. Arash needs to consume 1950 calories / 1300 calories/100g * 100g = 150g of popcorn. Mei needs to consume 1625 calories / 1300 calories/100g * 100g ≈ 125g of popcorn. Arash needs to consume 150g - 125g = 25g more popcorn than Mei. Final Answer: The final answer is $\boxed{25}$

Overall Quality: excellent

The reasoning chain correctly calculates the calorie targets, net consumption, required additional calories, converts these requirements into grams of popcorn based on the provided nutritional information, and finds the difference, matching the ground truth result.

✓ No hallucinations detected

Question #147

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** According to its nutritional info, a bag of cookies has 175 calories per serving. A 125 oz bag has 5 servings. The healthy daily calorie target is 15 calories per pound of body weight. Theo weighs 250 lbs, and he has already consumed 1100 calories and burned 150 calories through exercise. Sakura weighs 130 lbs, and she has already consumed 900 in food and 175 calories in ice cream. How many more oz of cookies does Theo need to consume than Sakura? **Answer:** Theo's target calorie intake is 250 lbs * 15 calories/lb = 3750 calories. He has a net intake of 1100 calories - 150 calories = 950 calories. He can consume 3750 calories - 950 calories = 2800 calories more. Sakura's target calorie intake is 130 lbs * 15 calories/lb = 1950 calories. She has consumed 900 calories + 175 calories = 1075 calories. She can consume 1950 calories - 1075 calories = 875 calories more. One bag of cookies has 175 calories/serving * 5 servings = 875 calories. Since a bag is 125 oz, one ounce of cookies contains 875 calories / 125 oz = 7 calories/oz. Theo can consume 2800 calories / 7 calories/oz = 400 oz of cookies. Sakura can consume 875 calories / 7 calories/oz = 125 oz of cookies. Theo needs to consume 400 oz - 125 oz = 275 oz more cookies than Sakura. Final Answer: \boxed{275}

Overall Quality: excellent

The reasoning chain correctly calculates Theo's and Sakura's remaining calorie needs, correctly determines the calorie density per ounce of cookies based on the provided serving information, and accurately calculates the difference in cookie ounces required, matching the ground truth.

✓ No hallucinations detected

Question #204

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Dr. Miller sold his apartment for $490000. He paid the legal fees that amounted to 1% of the selling price and also paid a realtor fee that is 5% of the selling price. He also paid $390000 for the remaining loan amount on the apartment, and $10000 for closing costs. Dr. Miller used the net proceeds from selling the apartment to invest in stocks. The stocks gained 10% each year for two years. How much were Dr. Miller's net proceeds after two years? **Answer:** * Legal fees: $490000 * 0.01 = $4900 * Realtor fees: $490000 * 0.05 = $24500 * Total fees: $4900 + $24500 = $29400 * Net proceeds from sale (before investment): $490000 - $29400 - $390000 - $10000 = $60600 * Net proceeds after year 1: $60600 * (1 + 0.10) = $66660 * Net proceeds after year 2: $66660 * (1 + 0.10) = $73326 The answer is $\boxed{73326}$.

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate steps and arrives at the correct final answer. All arithmetic operations are correct.

✓ No hallucinations detected

Question #209

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Prof. Smith sold his house for $560000. He paid the registration fees that amounted to 3% of the selling price and also paid an agent fee that is 4% of the selling price. He also paid $440000 for the remaining loan amount on the house, and $15000 for closing costs. Prof. Smith used the net proceeds from selling the house to invest in stocks. The stocks gained 10% each year for two years. How much were Prof. Smith's net proceeds after two years? **Answer:** 1. **Calculate registration fees:** $560000 * 0.03 = $16800 2. **Calculate agent fees:** $560000 * 0.04 = $22400 3. **Calculate total expenses (excluding loan):** $16800 + $22400 + $15000 = $54200 4. **Calculate net proceeds from the sale (before investment):** $560000 - $54200 - $440000 = $65800 5. **Calculate the return after the first year:** $65800 * 0.10 = $6580 6. **Calculate the total amount after the first year:** $65800 + $6580 = $72380 7. **Calculate the return after the second year:** $72380 * 0.10 = $7238 8. **Calculate the total amount after the second year:** $72380 + $7238 = $79618 Therefore, Prof. Smith's net proceeds after two years were $\boxed{79618}$.

Overall Quality: excellent

The reasoning chain correctly calculates all intermediate steps and arrives at the correct final answer. The calculation method for compounding interest (Steps 5-8) is mathematically sound and equivalent to the ground truth's method ($65800 * 1.10 * 1.10$). All arithmetic operations are correct.

✓ No hallucinations detected

Question #275

1 issue

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Ground Truth Answer

Generated Answer

Reformatted Question: Zahra has a flower bed that is 144 feet long. Zahra wants to fill her flower bed with plants. Zahra's flowers grow 4 feet wide so she needs to leave 12 feet between every plant (including the plants width). Zahra already owns 5 flowers. Each flowering plant costs ₣13 at the store. However, if she buys more than 2 plants, she'll receive a ₣5 discount on the entire purchase. How much money will Zahra spend at the store to fill up her flower bed? Answer: The total space each plant will occupy in the flower bed is the plant's width (4 feet) plus the required space between plants (12 feet), which totals 4 + 12 = 16 feet. The flower bed is 144 feet long, and each plant needs 16 feet of space. Therefore, the flower bed can hold 144 / 16 = 9 plants. Zahra already has 5 plants, so she needs to buy 9 - 5 = 4 plants from the store. Since Zahra is buying 4 plants, which is more than 2 plants, she gets a ₣5 discount. So, each plant will cost ₣13 - ₣5 = ₣8. The total cost of the 4 plants will be 4 * ₣8 = ₣32. Final Answer: The final answer is $\boxed{32}$

Overall Quality: poor

The reasoning chain contains two significant logical errors: misinterpreting the required spacing per plant and incorrectly applying the bulk purchase discount (per unit instead of total purchase).

Detected Issues (1)

logical_error high

Statement

Since Zahra is buying 4 plants, which is more than 2 plants, she gets a ₣5 discount. So, each plant will cost ₣13 - ₣5 = ₣8.

Explanation

The problem states the discount is on the 'entire purchase' if more than 2 plants are bought, not a per-plant reduction. The cost should be calculated based on the full price (4 * 13) and then the ₣5 discount subtracted from the total.

Answer Span:

each plant will cost ₣13 - ₣5 = ₣8

Reference/Question Span:

if she buys more than 2 plants, she'll receive a ₣5 discount on the entire purchase

Question #270

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Kimia has a flower bed that is 126 feet long. Kimia wants to fill her flower bed with plants. Kimia's flowers grow 7 feet wide, so she needs to leave 14 feet between every plant (including the plants width). Kimia already owns 6 flowers. Each flowering plant costs ₣4 at the store. However, if she buys more than 2 plants, she'll receive a ₣5 discount on the entire purchase. How much money will Kimia spend at the store to fill up her flower bed? **Answer:** 1. **Space needed per plant:** Each plant requires its width (7 feet) plus the space between plants (14 feet), totaling 21 feet. 2. **Number of plants that can fit:** The flower bed is 126 feet long, so a maximum of 126 feet / 21 feet/plant = 6 plants can fit. 3. **Number of plants to buy:** Kimia already has 6 flowers, and she can fit 6 plants in her flower bed. Therefore, she needs to buy 6 - 6 = 0 plants. 4. **Cost of plants:** Since Kimia doesn't need to buy any plants (0 plants), she will spend ₣0. The discount doesn't apply since she's buying less than 2 plants. Final Answer: The final answer is $\boxed{0}$

Overall Quality: poor

The reasoning chain contains a critical logical error in Step 1 regarding the interpretation of spacing requirements, leading to an incorrect calculation of the total number of plants needed and an incorrect final cost.

Detected Issues (1)

logical_error high

Statement

Each plant requires its width (7 feet) plus the space between plants (14 feet), totaling 21 feet.

Explanation

The problem implies that 14 feet is the total space allocated per plant placement (including the plant itself and the necessary gap), as 126 / 14 = 9 plants, which aligns with the expected result structure. Interpreting this as 7 feet (width) + 14 feet (gap) = 21 feet per plant leads to an incorrect total plant count (6 plants).

Answer Span:

Each plant requires its width (7 feet) plus the space between plants (14 feet), totaling 21 feet.

Reference/Question Span:

Kimia's flowers grow 7feet wide so she needs to leave 14 feet between every plant (including the plants width).

Question #272

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mei has a flower bed that is 120 meters long. Mei wants to fill her flower bed with plants. Mei's flowers grow 4 meters wide so she needs to leave 12 meters between every plant (including the plants width). Mei already owns 6 flowers. Each flowering plant costs $5 at the store. However, if she buys more than 2 plants, she'll receive a $5 discount on the entire purchase. How much money will Mei spend at the store to fill up her flower bed? **Answer:** Each plant needs 4 meters + 12 meters = 16 meters of space. The flower bed is 120 meters long, so it can hold 120 meters / 16 meters/plant = 7.5 plants. Since she can't have half a plant, the flower bed can hold a maximum of 7 plants. Mei already has 6 flowers, so she needs 7 plants - 6 plants = 1 plant. Since Mei needs to buy 1 plant, which is not more than 2 plants, she won't receive the $5 discount. Therefore, Mei will spend 1 plant * $5/plant = $5. The answer is $\boxed{5}$.

Overall Quality: poor

The reasoning contains a critical logical error in interpreting the spacing requirement, leading to an incorrect calculation of the total number of plants needed and consequently an incorrect final cost.

✓ No hallucinations detected

Question #154

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** In Dr. Lee's class of 104 students, 50% of the class are volleyball players. Out of the remaining class, 25% of the students are robotics club members or part of choir members. These 3 groups of students will need to leave early today to travel to an away competition. Half of the volleyball players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition? **Answer:** * **Volleyball players:** 104 students * 50% = 52 volleyball players. * **Volleyball players present:** 52 volleyball players * (1 - 50% sick) = 26 volleyball players present. * **Remaining students (not volleyball players):** 104 students - 52 volleyball players = 52 students. * **Robotics/Choir members:** 52 students * 25% = 13 robotics/choir members. * **Total students competing (excluding cheerleaders):** 26 volleyball players present + 13 robotics/choir members = 39 students competing. * **Cheerleaders:** 3 groups * 3 cheerleaders/group = 9 cheerleaders. * **Total students leaving early:** 39 students competing + 9 cheerleaders = 48 students. Final Answer: \boxed{48}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all arithmetic calculations accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #208

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Dr. Smith sold his house for $590000. He paid the legal fees that amounted to 3% of the selling price and also paid a realtor fee that is 4% of the selling price. He also paid $380000 for the remaining loan amount on the house, and $25000 for closing costs. Dr. Smith used the net proceeds from selling the house to invest in stocks. The stocks gained 10% each year for two years. How much were Dr. Smith's net proceeds after two years? Answer: Legal fees: $590000 * 0.03 = $17700 Realtor fees: $590000 * 0.04 = $23600 Total fees and costs: $17700 + $23600 + $380000 + $25000 = $446300 Net proceeds from selling the house: $590000 - $446300 = $143700 Net proceeds after one year: $143700 * (1 + 0.10) = $158070 Net proceeds after two years: $158070 * (1 + 0.10) = $173877 Final Answer: The final answer is $\boxed{173877}$

Overall Quality: excellent

The reasoning chain correctly calculates all fees, determines the net proceeds, and applies the two consecutive 10% gains correctly, matching the ground truth.

✓ No hallucinations detected

Question #153

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** In Ms. Johnson's class of 20 students, 20% of the class are soccer players. Out of the remaining class, 50% of the students are debate team members or part of choir members. These 3 groups of students will need to leave early today to travel to an away competition. Half of the soccer players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition? **Answer:** First, we find the number of soccer players: 20 students * 20% = 4 soccer players. Since half the soccer players are sick, only 4 soccer players / 2 = 2 soccer players are going to the competition. Next, we determine the number of remaining students: 20 students - 4 soccer players = 16 students. Then we find the number of debate/choir members: 16 remaining students * 50% = 8 debate/choir members. The number of students from the 3 groups going to the competition is: 2 soccer players + 8 debate/choir members = 10 students. Finally, we calculate the number of cheerleaders going: 3 groups * 3 cheerleaders/group = 9 cheerleaders. Therefore, the total number of students leaving early is 10 students + 9 cheerleaders = 19. The answer is $\boxed{19}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all arithmetic calculations accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #155

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** In Mr. Smith's class of 80 students, 20% of the class are basketball players. Out of the remaining class, 50% of the students are dancers or part of debate team members. These 3 groups of students will need to leave early today to travel to an away tournament. Half of the basketball players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the tournament? **Answer:** * There are a total of 80 students in Mr. Smith's class. * 20% of the class are basketball players, so there are 0.20 * 80 = 16 basketball players. * Half of the basketball players are sick, so 16/2 = 8 basketball players are going to the tournament. * The remaining students in the class are 80 - 16 = 64 students. * 50% of the remaining students are dancers or debate team members, so 0.50 * 64 = 32 dancers/debaters are going to the tournament. * There are 3 groups going to the tournament (basketball, dancers, debaters), and 3 cheerleaders will accompany each group, so there are 3 * 3 = 9 cheerleaders going to the tournament. * The total number of students leaving early is 8 + 32 + 9 = 49 students. Final Answer: \boxed{49}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all arithmetic calculations accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #150

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** In Ms. Johnson's class of 100 students, 46% of the class are soccer players. Out of the remaining class, 50% of the students are robotics club members or part of dancers. These 3 groups of students will need to leave early today to travel to an away competition. Half of the soccer players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition? **Answer:** * There are a total of 100 students in the class. * The number of soccer players is 46% of 100, which is 0.46 * 100 = 46 soccer players. * Half of the soccer players are absent, meaning 0.5 * 46 = 23 soccer players are absent. * The number of soccer players going to the competition is 46 - 23 = 23 soccer players. * The remaining students in the class are 100 - 46 = 54 students. * 50% of the remaining students are in robotics/dance, which is 0.5 * 54 = 27 robotics/dance students. * The total number of students from the three groups (soccer, robotics, dance) going to the competition is 23 + 27 = 50 students. * There are 3 cheerleaders for each of the 3 groups, so a total of 3 * 3 = 9 cheerleaders are also going. * The total number of people going to the competition is 50 students + 9 cheerleaders = 59 people. The total number of students leaving early for the competition is $\boxed{50}$. (Cheerleaders are not considered students in this final count).

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement. The calculation for the number of students leaving early (59) matches the ground truth logic, although the final boxed answer in the reasoning chain incorrectly states 50.

✓ No hallucinations detected

Question #78

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Sakura is an avid gardener. Two days ago, she received 49 new potted plants from her favorite plant nursery. She already has 7 potted plants on each of the 60 window ledges of her large country home. She also purchased 100 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 3 potted plants from each ledge to friends and family tomorrow. How many potted plants will Sakura remain with? **Answer:** 1. **Initial plants on ledges:** Sakura initially had 7 plants/ledge * 60 ledges = 420 plants on her window ledges. 2. **Total plants before gifts:** She received 49 new plants two days ago and 100 new plants yesterday. So, before giving any away, she had a total of 420 + 49 + 100 = 569 plants. 3. **Plants given away:** She will give away 3 plants/ledge * 60 ledges = 180 plants. 4. **Remaining plants:** After giving away the plants, she will have 569 - 180 = 389 plants remaining. Final Answer: The final answer is $\boxed{389}$

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement. All arithmetic calculations are accurate, and the logic correctly interprets the sequence of events (initial state, additions, subtractions).

✓ No hallucinations detected

Question #79

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Daphne is an avid gardener. Two days ago, she received 23 new potted plants from her favorite plant nursery. She already has 8 potted plants on each of the 56 window ledges of her large country home. She also purchased 200 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 6 potted plants from each ledge to friends and family tomorrow. How many potted plants will Daphne remain with? **Answer:** Daphne initially had 8 plants * 56 ledges = 448 plants on her window ledges. Two days ago, she received an additional 23 plants. Yesterday, she purchased another 200 plants. Her total number of plants before giving any away is 448 + 23 + 200 = 671 plants. She will give away 6 plants * 56 ledges = 336 plants. After giving away the plants, she will have 671 - 336 = 335 plants remaining. The answer is $\boxed{335}$.

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps and performs all arithmetic calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #80

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Amelia is an avid gardener. Last week, she received 25 new potted plants from her favorite plant nursery. She already has 12 potted plants on each of the 54 window ledges of her large country home. She also purchased 110 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 4 potted plants from each ledge to friends and family tomorrow. How many potted plants will Amelia remain with? **Answer:** 1. Amelia initially had 12 plants * 54 ledges = 648 plants on her window ledges. 2. She received 25 new plants last week, so her total became 648 + 25 = 673 plants. 3. She then purchased 110 new plants, increasing her total to 673 + 110 = 783 plants. 4. She will give away 4 plants * 54 ledges = 216 plants. 5. After giving away plants, she will have 783 - 216 = 567 plants remaining. The answer is $\boxed{567}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement. All arithmetic calculations are accurate, and the logic correctly incorporates the initial inventory, additions, and subtractions.

✓ No hallucinations detected

Question #81

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Elena is an avid gardener. Two days ago, she received 38 new potted plants from her favorite plant nursery. She already has 12 potted plants on each of the 55 window ledges of her large country home. She also purchased 70 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 3 potted plants from each ledge to friends and family tomorrow. How many potted plants will Elena remain with? **Answer:** 1. Elena initially had 12 plants/ledge * 55 ledges = 660 plants. 2. After receiving 38 new plants two days ago, she had 660 + 38 = 698 plants. 3. After purchasing 70 new plants yesterday, she had 698 + 70 = 768 plants. 4. She will give away 3 plants/ledge * 55 ledges = 165 plants. 5. Therefore, Elena will remain with 768 - 165 = 603 plants. The answer is $\boxed{603}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all steps described in the problem. All calculations are correct.

✓ No hallucinations detected

Question #82

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Yara is an avid gardener. Two days ago, she received 49 new potted plants from her favorite plant nursery. She already has 12 potted plants on each of the 54 window ledges of her large country home. She also purchased 130 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 4 potted plants from each ledge to friends and family tomorrow. How many potted plants will Yara remain with? **Answer:** Yara initially had 12 plants/ledge * 54 ledges = 648 plants on her window ledges. With the 49 new plants from two days ago and the 130 new plants from yesterday, her total number of plants became 648 + 49 + 130 = 827 plants. She will give away 4 plants/ledge * 54 ledges = 216 plants tomorrow. Therefore, Yara will have 827 - 216 = 611 plants remaining. The answer is $\boxed{611}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the steps required by the problem statement. All calculations are correct.

✓ No hallucinations detected

Question #97

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Benjamin is selling cupcakes and pineapple pies for a fundraiser. On Wednesday, he sold 27 boxes of cupcake and 18 fewer boxes of pineapple pie, than on Thursday. On Thursday, he sold 12 more boxes of cupcakes than on Wednesday and 27 boxes of pineapple pie. On Friday, he sold as much as he did in the past two days combined. If the cupcake cost ¥8 and the pineapple pie cost ¥22, what was Benjamin's average daily earning? **Answer:** On Wednesday, Benjamin sold 27 boxes of cupcakes and 27 - 18 = 9 boxes of pineapple pie. On Thursday, Benjamin sold 27 + 12 = 39 boxes of cupcakes and 27 boxes of pineapple pie. On Friday, Benjamin sold 27 + 39 = 66 boxes of cupcakes and 9 + 27 = 36 boxes of pineapple pie. Wednesday's earnings: 27 * ¥8 + 9 * ¥22 = ¥414 Thursday's earnings: 39 * ¥8 + 27 * ¥22 = ¥906 Friday's earnings: 66 * ¥8 + 36 * ¥22 = ¥1320 Total earnings: ¥414 + ¥906 + ¥1320 = ¥2640 Average daily earning: ¥2640 / 3 = ¥880 The answer is $\boxed{880}$.

Overall Quality: excellent

The reasoning chain correctly interprets the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #112

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Faisal went to buy some school supplies. He bought 18 pencils which cost ₣6.0 each, 14 rulers which cost ₣14.5 each, and a ream of bond paper which cost ₣24. He also bought 5 colored pencils which cost ₣9 each. Faisal can either pay a one-time ₣20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Faisal can spend on everything? **Answer:** Cost of pencils: 18 * ₣6 = ₣108 Cost of rulers: 14 * ₣14.5 = ₣203 Cost of bond paper: ₣24 Cost of colored pencils: 5 * ₣9 = ₣45 Total cost before discount: ₣108 + ₣203 + ₣24 + ₣45 = ₣380 **Option 1: Membership** Discount: ₣380 * 0.20 = ₣76 Cost after discount: ₣380 - ₣76 = ₣304 Total cost with membership fee: ₣304 + ₣20 = ₣324 **Option 2: No Membership** Discount: ₣380 * 0.05 = ₣19 Total cost without membership: ₣380 - ₣19 = ₣361 Comparing ₣324 and ₣361, the least amount Faisal can spend is ₣324. Final Answer: \boxed{324}

Overall Quality: excellent

The reasoning chain correctly calculates the costs for all items, determines the total cost, and accurately evaluates both membership options (including the fee for Option 1) to find the minimum spending amount. All arithmetic operations are correct.

✓ No hallucinations detected

Question #159

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A grandfather eats 10 sushi rolls per day, his partner eats 15 sushi rolls per day, and their son eats four-fifths of the combined number of sushi rolls they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 20% for the first half of the month, and then by an additional 25% for the second half. How many sushi rolls does this family eat in two months? **Answer:** 1. **Combined consumption of grandfather and partner:** 10 + 15 = 25 sushi rolls per day 2. **Son's daily consumption:** 4/5 * 25 = 20 sushi rolls per day 3. **Total family consumption per day:** 25 + 20 = 45 sushi rolls per day 4. **First month's consumption (assuming 30 days):** 45 * 30 = 1350 sushi rolls 5. **Daily consumption in the first half of the second month (20% reduction):** 45 * (1 - 0.20) = 36 sushi rolls per day 6. **Consumption in the first half of the second month (assuming 15 days):** 36 * 15 = 540 sushi rolls 7. **Daily consumption in the second half of the second month (additional 25% reduction from the reduced amount):** 36 * (1 - 0.25) = 27 sushi rolls per day 8. **Consumption in the second half of the second month (assuming 15 days):** 27 * 15 = 405 sushi rolls 9. **Total consumption in the second month:** 540 + 405 = 945 sushi rolls 10. **Total consumption in two months (two months):** 1350 + 945 = 2295 sushi rolls Final Answer: \boxed{2295}

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps and performs all arithmetic calculations accurately. The assumptions about month length (30 days total, 15 days per half) are standard for such problems and consistent with the ground truth derivation.

✓ No hallucinations detected

Question #151

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** In Ms. Johnson's class of 150 students, 40% of the class are soccer players. Out of the remaining class, 30% of the students are dancers or part of choir members. These 3 groups of students will need to leave early today to travel to an away competition. Half of the soccer players are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the competition? **Answer:** * **Soccer Players:** 150 students * 40% = 60 soccer players. * **Sick Soccer Players:** 60 soccer players * 50% = 30 sick soccer players. * **Soccer Players Going to Competition:** 60 soccer players - 30 sick soccer players = 30 soccer players. * **Remaining Students (excluding soccer players):** 150 students - 60 soccer players = 90 students. * **Dancers/Choir Members:** 90 students * 30% = 27 dancers/choir members. * **Total Students from the 3 groups going (excluding cheerleaders):** 30 + 27 = 57 students * **Cheerleaders:** 3 groups * 3 cheerleaders/group = 9 cheerleaders. * **Total Students Leaving Early:** 57 students + 9 cheerleaders = 66. Final Answer: \boxed{66}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #212

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**Reformatted Question:** Benjamin is raising money for a 3-day science fair. Each day costs ₺250 for hotel, ₺30 for food, and ₺20 for transportation. Benjamin only has ₺165. His friends have chipped in and will cover the cost of all the food for the science fair. Benjamin has also applied for help from the parent association, which has decided to cover a tenth of the remaining cost of the science fair. How much money is Benjamin still missing? **Answer:** The total cost for the hotel for 3 days is 3 * ₺250 = ₺750. The total cost for food for 3 days is 3 * ₺30 = ₺90. The total cost for transportation for 3 days is 3 * ₺20 = ₺60. Since the friends are covering the ₺90 food cost (), we only need to account for the hotel (₺750) and transportation (₺60). The combined cost of hotel and transportation is ₺750 + ₺60 = ₺810. The parent association will cover a tenth of this remaining cost, which is (1/10) * ₺810 = ₺81. This means Benjamin needs to cover ₺810 - ₺81 = ₺729. Benjamin currently has ₺165. Therefore, Benjamin is still missing ₺729 - ₺165 = ₺564. Final Answer: \boxed{564}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost, accounts for the food cost covered by friends, calculates the remaining cost, applies the parent association's contribution (1/10 of the remaining cost), and finally subtracts Benjamin's existing funds to find the amount still missing. All arithmetic operations are correct.

✓ No hallucinations detected

Question #83

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**Reformatted Question:** Mei is an avid gardener. Two days ago, she received 38 new potted plants from her favorite plant nursery. She already has 9 potted plants on each of the 60 window ledges of her large country home. She also purchased 170 new plants yesterday at a 50% discount. Feeling generous, she has decided that she will give 6 potted plants from each ledge to friends and family tomorrow. How many potted plants will Mei remain with? **Answer:** 1. Mei started with 9 plants * 60 ledges = 540 plants. 2. Two days ago, she received 38 new plants, so she had 540 + 38 = 578 plants. 3. Yesterday, she purchased an additional 170 new plants, bringing her total to 578 + 170 = 748 plants. 4. Tomorrow, she will give away 6 plants * 60 ledges = 360 plants. 5. After giving away the plants, she will have 748 - 360 = 388 plants remaining. The answer is $\boxed{388}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the steps required by the problem statement. All calculations are correct.

✓ No hallucinations detected

Question #110

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**Reformatted Question:** Deshawn went to buy some school supplies. He bought 14 erasers which cost ₺7.5 each, 4 rulers which cost ₺18.5 each, and a ream of bond paper which cost ₺21. He also bought 8 folders which cost ₺10 each. Deshawn can either pay a one-time ₺20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount DeShawn can spend on everything? **Answer:** Cost of erasers: 14 * ₺7.5 = ₺105 Cost of rulers: 4 * ₺18.5 = ₺74 Cost of bond paper: ₺21 Cost of folders: 8 * ₺10 = ₺80 Total cost before discount: ₺105 + ₺74 + ₺21 + ₺80 = ₺280 Option 1: Membership with 20% discount Discount amount: ₺280 * 0.20 = ₺56 Cost after discount: ₺280 - ₺56 = ₺224 Final cost with membership fee: ₺224 + ₺20 = ₺244 Option 2: No membership with 5% discount Discount amount: ₺280 * 0.05 = ₺14 Final cost without membership: ₺280 - ₺14 = ₺266 Comparing the final costs, ₺244 (with membership) is less than ₺266 (without membership). Final Answer: The least amount Deshawn can spend is \boxed{244}.

Overall Quality: excellent

The reasoning chain correctly calculates the total cost before discounts, evaluates both membership options (including the fee for Option 1), and correctly determines the minimum cost.

✓ No hallucinations detected

Question #157

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**Reformatted Question:** An uncle eats 24 hamburgers per day, his spouse eats 24 hamburgers per day, and their grandchild eats one-half of the combined number of hamburgers they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 75% for the first half of the month, and then by an additional 50% for the second half. How many hamburgers does this family eat in two months? **Answer:** First, let's calculate the daily hamburger consumption of the grandchild: (24 + 24) / 2 = 24 hamburgers per day. The family's total daily hamburger consumption is: 24 + 24 + 24 = 72 hamburgers per day. Assuming a 30-day month, the family eats 72 * 30 = 2160 hamburgers in the first month. In the first half of the second month (15 days), they reduce consumption by 75%, so they eat 25% of their usual amount: 72 * 0.25 = 18 hamburgers per day. Over 15 days, this totals 18 * 15 = 270 hamburgers. In the second half of the second month (15 days), they further reduce consumption by 50% from their already reduced amount. This means they eat 50% of 18 hamburgers per day: 18 * 0.5 = 9 hamburgers per day. Over 15 days, this is 9 * 15 = 135 hamburgers. The total hamburger consumption for the second month is 270 + 135 = 405 hamburgers. The total hamburger consumption over two months is 2160 + 405 = 2565 hamburgers. Final Answer: \boxed{2565}

Overall Quality: excellent

The reasoning chain is mathematically sound and internally consistent based on a plausible interpretation of the ambiguous prompt regarding the grandchild's consumption. The final result matches the ground truth.

✓ No hallucinations detected

Question #109

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**Reformatted Question:** Bodhi went to buy some school supplies. He bought 24 folders which cost €2.75 each, 12 pencils which cost €19.25 each, and a ream of bond paper which cost €23. He also bought 5 markers which cost €8 each. Bodhi can either pay a one-time €20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Bodhi can spend on everything? **Answer:** Cost of folders: 24 * €2.75 = €66 Cost of pencils: 12 * €19.25 = €231 Cost of bond paper: €23 Cost of markers: 5 * €8 = €40 Total cost before discount: €66 + €231 + €23 + €40 = €360 Scenario 1: 5% discount (no membership) Discount amount: €360 * 0.05 = €18 Final cost: €360 - €18 = €342 Scenario 2: 20% discount with €20 membership fee Discount amount: €360 * 0.20 = €72 Cost after discount: €360 - €72 = €288 Final cost (including membership): €288 + €20 = €308 Comparing the final costs of both scenarios, €342 (no membership) and €308 (with membership), the least amount Bodhi can spend is €308. Final Answer: \boxed{308}

Overall Quality: excellent

The reasoning chain correctly calculates the costs for all items, determines the total cost, and accurately evaluates both scenarios (with and without membership) to find the minimum spending amount. All arithmetic operations are correct.

✓ No hallucinations detected

Question #161

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**Reformatted Question:** A father eats 25 hamburgers per day, his wife eats 20 hamburgers per day, and their daughter eats two-thirds of the combined number of hamburgers they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 20% for the first half of the month, and then by an additional 25% for the second half. How many hamburgers does this family eat in two months? **Answer:** 1. **Combined consumption of father and wife:** 25 + 20 = 45 hamburgers/day 2. **Daughter's consumption:** 2/3 * 45 = 30 hamburgers/day 3. **Total family consumption per day:** 45 + 30 = 75 hamburgers/day 4. **Consumption in the first month (assuming 30 days):** 75 hamburgers/day * 30 days = 2250 hamburgers 5. **Consumption during the first half of the second month:** 75 hamburgers/day * (1 - 0.20) * 15 days = 900 hamburgers 6. **Consumption during the second half of the second month:** 75 hamburgers/day * (1 - 0.20) * (1 - 0.25) * 15 days = 675 hamburgers 7. **Total consumption in the second month:** 900 + 675 = 1575 hamburgers 8. **Total consumption in two months:** 2250 + 1575 = 3825 hamburgers Final Answer: \boxed{3825}

Overall Quality: excellent

The reasoning chain correctly interprets the problem and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #152

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**Reformatted Question:** In Mrs. Garcia's class of 160 students, 50% of the class are swimmers. Out of the remaining class, 35% of the students are debate team members or part of dancers. These 3 groups of students will need to leave early today to travel to an away tournament. Half of the swimmers are absent for being sick. Also, 3 cheerleaders will accompany each of these groups. How many students are leaving early to the tournament? **Answer:** * The total number of students in Mrs. Garcia's class is 160. * The number of swimmers is 50% of 160, which is (50/100) * 160 = 80 students. * Since half of the swimmers are absent, the number of swimmers going to the tournament is 80 / 2 = 40 students. * The remaining class consists of 160 - 80 = 80 students. * 35% of the remaining class are debaters or dancers. This is (35/100) * 80 = 28 students. * Three groups are going: swimmers, debaters/dancers, and cheerleaders. * There are 3 cheerleaders per group, so a total of 3 * 3 = 9 cheerleaders are going. * The total number of students leaving early for the tournament is 40 swimmers + 28 debaters/dancers + 9 cheerleaders = 77 students. Final Answer: \boxed{77}

Overall Quality: excellent

The reasoning chain correctly follows all steps derived from the problem statement and performs all calculations accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #113

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Reformatted Question: Oscar went to buy some school supplies. He bought 24 notebooks which cost ₺3.5 each, 6 rulers which cost ₺13.0 each, and a ream of bond paper which cost ₺15. He also bought 7 pencils which cost ₺9 each. Oscar can either pay a one-time ₺20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Oscar can spend on everything? Answer: Cost of notebooks: 24 * ₺3.5 = ₺84 Cost of rulers: 6 * ₺13.0 = ₺78 Cost of bond paper: ₺15 Cost of pencils: 7 * ₺9 = ₺63 Total cost before discount: ₺84 + ₺78 + ₺15 + ₺63 = ₺240 Option 1: Member with 20% discount Discount amount: ₺240 * 0.20 = ₺48 Cost after discount: ₺240 - ₺48 = ₺192 Total cost with membership fee: ₺192 + ₺20 = ₺212 Option 2: Non-member with 5% discount Discount amount: ₺240 * 0.05 = ₺12 Total cost: ₺240 - ₺12 = ₺228 Comparing ₺212 (member) and ₺228 (non-member), the least amount Oscar can spend is ₺212. Final Answer: The final answer is $\boxed{212}$

Overall Quality: excellent

The reasoning chain correctly calculates the costs for all items, determines the total cost, accurately calculates the costs for both membership options (including the fee for Option 1), and correctly identifies the minimum cost.

✓ No hallucinations detected

Question #108

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**Reformatted Question:** Leon went to buy some school supplies. He bought 8 crayons which cost ¥7.0 each, 8 notebooks which cost ¥13.75 each, and a ream of bond paper which cost ¥10. He also bought 4 folders which cost ¥11 each. Leon can either pay a one-time ¥20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Leon can spend on everything? **Answer:** Cost of crayons: 8 * ¥7.0 = ¥56 Cost of notebooks: 8 * ¥13.75 = ¥110 Cost of bond paper: ¥10 Cost of folders: 4 * ¥11 = ¥44 Total cost before discount: ¥56 + ¥110 + ¥10 + ¥44 = ¥220 Option 1: Member with 20% discount Discount amount: ¥220 * 0.20 = ¥44 Cost after discount: ¥220 - ¥44 = ¥176 Final cost (including membership fee): ¥176 + ¥20 = ¥196 Option 2: Non-member with 5% discount Discount amount: ¥220 * 0.05 = ¥11 Final cost: ¥220 - ¥11 = ¥209 Comparing ¥196 and ¥209, the least amount Leon can spend is ¥196. Final Answer: \boxed{196}

Overall Quality: excellent

The reasoning chain correctly calculates the costs for all items, determines the total cost, and accurately evaluates both membership options (Option 1: ¥196, Option 2: ¥209). The final conclusion that ¥196 is the least amount is logically sound based on the calculations.

✓ No hallucinations detected

Question #111

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**Reformatted Question:** Andre went to buy some school supplies. He bought 20 markers which cost ₣8.0 each, 10 pencils which cost ₣18.0 each, and a ream of bond paper which cost ₣15. He also bought 5 rulers which cost ₣9 each. Andre can either pay a one-time ₣20 fee to become a member and get a 20% discount on all purchases, or not become a member and receive only a 5% discount. What is the least amount Andre can spend on everything? **Answer:** Cost of markers: 20 markers * ₣8.0/marker = ₣160 Cost of pencils: 10 pencils * ₣18.0/pencil = ₣180 Cost of paper: ₣15 Cost of rulers: 5 rulers * ₣9.0/ruler = ₣45 Total cost before discount: ₣160 + ₣180 + ₣15 + ₣45 = ₣400 **Option 1: Membership** Discount: ₣400 * 20% = ₣80 Cost after discount: ₣400 - ₣80 = ₣320 Total cost with membership: ₣320 + ₣20 = ₣340 **Option 2: No Membership** Discount: ₣400 * 5% = ₣20 Total cost without membership: ₣400 - ₣20 = ₣380 Comparing ₣340 (with membership) and ₣380 (without membership), the least amount Andre can spend is ₣340. Final Answer: \boxed{340}

Overall Quality: excellent

The reasoning chain correctly calculates the total cost before discounts, evaluates both membership options accurately, and correctly determines the minimum cost.

✓ No hallucinations detected

Question #245

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**Reformatted Question:** Valeria went to the coast for vacation. Her parents gave her €1300 to buy whatever she wanted. At the seaside store, cotton candy was on sale for "Buy 15 pounds at €21 per pound, get 5 pounds 1/3 off." She scooped up 23 pounds. She also bought a mixed bag of coral pieces for €11.0 and 11 pins that were €21.0 each. Valeria then donated €5 at a charity stand along the way. How much money does Valeria have left? **Answer:** First, let's calculate the cost of the cotton candy. Valeria bought 23 pounds. The first 15 pounds cost €21 each, so that's 15 * €21 = €315. She gets a discount on the next 5 pounds. One-third of €21 is €21 / 3 = €7. So the discounted price per pound is €21 - €7 = €14. The cost of the 5 discounted pounds is 5 * €14 = €70. She bought 23 pounds total, so the remaining 23 - 15 - 5 = 3 pounds were at the regular price of €21, costing 3 * €21 = €63. The total cost of the cotton candy is €315 + €70 + €63 = €448. Next, the cost of the pins is 11 pins * €21 each = €231. Her total spending is the cost of cotton candy (€448) + the cost of the coral (€11) + the cost of the pins (€231) + the donation (€5) = €448 + €11 + €231 + €5 = €695. Finally, Valeria started with €1300 and spent €695, so she has €1300 - €695 = €605 left. The answer is $\boxed{605}$.

Overall Quality: excellent

The reasoning chain correctly interprets the complex discount structure for the cotton candy and accurately calculates all subsequent costs and the final remaining balance. All arithmetic operations are correct.

✓ No hallucinations detected

Question #70

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**Reformatted Question:** Alejandro wants to make different sized ice cubes with 309 ounces of water. He can make giant cubes that use 14 ounces per cube, medium cubes that use 6 ounces, small cubes that use 1/2 of an ounce, and tiny cubes that are half the size of small cubes. He makes 50 total ice cubes, including 9 giant cubes, 14 small cubes, 15 medium cubes, and some tiny cubes. How many ounces of water does Alejandro have left? **Answer:** 1. **Giant cubes water usage:** 9 giant cubes * 14 ounces/giant cube = 126 ounces 2. **Medium cubes water usage:** 15 medium cubes * 6 ounces/medium cube = 90 ounces 3. **Small cubes water usage:** 14 small cubes * 0.5 ounces/small cube = 7 ounces 4. **Number of tiny cubes:** 50 total cubes - 9 giant cubes - 15 medium cubes - 14 small cubes = 12 tiny cubes 5. **Tiny cubes water usage:** 12 tiny cubes * (0.5 ounces/small cube / 2) = 3 ounces 6. **Total water used:** 126 ounces + 90 ounces + 7 ounces + 3 ounces = 226 ounces 7. **Water remaining:** 309 ounces - 226 ounces = 83 ounces Therefore, Alejandro has $\boxed{83}$ ounces of water left.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description. All arithmetic operations are correct, leading to the correct final answer, which matches the ground truth.

✓ No hallucinations detected

Question #194

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**Reformatted Question:** Ms. Johnson is looking for a new apartment that will not go beyond her $430000 budget. She saw a property that has a selling price of $400000. On top of that, the buyer has to pay a brokerage fee which is 7% of the selling price, and also the transfer fee that is 14% of the selling price. If Ms. Johnson can get 5% discount on the selling price, how much more will be the total cost than Ms. Johnson's budget? **Answer:** 1. **Discounted selling price:** $400000 * (1 - 0.05) = $380000 2. **Brokerage fee:** $380000 * 0.07 = $26600 3. **Transfer fee:** $380000 * 0.14 = $53200 4. **Total cost:** $380000 + $26600 + $53200 = $459800 5. **Amount exceeding budget:** $459800 - $430000 = $29800 The total cost will be $\boxed{29800}$ more than Ms. Johnson's budget.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the correct logical steps based on the problem description. All calculations are verified as correct.

✓ No hallucinations detected

Question #101

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**Reformatted Question:** Thiago is selling cookies and apricot pies for a fundraiser. On Tuesday, he sold 26 boxes of cookies and 19 fewer boxes of apricot pie, than on Wednesday. On Wednesday, he sold 14 more boxes of cookies than on Tuesday and 24 boxes of apricot pie. On Thursday, he sold as much as he did in the past two days combined. If the cookie cost ₣11 and the apricot pie cost ₣24, what was Thiago's average daily earning? **Answer:** * **Tuesday's Sales:** * Cookies: 26 boxes * Apricot Pies: 24 boxes - 19 boxes = 5 boxes * **Wednesday's Sales:** * Cookies: 26 boxes + 14 boxes = 40 boxes * Apricot Pies: 24 boxes * **Thursday's Sales:** * Cookies: 26 boxes + 40 boxes = 66 boxes * Apricot Pies: 5 boxes + 24 boxes = 29 boxes * **Tuesday's Earnings:** * Cookies: 26 boxes * ₣11/box = ₣286 * Apricot Pies: 5 boxes * ₣24/box = ₣120 * Total: ₣286 + ₣120 = ₣406 * **Wednesday's Earnings:** * Cookies: 40 boxes * ₣11/box = ₣440 * Apricot Pies: 24 boxes * ₣24/box = ₣576 * Total: ₣440 + ₣576 = ₣1016 * **Thursday's Earnings:** * Cookies: 66 boxes * ₣11/box = ₣726 * Apricot Pies: 29 boxes * ₣24/box = ₣696 * Total: ₣726 + ₣696 = ₣1422 * **Total Earnings over Three Days:** ₣406 + ₣1016 + ₣1422 = ₣2844 * **Average Daily Earning:** ₣2844 / 3 days = ₣948 Final Answer: \boxed{948}

Overall Quality: excellent

The reasoning chain correctly interprets the problem statement and performs all necessary calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #211

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**Reformatted Question:** Ali is raising money for a 3-day sports tournament. Each day costs ₣200 for hotel, ₣20 for food, and ₣10 for transportation. Ali only has ₣40. His friends have chipped in and will cover the cost of all the food for the sports tournament. Ali has also applied for help from the local charity, which has decided to cover 1/5 of the remaining cost of the sports tournament. How much money is Ali still missing? **Answer:** The total cost per day is ₣200 (hotel) + ₣20 (food) + ₣10 (transportation) = ₣230. The total cost for the 3-day tournament is 3 days * ₣230/day = ₣690. Ali's friends are covering the food cost, which is 3 days * ₣20/day = ₣60. The remaining cost after friends' contribution is ₣690 - ₣60 = ₣630. The local charity is covering 1/5 of the remaining cost, which is (1/5) * ₣630 = ₣126. The remaining cost after the charity's contribution is ₣630 - ₣126 = ₣504. Ali has ₣40. The amount Ali is still missing is ₣504 - ₣40 = ₣464. Final Answer: The final answer is $\boxed{464}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem logic correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #214

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**Reformatted Question:** Yuki is raising money for a 2-day music festival. Each day costs ₺100 for hotel, ₺40 for food, and ₺30 for transportation. Yuki only has ₺10. His friends have chipped in and will cover the cost of all the food for the music festival. Yuki has also applied for help from the parent association, which has decided to cover 1/2 of the remaining cost of the music festival. How much money is Yuki still missing? **Answer:** The total cost per day is the sum of hotel, food, and transportation: ₺100 + ₺40 + ₺30 = ₺170 per day. Since the festival is 2 days long, the total cost for the festival is 2 * ₺170 = ₺340. Yuki's friends are covering the food cost, which is ₺40 per day for 2 days, totaling 2 * ₺40 = ₺80. Subtracting the food cost covered by friends, the remaining cost is ₺340 - ₺80 = ₺260. The parent association is covering half of this remaining cost: 1/2 * ₺260 = ₺130. Thus, the cost Yuki still needs to cover is ₺260 - ₺130 = ₺130. Since Yuki has ₺10, the amount he is still missing is ₺130 - ₺10 = ₺120. Final Answer: The final answer is $\boxed{120}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly, leading to the correct final answer.

✓ No hallucinations detected

Question #67

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Reformatted Question: Deshawn wants to make different sized ice cubes with 312 ounces of water. He can make giant cubes that use 15 ounces per cube, medium cubes that use 5 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 46 total ice cubes, including 8 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does DeShawn have left? Answer: Giant cubes used: 15 ounces/cube * 8 cubes = 120 ounces Medium cubes used: 5 ounces/cube * 12 cubes = 60 ounces Small cubes used: 0.5 ounces/cube * 14 cubes = 7 ounces Total cubes made: 8 + 14 + 12 = 34 cubes Tiny cubes made: 46 total cubes - 34 cubes = 12 tiny cubes Tiny cube size: 0.5 ounces * 1/2 = 0.25 ounces/cube Tiny cubes used: 12 cubes * 0.25 ounces/cube = 3 ounces Total water used: 120 ounces + 60 ounces + 7 ounces + 3 ounces = 190 ounces Water left: 312 ounces - 190 ounces = 122 ounces Final Answer: \boxed{122}

Overall Quality: excellent

The reasoning chain correctly calculates the water usage for each cube size, determines the number of tiny cubes, calculates the water used by tiny cubes, sums the total water used, and finds the remaining water. All arithmetic operations are correct, and the logic follows the problem statement accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #99

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**Reformatted Question:** Tariq is selling brownies and apricot pies for a fundraiser. On Thursday, he sold 25 boxes of brownie and 12 fewer boxes of apricot pie, than on Friday. On Friday, he sold 14 more boxes of brownies than on Thursday and 24 boxes of apricot pie. On Saturday, he sold as much as he did in the past two days combined. If the brownie cost ₣9 and the apricot pie cost ₣20, what was Tariq's average daily earning? **Answer:** * **Thursday's sales:** * Brownies: 25 boxes * Apricot pies: 24 boxes - 12 boxes = 12 boxes * **Friday's sales:** * Brownies: 25 boxes + 14 boxes = 39 boxes * Apricot pies: 24 boxes * **Saturday's sales:** * Brownies: 25 boxes + 39 boxes = 64 boxes * Apricot pies: 12 boxes + 24 boxes = 36 boxes * **Thursday's earnings:** * Brownies: 25 boxes * ₣9/box = ₣225 * Apricot pies: 12 boxes * ₣20/box = ₣240 * Total: ₣225 + ₣240 = ₣465 * **Friday's earnings:** * Brownies: 39 boxes * ₣9/box = ₣351 * Apricot pies: 24 boxes * ₣20/box = ₣480 * Total: ₣351 + ₣480 = ₣831 * **Saturday's earnings:** * Brownies: 64 boxes * ₣9/box = ₣576 * Apricot pies: 36 boxes * ₣20/box = ₣720 * Total: ₣576 + ₣720 = ₣1296 * **Total earnings over three days:** ₣465 + ₣831 + ₣1296 = ₣2592 * **Average daily earnings:** ₣2592 / 3 days = ₣864 Final Answer: \boxed{864}

Overall Quality: excellent

The reasoning chain correctly interprets the problem statement and performs all calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #69

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**Reformatted Question:** Viktor wants to make different sized ice cubes with 313 ounces of water. He can make giant cubes that use 12 ounces per cube, medium cubes that use 4 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 50 total ice cubes, including 12 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does Viktor have left? **Answer:** * **Giant cubes:** Viktor uses 12 ounces/cube * 12 cubes = 144 ounces of water for giant cubes. * **Medium cubes:** He uses 4 ounces/cube * 12 cubes = 48 ounces of water for medium cubes. * **Small cubes:** He uses 0.5 ounces/cube * 14 cubes = 7 ounces of water for small cubes. * **Tiny cubes:** Since he makes 50 cubes total, and has already made 12 + 12 + 14 = 38 cubes, he must make 50 - 38 = 12 tiny cubes. Tiny cubes use 0.5 / 2 = 0.25 ounces/cube. He uses 0.25 ounces/cube * 12 cubes = 3 ounces for tiny cubes. * **Total water used:** 144 + 48 + 7 + 3 = 202 ounces. * **Water remaining:** Viktor started with 313 ounces and used 202 ounces, leaving him with 313 - 202 = 111 ounces. Final Answer: \boxed{111}

Overall Quality: excellent

The reasoning chain correctly calculates the water usage for each cube size based on the provided quantities and water usage rates, correctly determines the number of tiny cubes based on the total cube constraint, and accurately calculates the remaining water. The final answer matches the ground truth.

✓ No hallucinations detected

Question #71

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Generated Answer

Reformatted Question: Oliver wants to make different sized ice cubes with 326 ounces of water. He can make giant cubes that use 14 ounces per cube, medium cubes that use 4 ounces, small cubes that use 2/4 of an ounce, and tiny cubes that are half the size of small cubes. He makes 48 total ice cubes, including 10 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does Oliver have left? Answer: First, let's calculate the water used for giant cubes: 10 giant cubes * 14 ounces/cube = 140 ounces. Next, the water used for medium cubes: 12 medium cubes * 4 ounces/cube = 48 ounces. Then, the water used for small cubes: 14 small cubes * 0.5 ounces/cube = 7 ounces. Now we find how many tiny cubes there are: 48 total cubes - 10 giant cubes - 12 medium cubes - 14 small cubes = 12 tiny cubes. Since tiny cubes are half the size of small cubes, they use 0.5 ounces / 2 = 0.25 ounces each. Water used for tiny cubes is 12 tiny cubes * 0.25 ounces/cube = 3 ounces. Total water used is 140 ounces + 48 ounces + 7 ounces + 3 ounces = 198 ounces. Finally, Oliver has 326 ounces - 198 ounces = 128 ounces left. The answer is $\boxed{128}$.

Overall Quality: excellent

The reasoning chain correctly calculates the water used for each cube type, correctly determines the number of tiny cubes, correctly calculates the water used by tiny cubes, and correctly finds the remaining water. All arithmetic operations are correct.

✓ No hallucinations detected

Question #158

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A father eats 5 burritos per day, his wife eats 25 burritos per day, and their daughter eats one-third of the combined number of burritos they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 60% for the first half of the month, and then by an additional 50% for the second half. How many burritos does this family eat in two months? **Answer:** 1. **Burritos eaten per day by the daughter:** The parents eat a combined total of 5 + 25 = 30 burritos per day. The daughter eats one-third of this, which is (30 * (1/3)) = 10 burritos per day. 2. **Total burritos eaten per day by the family:** The family eats a total of 30 + 10 = 40 burritos per day. 3. **Burritos eaten in the first month:** Assuming a 30-day month, the family eats 40 burritos/day * 30 days = 1200 burritos in the first month. 4. **Burritos eaten in the first half of the second month:** They reduce consumption by 60%, so they eat 40% of their usual amount. That's 40 * 0.40 = 16 burritos/day. For half the month (15 days), they eat 16 * 15 = 240 burritos. 5. **Burritos eaten in the second half of the second month:** They further reduce their consumption by 50% from the reduced amount. So, they eat 50% of 16 burritos/day, which is 16 * 0.50 = 8 burritos/day. For the remaining half of the month (15 days), they eat 8 * 15 = 120 burritos. 6. **Total burritos eaten in the second month:** In the second month, they ate a total of 240 + 120 = 360 burritos. 7. **Total burritos eaten in two months:** Over two months, the family eats 1200 + 360 = 1560 burritos. Final Answer: \boxed{1560}

Overall Quality: excellent

The reasoning chain correctly calculates the consumption for the first month and accurately models the two-stage reduction in consumption for the second month, leading to the correct final total.

✓ No hallucinations detected

Question #192

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mrs. Smith is looking for a new house that will not go beyond her $410000 budget. She saw a property that has a selling price of $500000. On top of that, the buyer has to pay a brokerage fee which is 7% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Smith can get 20% discount on the selling price, how much more will be the total cost than Mrs. Smith's budget? **Answer:** 1. **Discounted Price:** Mrs. Smith gets a 20% discount on the $500,000 selling price. So, the discount amount is 500000 * 0.20 = $100,000. The discounted price is then 500000 - 100000 = $400,000. 2. **Brokerage Fee:** The brokerage fee is 7% of the discounted price ($400,000). 400000 * 0.07 = $28,000. 3. **Transfer Fee:** The transfer fee is 12% of the discounted price ($400,000). 400000 * 0.12 = $48,000. 4. **Total Cost:** The total cost of the house is the discounted price plus the brokerage fee plus the transfer fee: 400000 + 28000 + 48000 = $476,000. 5. **Amount Over Budget:** Mrs. Smith's budget is $410,000. The total cost (476000) exceeds her budget by 476000 - 410000 = $66,000. Final Answer: The final answer is $\boxed{66000}$

Overall Quality: excellent

The reasoning chain correctly calculates the discounted price, brokerage fee, transfer fee, total cost, and the difference from the budget. All arithmetic operations are correct, and the logic follows the problem statement accurately.

✓ No hallucinations detected

Question #197

Clean

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Mrs. Smith is looking for a new house that will not go beyond her $310000 budget. She saw a property that has a selling price of $400000. On top of that, the buyer has to pay a brokerage fee which is 5% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Smith can get a 10% discount on the selling price, how much more will be the total cost than Mrs. Smith's budget? **Answer:** 1. **Discounted selling price:** Mrs. Smith gets a 10% discount on the $400,000 selling price. The discount amount is 0.10 * $400,000 = $40,000. So, the discounted price is $400,000 - $40,000 = $360,000. 2. **Brokerage fee:** The brokerage fee is 5% of the discounted selling price ($360,000). So, the brokerage fee is 0.05 * $360,000 = $18,000. 3. **Transfer fee:** The transfer fee is 12% of the discounted selling price ($360,000). So, the transfer fee is 0.12 * $360,000 = $43,200. 4. **Total cost:** The total cost of the house is the discounted selling price + brokerage fee + transfer fee = $360,000 + $18,000 + $43,200 = $421,200. 5. **Amount over budget:** The total cost ($421,200) exceeds Mrs. Smith's $310,000 budget by $421,200 - $310,000 = $111,200. Final Answer: The final answer is $\boxed{111200}$

Overall Quality: excellent

The reasoning chain correctly calculates the discounted price, the brokerage fee, the transfer fee based on the discounted price, the total cost, and the difference from the budget. All arithmetic operations are correct.

✓ No hallucinations detected

Question #195

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mrs. Smith is looking for a new house that will not go beyond her $410000 budget. She saw a property that has a selling price of $480000. On top of that, the buyer has to pay a brokerage fee which is 3% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Smith can get a 5% discount on the selling price, how much more will be the total cost than Mrs. Smith's budget? **Answer:** 1. **Discounted selling price:** $480000 * (1 - 0.05) = $456000 2. **Brokerage fee:** $456000 * 0.03 = $13680 3. **Transfer fee:** $456000 * 0.012 = $54720 4. **Total cost:** $456000 + $13680 + $54720 = $524400 5. **Amount over budget:** $524400 - $410000 = $114400 The total cost is $114400 more than Mrs. Smith's budget. Final Answer: The final answer is $\boxed{114400}$

Overall Quality: fair

The reasoning correctly identifies the steps required (discount, fees, total, comparison). However, there is a calculation error in step 3 where 12% (0.12) was incorrectly entered as 0.012 (1.2%). Interestingly, the resulting value $54720 happens to be the correct value for 12% of $456000 ($456000 * 0.12 = $54720). This means the error in the multiplier (0.012 instead of 0.12) was compensated by an error in the expected result, leading to the correct numerical value for that step, but the calculation shown is mathematically incorrect based on the multiplier used. Since the ground truth calculation also uses 12/100 = 0.12, and the model used 0.012, this is a calculation error in the representation, even though the resulting number matches the correct result derived from the problem statement (12%). Given the strict instruction to check arithmetic correctness, using 0.012 for 12% is an arithmetic error in the representation of the percentage.

Detected Issues (1)

calculation_error high

Statement

Transfer fee: $456000 * 0.012 = $54720

Explanation

The transfer fee is stated as 12% of the selling price (which is 12% of the discounted price, $456000, as calculated). 12% is 0.12, not 0.012. The calculation used 1.2% instead of 12%.

Answer Span:

$456000 * 0.012 = $54720

Reference/Question Span:

the transfer fee that is 12% of the selling price

Question #196

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mrs. Lee is looking for a new townhouse that will not go beyond her $330000 budget. She saw a property that has a selling price of $440000. On top of that, the buyer has to pay a brokerage fee which is 5% of the selling price, and also the transfer fee that is 12% of the selling price. If Mrs. Lee can get 25% discount on the selling price, how much more will be the total cost than Mrs. Lee's budget? **Answer:** 1. **Discounted price:** Mrs. Lee gets a 25% discount on the $440000 selling price. So, the discount amount is 0.25 * $440000 = $110000. The discounted price is $440000 - $110000 = $330000. 2. **Brokerage fee:** The brokerage fee is 5% of the selling price. Since the discounted selling price is now $330000, the brokerage fee is 0.05 * $330000 = $16500. 3. **Transfer fee:** The transfer fee is 12% of the selling price, which is now $330000. So, the transfer fee is 0.12 * $330000 = $39600. 4. **Total cost:** The total cost of the townhouse for Mrs. Lee is the discounted price + brokerage fee + transfer fee, which is $330000 + $16500 + $39600 = $386100. 5. **Amount over budget:** Mrs. Lee's budget is $330000. The total cost is $386100. The amount over budget is $386100 - $330000 = $56100. Final Answer: The final answer is $\boxed{56100}$

Overall Quality: excellent

The reasoning chain correctly calculates the discounted price, brokerage fee, and transfer fee based on the discounted price, sums them to find the total cost, and correctly determines the difference from the budget. All arithmetic operations are correct.

✓ No hallucinations detected

Question #98

Clean

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Generated Answer

**Reformatted Question:** Umar is selling muffins and apricot pies for a fundraiser. On Thursday, he sold 28 boxes of muffin and 13 fewer boxes of apricot pie, than on Friday. On Friday, he sold 13 more boxes of muffins than on Thursday and 21 boxes of apricot pie. On Saturday, he sold as much as he did in the past two days combined. If the muffin cost $11 and the apricot pie cost $30, what was Umar's average daily earning? **Answer:** * **Thursday's Apricot Pie Sales:** Umar sold 21 - 13 = 8 boxes of apricot pie on Thursday. * **Thursday's Earnings:** 28 muffins * $11/muffin + 8 apricot pies * $30/pie = $308 + $240 = $548. * **Friday's Muffin Sales:** Umar sold 28 + 13 = 41 boxes of muffins on Friday. * **Friday's Earnings:** 41 muffins * $11/muffin + 21 apricot pies * $30/pie = $451 + $630 = $1081. * **Saturday's Sales:** Umar sold the same amount as Thursday and Friday combined, so he sold 28 + 41 = 69 muffins and 8 + 21 = 29 apricot pies. * **Saturday's Earnings:** 69 muffins * $11/muffin + 29 apricot pies * $30/pie = $759 + $870 = $1629. * **Total Earnings:** Over the three days, Umar earned $548 + $1081 + $1629 = $3258. * **Average Daily Earnings:** $3258 / 3 days = $1086. Final Answer: $\boxed{1086}$

Overall Quality: excellent

The reasoning chain correctly interprets the problem constraints and performs all arithmetic calculations accurately, leading to the correct final answer.

✓ No hallucinations detected

Question #156

Clean

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Generated Answer

**Reformatted Question:** An uncle eats 16 pizzas per day, his spouse eats 16 pizzas per day, and their grandchild eats one-half of the combined number of pizzas they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 25% for the first half of the month, and then by an additional 50% for the second half. How many pizzas does this family eat in two months? **Answer:** First, we calculate the grandchild's daily pizza consumption: (16 + 16) / 2 = 16 pizzas. The family's total daily pizza consumption is: 16 + 16 + 16 = 48 pizzas. Assuming a 30-day month, the family consumes 48 pizzas/day * 30 days = 1440 pizzas in the first month (one month). In the first half of the second month (first half of the month), they reduce consumption by 25%. This means they eat 100% - 25% = 75% of their usual amount. So they eat 0.75 * 48 pizzas/day = 36 pizzas/day. Over 15 days, this amounts to 36 pizzas/day * 15 days = 540 pizzas. In the second half of the second month (second half), they further reduce their intake by 50% from the reduced amount. They now eat 50% of 36 pizzas/day = 18 pizzas/day. This means they eat 18 pizzas/day * 15 days = 270 pizzas in the second half of the month. The total pizza consumption in the second month is 540 + 270 = 810 pizzas. Finally, the total pizza consumption for two months is 1440 + 810 = 2250 pizzas. Final Answer: \boxed{2250}

Overall Quality: excellent

The reasoning chain correctly interprets the problem steps and performs all calculations accurately based on the assumptions made (30-day month, 15 days for each half of the second month). The final answer matches the ground truth.

✓ No hallucinations detected

Question #193

Clean

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Dr. Patel is looking for a new condo that will not go beyond her $390000 budget. She saw a property that has a selling price of $560000. On top of that, the buyer has to pay a brokerage fee which is 7% of the selling price, and also the transfer fee that is 14% of the selling price. If Dr. Patel can get 25% discount on the selling price, how much more will be the total cost than Dr. Patel's budget? **Answer:** 1. **Discounted selling price:** $560000 * (1 - 0.25) = $420000 2. **Brokerage fee:** $420000 * 0.07 = $29400 3. **Transfer fee:** $420000 * 0.14 = $58800 4. **Total cost:** $420000 + $29400 + $58800 = $508200 5. **Amount over budget:** $508200 - $390000 = $118200 The answer is $\boxed{118200}$.

Overall Quality: excellent

The reasoning chain correctly applies the discount, calculates the fees based on the discounted price, sums the total cost, and finds the difference from the budget. All arithmetic operations are correct.

✓ No hallucinations detected

Question #215

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ibrahim is raising money for a 2-day conference. Each day costs $200 for hotel, $30 for food, and $30 for transportation. Ibrahim only has $95. His friends have chipped in and will cover the cost of all the food for the conference. Ibrahim has also applied for help from the school, which has decided to cover a quarter of the remaining cost of the conference. How much money is Ibrahim still missing? **Answer:** The total cost for the hotel per day is $200. Since it's a 2-day conference, the total hotel cost is 2 * $200 = $400. The total cost for food per day is $30. For two days, the total food cost would be 2 * $30 = $60. However, Ibrahim’s friends are covering the food cost, so Ibrahim doesn't need to pay for this. The total cost of transportation per day is $30. For a 2-day conference, the total transportation cost is 2 * $30 = $60. So, excluding the food cost (covered by friends), the total cost of the conference for Ibrahim is $400 (hotel) + $60 (transportation) = $460. The school is covering a quarter of the remaining cost, which is (1/4) * $460 = $115. So, after the school's contribution, Ibrahim still needs to pay $460 - $115 = $345. Ibrahim currently has $95. He still needs $345 - $95 = $250. Therefore, Ibrahim is still missing $\boxed{250}$ dollars.

Overall Quality: excellent

The reasoning chain correctly calculates the total cost, accounts for the food cost covered by friends, calculates the school's contribution (1/4 of the remaining cost), subtracts the school's contribution, and finally subtracts the money Ibrahim already has to find the missing amount. All arithmetic operations are correct.

✓ No hallucinations detected

Question #240

Clean

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Sakura went to the boardwalk for vacation. Her parents gave her €1300 to buy whatever she wanted. At the gift shop, saltwater taffy was on sale for "Buy 16 kgs at €22 per kg, get 4 kgs 1/4 off." She scooped up 22 kgs. She also bought a mixed bag of starfish for €11.0 and 12 keychains that were €20.0 each. Sakura then donated €5 at a charity stand along the way. How much money does Sakura have left? **Answer:** Sakura started with €1300. * **Cost of Taffy:** The first 16 kgs of taffy cost €22/kg * 16 kg = €352. The remaining 22 kg - 16 kg = 6 kg of taffy. Since the discount applies to 4kgs only, the remaining 2kg will be charged with the original price: €22/kg * 2 kg = €44 The discounted 4kgs of taffy were 1/4 off, meaning they cost €22/kg * (1-1/4) * 4 kg = €16.5/kg * 4kg = €66. The total cost of taffy is thus €352+€44 + €66 = €462. * **Cost of Starfish:** Sakura spent €11.0 on starfish. * **Cost of Keychains:** Sakura bought 12 keychains at €20.0 each, costing 12 * €20.0 = €240. * **Charity Donation:** Sakura donated €5. * **Total Spending:** €462 (taffy) + €11 (starfish) + €240 (keychains) + €5 (donation) = €718. * **Money Left:** Sakura started with €1300 and spent €718, leaving her with €1300 - €718 = \boxed{€582}.

Overall Quality: excellent

The reasoning chain correctly interprets the complex taffy pricing structure (16kg full price + 4kg discounted + 2kg full price to reach 22kg total) and performs all subsequent arithmetic operations accurately, leading to the correct final result.

✓ No hallucinations detected

Question #66

Clean

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Luca wants to make different sized ice cubes with 337 ounces of water. He can make giant cubes that use 14 ounces per cube, medium cubes that use 3 ounces, small cubes that use 1/2 of a ounce, and tiny cubes that are half the size of small cubes. He makes 47 total ice cubes, including 9 giant cubes, 14 small cubes, 12 medium cubes, and some tiny cubes. How many ounces of water does Luca have left? **Answer:** First, let's calculate the water used for the giant cubes: 9 giant cubes * 14 ounces/cube = 126 ounces. Next, the water used for the medium cubes: 12 medium cubes * 3 ounces/cube = 36 ounces. Then, the water used for the small cubes: 14 small cubes * 0.5 ounces/cube = 7 ounces. Now, let's figure out how many tiny cubes there are. He made a total of 47 ice cubes, and we know the number of all the other types: 47 total - 9 giant - 12 medium - 14 small = 12 tiny cubes. Since tiny cubes are half the size of small cubes, they use 0.5 ounces / 2 = 0.25 ounces/cube. The water used for tiny cubes is: 12 tiny cubes * 0.25 ounces/cube = 3 ounces. The total water used is 126 ounces + 36 ounces + 7 ounces + 3 ounces = 172 ounces. Finally, Luca started with 337 ounces and used 172 ounces, so he has 337 - 172 = 165 ounces left. The answer is $\boxed{165}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all constraints provided in the problem description. All calculations are correct, and the final answer matches the ground truth.

✓ No hallucinations detected

Question #68

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Noah wants to make different sized ice cubes with 336 ounces of water. He can make giant cubes that use 15 ounces per cube, medium cubes that use 4 ounces, small cubes that use 1/2 of an ounce, and tiny cubes that are half the size of small cubes. He makes 49 total ice cubes, including 8 giant cubes, 14 small cubes, 15 medium cubes, and some tiny cubes. How many ounces of water does Noah have left? **Answer:** 1. **Giant cubes:** Noah makes 8 giant cubes that use 15 ounces of water per cube. This uses 8 * 15 = 120 ounces. 2. **Medium cubes:** He makes 15 medium cubes that use 4 ounces per cube. This uses 15 * 4 = 60 ounces. 3. **Small cubes:** He makes 14 small cubes that use 1/2 an ounce per cube. This uses 14 * 0.5 = 7 ounces. 4. **Tiny cubes:** He makes 49 cubes in total. Subtracting the other cubes, there are 49 - 8 - 15 - 14 = 12 tiny cubes. Since tiny cubes are half the size of small cubes, they use 0.5 / 2 = 0.25 ounces per cube. This uses 12 * 0.25 = 3 ounces. 5. **Total water used:** The total water used is 120 + 60 + 7 + 3 = 190 ounces. 6. **Water remaining:** Noah started with 336 ounces and used 190 ounces. He has 336 - 190 = 146 ounces left. Final Answer: The final answer is $\boxed{146}$

Overall Quality: excellent

The reasoning chain correctly calculates the number of tiny cubes, the water used by each type of cube, the total water used, and the remaining water. All arithmetic operations are correct, and the logic follows the problem statement accurately.

✓ No hallucinations detected

Question #244

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ava went to the coast for vacation. Her parents gave her $1400 to buy whatever she wanted. At the seaside store, cotton candy was on sale for "Buy 17 pounds at $22 per pound, get 4 pounds 1/2 off." She scooped up 23 pounds. She also bought a mixed bag of coral pieces for $11.0 and 18 pins that were $20.5 each. Ava then donated $5 at a charity stand along the way. How much money does Ava have left? **Answer:** Ava started with $1400. For the cotton candy, she bought 17 pounds at the full price of $22 per pound, costing 17 * $22 = $374. She bought an additional 23 - 17 = 6 pounds. Since the deal is 4 pounds for half off, the first 4 of these additional pounds cost 4 * ($22 / 2) = $44. The remaining 6 - 4 = 2 pounds cost 2 * $22 = $44. The total cost of the cotton candy is $374 + $44 + $44 = $462. The 18 pins cost 18 * $20.5 = $369. The coral cost $11.00. Her total spending is $462 (cotton candy) + $369 (pins) + $11 (coral) + $5 (donation) = $847. The money Ava has left is her starting amount minus her total spending: $1400 - $847 = $\boxed{553}$.

Overall Quality: unknown

Failed to parse: Invalid \escape: line 12 column 2528 (char 3293)

✓ No hallucinations detected

Question #287

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Olga initially had 8 dozen pancakes, then ate 5 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Gabrielle finds 3 pancakes. Jasmine finds four times as many as Gabrielle. Tariq finds 2 less than Jasmine. Ravi finds 1/5 as many as Tariq, and Alejandro finds two dozen pancakes more than Jasmine and Gabrielle combined. How many pancakes are still hidden in the yard? **Answer:** Olga started with 8 dozen pancakes, which is 8 * 12 = 96 pancakes. She ate 5, leaving 96 - 5 = 91 pancakes. Gabrielle found 3. Jasmine found 4 times as many as Gabrielle, so Jasmine found 4 * 3 = 12 pancakes. Tariq found 2 less than Jasmine, so Tariq found 12 - 2 = 10 pancakes. Ravi found 1/5 as many as Tariq, so Ravi found (1/5) * 10 = 2 pancakes. Alejandro found two dozen more than Jasmine and Gabrielle combined. Jasmine and Gabrielle found 12 + 3 = 15 pancakes. Two dozen is 2 * 12 = 24, so Alejandro found 15 + 24 = 39 pancakes. The total number of pancakes found is 3 + 12 + 10 + 2 + 39 = 66 pancakes. Since Olga hid 91 pancakes and 66 were found, there are 91 - 66 = $\boxed{25}$ pancakes still hidden.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations are accurate.

✓ No hallucinations detected

Question #100

2 issues

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ali is selling muffins and orange pies for a fundraiser. On Tuesday, he sold 22 boxes of muffin and 13 fewer boxes of orange pie, than on Wednesday. On Wednesday, he sold 13 more boxes of muffins than on Tuesday and 23 boxes of orange pie. On Thursday, he sold as much as he did in the past two days combined. If the muffin cost €9 and the orange pie cost €32, what was Ali's average daily earning? **Answer:** * **Muffins sold on Tuesday:** 22 boxes * **Orange pies sold on Tuesday:** 23 boxes (Wednesday) - 13 boxes = 10 boxes * **Muffins sold on Wednesday:** 22 boxes + 13 boxes = 35 boxes * **Orange pies sold on Wednesday:** 23 boxes * **Muffins sold on Thursday:** 22 boxes + 35 boxes = 57 boxes * **Orange pies sold on Thursday:** 10 boxes + 23 boxes = 33 boxes * **Tuesday's earnings:** (22 boxes * €9/box) + (10 boxes * €32/box) = €518 * **Wednesday's earnings:** (35 boxes * €9/box) + (23 boxes * €32/box) = €1041 * **Thursday's earnings:** (57 boxes * €9/box) + (33 boxes * €32/box) = €1557 * **Total earnings:** €518 + €1041 + €1557 = €3116 * **Average daily earning:** €3116 / 3 days = €1038.67 (approximately) Final Answer: \boxed{1038.67}

Overall Quality: fair

The AI correctly derived the quantities sold for Tuesday, Wednesday, and Thursday based on one plausible interpretation of the ambiguous Thursday sales instruction. However, it made two distinct calculation errors when determining Wednesday's and Thursday's total earnings.

Detected Issues (2)

calculation_error medium

Statement

* **Wednesday's earnings:** (35 boxes * €9/box) + (23 boxes * €32/box) = €1041

Explanation

The arithmetic calculation for Wednesday's earnings is incorrect. 35*9 + 23*32 = 315 + 736 = 1051.

Answer Span:

€1041

calculation_error medium

Statement

* **Thursday's earnings:** (57 boxes * €9/box) + (33 boxes * €32/box) = €1557

Explanation

The arithmetic calculation for Thursday's earnings is incorrect. 57*9 + 33*32 = 513 + 1056 = 1569.

Answer Span:

€1557

Question #160

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A father eats 20 pizzas per day, his wife eats 5 pizzas per day, and their daughter eats one-fifth of the combined number of pizzas they eat per day. After one month, the family decides to go on a diet in the second month, reducing their food consumption by 20% for the first half of the month, and then by an additional 75% for the second half. How many pizzas does this family eat in two months? **Answer:** First, let's calculate the daughter's daily pizza consumption: The parents eat a combined 20 + 5 = 25 pizzas per day. The daughter eats one-fifth of 25, which is 25 * (1/5) = 5 pizzas per day. The family's total daily pizza consumption is 20 + 5 + 5 = 30 pizzas. In the first month (assume 30 days), they eat 30 pizzas/day * 30 days = 900 pizzas. In the first half of the second month (15 days), their consumption is reduced by 20%. So, they eat 30 pizzas/day * (1 - 0.20) = 24 pizzas/day. Over those 15 days, they eat 24 pizzas/day * 15 days = 360 pizzas. In the second half of the second month (15 days), consumption is reduced by an additional 75% from the already reduced amount. So, they eat 24 pizzas/day * (1 - 0.75) = 6 pizzas/day. Over those 15 days, they eat 6 pizzas/day * 15 days = 90 pizzas. The total pizza consumption over two months is 900 + 360 + 90 = 1350 pizzas. Final Answer: \boxed{1350}

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description. All calculations are correct.

✓ No hallucinations detected

Question #210

Clean

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Ground Truth Answer

Generated Answer

**Reformatted Question:** Thiago is raising money for a 3-day science fair. Each day costs $250 for hotel, $30 for food, and $30 for transportation. Thiago only has $35. His friends have chipped in and will cover the cost of all the food for the science fair. Thiago has also applied for help from the school, which has decided to cover 1/4 of the remaining cost of the science fair. How much money is Thiago still missing? **Answer:** The total cost per day is the sum of hotel, food, and transportation: $250 + $30 + $30 = $250+$30+$30=$310. Since the science fair lasts for 3 days, the total cost is: 3 * $310 = $930. Thiago's friends are covering the food cost, which is $30 per day for 3 days: 3 * $30 = $90. Subtracting the food cost from the total cost gives the remaining cost: $930 - $90 = $840. The school is covering 1/4 of the remaining cost: 1/4 * $840 = $210. Subtracting the school's contribution from the remaining cost gives the amount Thiago still needs to cover: $840 - $210 = $630. Since Thiago already has $35, the amount he is still missing is: $630 - $35 = $595. Final Answer: The final answer is $\boxed{595}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem constraints correctly. All calculations are accurate.

✓ No hallucinations detected

Question #242

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Chen went to the boardwalk for vacation. Her parents gave her $1300 to buy whatever she wanted. At the gift shop, saltwater taffy was on sale for "Buy 16 kgs at $22 per kg, get 6 kgs 1/4 off." She scooped up 23 kgs. She also bought a mixed bag of starfish for $11.0 and 11 keychains that were $21.0 each. Chen then donated $5 at a charity stand along the way. How much money does Chen have left? **Answer:** Chen bought 23 kgs of taffy. The first 16 kgs cost $22 per kg, so that's 16 * $22 = $352. The remaining 23 - 16 = 7 kgs were 1/4 off, so each kg cost $22 * (1 - 1/4) = $22 * (3/4) = $16.50. The cost of these 7 kgs is 7 * $16.50 = $115.50. The total cost of the taffy is $352 + $115.50 = $467.50. The cost of the 11 keychains at $21 each is 11 * $21 = $231. The total cost of everything Chen bought is $467.50 (taffy) + $11.00 (starfish) + $231 (keychains) + $5 (donation) = $714.50. Chen started with $1300 and spent $714.50, so she has $1300 - $714.50 = $585.50 left. The answer is $\boxed{585.50}$.

Overall Quality: poor

The AI performed all arithmetic correctly based on its chosen (but flawed) interpretation of the discount structure. However, it logically misinterpreted the quantity eligible for the discount specified in the problem statement, leading to an incorrect final result.

✓ No hallucinations detected

Question #243

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Fatima went to the pier for vacation. Her parents gave her ₣1200 to buy whatever she wanted. At the beach shop, rock candy was on sale for "Buy 16 kgs at ₣20 per kg, get 6 kgs 1/3 off." She scooped up 23 kgs. She also bought a mixed bag of sea glass for ₣11.0 and 13 stickers that were ₣20.0 each. Fatima then donated ₣5 at a charity stand along the way. How much money does Fatima have left? **Answer:** * **Cost of the first 16 kg of rock candy:** 16 kg * ₣20/kg = ₣320 * **Cost of the remaining 7 kg of rock candy (23 kg - 16 kg = 7 kg, but only 6 kg are discounted):** 6 kg * (₣20/kg * (2/3)) = ₣80 * **Cost of the last 1 kg of rock candy:** 1 kg * ₣20/kg = ₣20 * **Total cost of rock candy:** ₣320 + ₣80 + ₣20 = ₣420 * **Cost of stickers:** 13 stickers * ₣20/sticker = ₣260 * **Total cost of purchases (before donation):** ₣420 + ₣11 + ₣260 = ₣691 * **Money left after purchases and donation:** ₣1200 - ₣691 - ₣5 = ₣504 Fatima has \boxed{504} ₣ left.

Overall Quality: excellent

The reasoning chain correctly calculates the cost of all items based on the complex pricing structure and accurately determines the remaining money. All arithmetic operations are correct.

✓ No hallucinations detected

Question #283

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ali initially had 11 dozen cookies, then ate 3 cookies for breakfast, and then hid the rest in the yard for the Easter egg hunt. Faisal finds 5 cookies. Hiroshi finds thrice as many as Faisal. Benjamin finds 3 less than Hiroshi. Wei finds a quarter as many as Benjamin, and Quinn finds three dozen cookies more than Hiroshi and Faisal combined. How many cookies are still hidden in the yard? **Answer:** 1. Ali starts with 11 dozen cookies, which is 11 * 12 = 132 cookies. 2. Ali eats 3 cookies, leaving 132 - 3 = 129 cookies. 3. These 129 cookies are hidden. 4. Faisal finds 5 cookies. 5. Hiroshi finds thrice as many as Faisal, so Hiroshi finds 5 * 3 = 15 cookies. 6. Benjamin finds 3 less than Hiroshi, so Benjamin finds 15 - 3 = 12 cookies. 7. Wei finds a quarter as many as Benjamin, so Wei finds 12 / 4 = 3 cookies. 8. Quinn finds three dozen cookies more than Hiroshi and Faisal combined. Hiroshi and Faisal found 15 + 5 = 20 cookies. Three dozen is 3 * 12 = 36 cookies. So Quinn finds 20 + 36 = 56 cookies. 9. The total number of cookies found is 5 + 15 + 12 + 3 + 56 = 91 cookies. 10. The number of cookies still hidden is 129 (initial hidden cookies) - 91 (found cookies) = 38 cookies. Final Answer: \boxed{38}

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly at every step. All calculations are accurate.

✓ No hallucinations detected

Question #96

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Wei is selling cupcakes and plum pies for a fundraiser. On Monday, he sold 28 boxes of cupcake and 19 fewer boxes of plum pie, than on Tuesday. On Tuesday, he sold 14 more boxes of cupcakes than on Monday and 27 boxes of plum pie. On Wednesday, he sold as much as he did in the past two days combined. If the cupcake cost $11 and the plum pie cost $23, what was Wei's average daily earning? **Answer:** * **Monday's sales:** * Cupcakes: 28 boxes * Plum pies: 27 boxes - 19 boxes = 8 boxes * **Tuesday's sales:** * Cupcakes: 28 boxes + 14 boxes = 42 boxes * Plum pies: 27 boxes * **Wednesday's sales:** * Cupcakes: 28 boxes + 42 boxes = 70 boxes * Plum pies: 8 boxes + 27 boxes = 35 boxes * **Monday's earnings:** * (28 boxes * $11/box) + (8 boxes * $23/box) = $308 + $184 = $492 * **Tuesday's earnings:** * (42 boxes * $11/box) + (27 boxes * $23/box) = $462 + $621 = $1083 * **Wednesday's earnings:** * (70 boxes * $11/box) + (35 boxes * $23/box) = $770 + $805 = $1575 * **Total earnings:** * $492 + $1083 + $1575 = $3150 * **Average daily earnings:** * $3150 / 3 days = $1050/day Final Answer: $\boxed{1050}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows a consistent interpretation of the ambiguous instruction regarding Wednesday's sales, leading to the correct final answer.

✓ No hallucinations detected

Question #120

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Diego picks 67 pineapples on Wednesday. Then he picks 176 pineapples on Thursday. On Friday, he picks quintuple the number of pineapples he did on Wednesday. On Saturday, he picks half the amount of what he picked in the past 3 days combined. On Sunday, Diego is going to sell pineapples in boxes of 17 pineapples each. He is going to sell each box for $12. How much is Diego going to make? **Answer:** On Wednesday, Diego picked 67 pineapples. On Thursday, Diego picked 176 pineapples. On Friday, Diego picked 67 * 5 = 335 pineapples. The total number of pineapples picked from Wednesday to Friday is 67 + 176 + 335 = 578 pineapples. On Saturday, Diego picked 578 * 1/2 = 289 pineapples. The total number of pineapples Diego picked from Wednesday to Saturday is 578 + 289 = 867 pineapples. Diego can make 867 / 17 = 51 boxes of pineapples. Diego will make 51 * $12 = $612. The answer is $\boxed{612}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #241

2 issues

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Kayla went to the pier for vacation. Her parents gave her ₺1400 to buy whatever she wanted. At the beach shop, rock candy was on sale for "Buy 16 kgs at ₺22 per kg, get 6 kgs 2/3 off." She scooped up 23 kgs. She also bought a mixed bag of sea glass for ₺11.0 and 14 stickers that were ₺20.5 each. Kayla then donated ₺5 at a charity stand along the way. How much money does Kayla have left? **Answer:** * **Rock Candy Cost:** * Cost for the first 16 kgs: 16 kgs * ₺22/kg = ₺352 * Discount for the remaining 7 kgs (since she bought 23 kgs - 23 and 16 + 6 is 22 and not 23. So we use the discount price on only (23-16)=7 instead of 6): (2/3) * ₺22/kg ≈ ₺14.67/kg * Cost for the remaining 7 kgs: 7 kgs * ₺14.67/kg ≈ ₺102.69 * Total cost of rock candy: ₺352 + ₺102.69 ≈ ₺454.69 * **Stickers Cost:** * Total cost of stickers: 14 stickers * ₺20.5/sticker = ₺287 * **Total Spending:** * Total spent: ₺454.69 (rock candy) + ₺11.0 (sea glass) + ₺287 (stickers) + ₺5 (donation) ≈ ₺757.69 * **Money Left:** * Money Kayla has left: ₺1400 (starting amount) - ₺757.69 (total spent) ≈ ₺642.31 Final Answer: \boxed{642.31}

Overall Quality: poor

The reasoning chain contains significant logical errors in interpreting the rock candy discount structure (applying discount to 7 kgs instead of 6 kgs) and calculation errors in determining the discounted price (using the discount amount instead of the remaining price). This leads to an incorrect final result.

Detected Issues (2)

calculation_error high

Statement

(2/3) * ₺22/kg ≈ ⇦14.67/kg

Explanation

If the price is 2/3 off, the remaining price is 1/3 of the original price. The AI calculated the amount of the discount (2/3 * 22) and used it as the new price. The correct price paid should be (1/3) * 22 ≈ 7.33.

Answer Span:

(2/3) * ⇦22/kg ≈ ⇦14.67/kg

calculation_error medium

Statement

Cost for the remaining 7 kgs: 7 kgs * ⇦14.67/kg ≈ ⇦102.69

Explanation

This calculation is based on the incorrect discounted price derived in the previous step. If we follow the logic implied by the Ground Truth (6 kgs discounted at 1/3 price), the cost for the discounted 6 kgs would be 6 * (1/3 * 22) = 44. The remaining 1 kg would be full price (22). Total discounted portion cost should be 44 + 22 = 66 (if 6 kgs discounted and 1 kg full price), or 7 * (1/3 * 22) = 7 * 7.33 = 51.31 (if 7 kgs were discounted at 1/3 price). Since the AI used 7 kgs and the wrong price, the resulting cost is incorrect.

Answer Span:

7 kgs * ⇦14.67/kg ≈ ⇦102.69

Question #213

1 issue

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Leon is raising money for a 2-day workshop. Each day costs ¥150 for hotel, ¥30 for food, and ¥10 for transportation. Leon only has ¥155. His friends have chipped in and will cover the cost of all the food for the workshop. Leon has also applied for help from the youth club, which has decided to cover a fifth of the remaining cost of the workshop. How much money is Leon still missing? Answer: The total cost for the hotel per day is ¥150. Since the workshop is 2 days long, the total hotel cost is ¥150 * 2 = ¥300. The total cost for food per day is ¥30. For 2 days, the total food cost would have been ¥30 * 2 = ¥60. However, since his friends are covering the food cost , Leon doesn't need to pay for food. The total cost for transportation per day is ¥10. For 2 days, the total transportation cost is ¥10 * 2 = ¥20. The total cost of the workshop for Leon (excluding food, which his friends are paying) is the cost of the hotel plus the cost of transportation : ¥300 + ¥20 = ¥320. Leon currently has ¥155. The remaining cost of the workshop after Leon uses his own money is - = ¥320 - ¥155 = ¥165. The youth club is covering one-fifth of this remaining cost, which is * (1/5) = ¥165 * (1/5) = ¥33. The cost Leon still needs to cover is the remaining cost after the youth club's contribution: - = ¥165 - ¥33 = ¥132. Final Answer: The final answer is \boxed{132}

Overall Quality: poor

The reasoning chain contains a critical logical error regarding the sequence of deductions. The model calculates the youth club contribution based on the amount remaining *after* Leon contributes his savings, instead of calculating it based on the total amount due after food is covered.

Detected Issues (1)

logical_error high

Statement

The youth club is covering one-fifth of this remaining cost, which is * (1/5) = ¥165 * (1/5) = ¥33.

Explanation

The youth club is supposed to cover 1/5 of the remaining cost of the workshop (which is ¥320, calculated after food is removed), not 1/5 of the cost remaining after Leon uses his ¥155 (which is ¥165).

Answer Span:

The youth club is covering one-fifth of this remaining cost, which is * (1/5) = ¥165 * (1/5) = ¥33.

Reference/Question Span:

youth club, which has decided to cover a fifth of the remaining cost of the workshop.

Question #284

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Beatriz initially had 10 dozen pancakes, then ate 3 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Kimia finds 6 pancakes. Sophia finds three times as many as Kimia. Mateo finds 2 less than Sophia. Umar finds half as many as Mateo, and Mei finds two dozen pancakes more than Sophia and Kimia combined. How many pancakes are still hidden in the yard? **Answer:** Beatriz started with 10 dozen pancakes, which is 10 * 12 = 120 pancakes. She ate 3, leaving 120 - 3 = 117 pancakes to hide. Kimia found 6 pancakes. Sophia found three times as many as Kimia, which is 3 * 6 = 18 pancakes. Mateo found 2 less than Sophia, which is 18 - 2 = 16 pancakes. Umar found half as many as Mateo, which is 16 / 2 = 8 pancakes. Sophia and Kimia together found 18 + 6 = 24 pancakes. Mei found two dozen more than this, which is 24 + (2 * 12) = 48 pancakes. The total number of pancakes found is 6 + 18 + 16 + 8 + 48 = 96 pancakes. The number of pancakes still hidden is 117 (originally hidden) - 96 (found) = 21 pancakes. The answer is $\boxed{21}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description logically at every step. All calculations are correct.

✓ No hallucinations detected

Question #286

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Kai initially had 7 dozen pancakes, then ate 2 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Nia finds 6 pancakes. Isabella finds two times as many as Nia. Roya finds 4 less than Isabella. Diego finds a quarter as many as Roya, and Yara finds two dozen pancakes more than Isabella and Nia combined. How many pancakes are still hidden in the yard? **Answer:** Kai started with 7 dozen pancakes, which is 7 * 12 = 84 pancakes. He then ate 2 pancakes, leaving 84 - 2 = 82 pancakes. Nia found 6 pancakes. Isabella found twice as many as Nia, so she found 6 * 2 = 12 pancakes. Roya found 4 less than Isabella, so she found 12 - 4 = 8 pancakes. Diego found a quarter as many as Roya, meaning he found 8 / 4 = 2 pancakes. Yara found two dozen pancakes more than Isabella and Nia combined. Isabella and Nia found 12 + 6 = 18 pancakes. Two dozen is 2 * 12 = 24 pancakes. So Yara found 18 + 24 = 42 pancakes. In total, the number of pancakes found is 6 + 12 + 8 + 2 + 42 = 70 pancakes. Since Kai hid 82 pancakes and 70 were found, there are 82 - 70 = 12 pancakes still hidden. The answer is $\boxed{12}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps described in the problem, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #282

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Viktor initially had 9 dozen pancakes, then ate 3 pancakes for breakfast, and then hid the rest in the yard for the Easter egg hunt. Liam finds 5 pancakes. Yusuf finds two times as many as Liam. Pavel finds 4 less than Yusuf. Daphne finds half as many as Pavel, and James finds four dozen pancakes more than Yusuf and Liam combined. How many pancakes are still hidden in the yard? **Answer:** 1. Viktor started with 9 dozen pancakes, which is 9 * 12 = 108 pancakes. 2. After eating 3 pancakes, Viktor had 108 - 3 = 105 pancakes remaining to hide. 3. Liam finds 5 pancakes. 4. Yusuf finds two times as many as Liam, so Yusuf finds 2 * 5 = 10 pancakes. 5. Pavel finds 4 less than Yusuf, so Pavel finds 10 - 4 = 6 pancakes. 6. Daphne finds half as many as Pavel, so Daphne finds 6 / 2 = 3 pancakes. 7. James finds four dozen pancakes more than Yusuf and Liam combined. Yusuf and Liam combined found 10 + 5 = 15 pancakes. Four dozen is 4 * 12 = 48 pancakes. So, James finds 15 + 48 = 63 pancakes. 8. The total number of pancakes found is 5 + 10 + 6 + 3 + 63 = 87 pancakes. 9. The number of pancakes still hidden is 105 (total hidden) - 87 (total found) = $\boxed{18}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly at every step. All calculations match the ground truth.

✓ No hallucinations detected

Question #285

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Zahra initially had 9 dozen waffles, then ate 5 waffles for breakfast, and then hid the rest in the yard for the Easter egg hunt. Viktor finds 5 waffles. Andre finds three times as many as Viktor. Rania finds 3 less than Andre. Uma finds 1/4 as many as Rania, and Arash finds three dozen waffles more than Andre and Viktor combined. How many waffles are still hidden in the yard? **Answer:** 1. Zahra started with 9 dozen waffles, which is 9 * 12 = 108 waffles. 2. After eating 5 waffles, she had 108 - 5 = 103 waffles left to hide. 3. Viktor found 5 waffles. 4. Andre found three times as many as Viktor, so Andre found 3 * 5 = 15 waffles. 5. Rania found 3 less than Andre, so Rania found 15 - 3 = 12 waffles. 6. Uma found 1/4 as many as Rania, so Uma found (1/4) * 12 = 3 waffles. 7. Arash found three dozen waffles more than Andre and Viktor combined. Andre and Viktor found 15 + 5 = 20 waffles combined. Three dozen is 3 * 12 = 36 waffles. So Arash found 20 + 36 = 56 waffles. The total number of waffles found is 5 + 15 + 12 + 3 + 56 = 91 waffles. Therefore, the number of waffles still hidden is 103 - 91 = $\boxed{12}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations are accurate, and the final result matches the ground truth.

✓ No hallucinations detected

Question #124

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Oliver picks 111 oranges on Tuesday. Then he picks 170 oranges on Wednesday. On Thursday, he picks quintuple the number of oranges he did on Tuesday. On Friday, he picks half the amount of what he picked in the past 3 days combined. On Saturday, Oliver is going to sell oranges in boxes of 19 oranges each. He is going to sell each box for $9. How much is Oliver going to make? **Answer:** On Tuesday, Oliver picked 111 oranges. On Wednesday, Oliver picked 170 oranges. On Thursday, Oliver picked 111 * 5 = 555 oranges. The total number of oranges picked from Tuesday to Thursday is 111 + 170 + 555 = 836 oranges. On Friday, Oliver picked 836 * 1/2 = 418 oranges. The total number of oranges picked from Tuesday to Friday is 836 + 418 = 1254 oranges. The number of boxes Oliver can make is 1254 / 19 = 66 boxes. The total amount Oliver will make is 66 * $9 = $594. Final Answer: The final answer is $\boxed{594}$

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement, and all arithmetic calculations are accurate.

✓ No hallucinations detected

Question #39

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Yusuf has 10 square yards of watermelon field. There are 19 watermelons per two-sixths of a square yard. Yusuf can harvest his watermelons every 2 months. In addition, Yusuf owns a 9-square yard grape field that produces 14 grapes per square yard. The grapes can be harvested every 4 months. In the span of two years, how many more watermelons does Yusuf harvest than grapes? **Answer:** First, let's figure out how many watermelons grow per square yard. Since 19 watermelons grow in two-sixths of a square yard, which is the same as one-third (2/6 = 1/3), then 19 * 3 = 57 watermelons grow in a full square yard. Yusuf has 10 square yards of watermelon field, so he can grow 57 * 10 = 570 watermelons in one harvest. Since he can harvest every 2 months, and there are 12 months in a year, he harvests 12 / 2 = 6 times per year. Over two years, he harvests 6 * 2 = 12 times. This means he harvests a total of 570 watermelons * 12 harvests = 6840 watermelons over two years. Now let's calculate the grape production. Yusuf's grape field is 9 square yards, and each square yard produces 14 grapes. So in one harvest, he gets 9 * 14 = 126 grapes. He harvests grapes every 4 months, so he harvests 12 / 4 = 3 times per year. Over two years, he harvests 3 * 2 = 6 times. This means he harvests 126 grapes * 6 harvests = 756 grapes over two years. Finally, the difference in harvested watermelons and grapes is 6840 - 756 = 6084. The answer is $\boxed{6084}$.

Overall Quality: excellent

The reasoning chain correctly calculates the total watermelons and grapes harvested over two years and finds the correct difference. All arithmetic operations and logical steps align with the problem statement and the ground truth.

✓ No hallucinations detected

Question #38

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Mohammed has 35 square meters of grape field. There are 12 grapes per 2/3 of a square meter. Mohammed can harvest his grapes every 6 months. In addition, Mohammed owns a 11-square meter apricot field that produces 18 apricots per square meter. The apricots can be harvested every 4 months. In the span of two years, how many more grapes does Mohammed harvest than apricots? **Answer:** 1. **Grapes per square meter:** Since there are 12 grapes per 2/3 of a square meter, there are 12 / (2/3) = 12 * (3/2) = 18 grapes per square meter. 2. **Total grapes per harvest:** Mohammed has 35 square meters of grape field, so he harvests 18 grapes/square meter * 35 square meters = 630 grapes per harvest. 3. **Number of grape harvests:** In two years (24 months), Mohammed harvests his grapes every 6 months, so he has 24 / 6 = 4 harvests. 4. **Total grapes in two years:** Over two years, Mohammed harvests 630 grapes/harvest * 4 harvests = 2520 grapes. 5. **Apricots per harvest:** Mohammed's apricot field is 11 square meters and produces 18 apricots per square meter, so he harvests 11 * 18 = 198 apricots per harvest. 6. **Number of apricot harvests:** In two years (24 months), Mohammed harvests his apricots every 4 months, so he has 24 / 4 = 6 harvests. 7. **Total apricots in two years:** Over two years, Mohammed harvests 198 apricots/harvest * 6 harvests = 1188 apricots. 8. **Difference:** Mohammed harvests 2520 grapes and 1188 apricots in two years. The difference is 2520 - 1188 = 1332. Final Answer: The final answer is $\boxed{1332}$

Overall Quality: excellent

The reasoning chain correctly calculates the total grapes and apricots harvested over two years based on the provided rates and frequencies, and accurately determines the final difference. All arithmetic operations are correct.

✓ No hallucinations detected

Question #235

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A maintenance worker has to clean a university with 150 floors. They have 6 days to get it done. It takes them 6 minutes per floor. However, due to a recent injury, the maintenance worker has become slower and it will take them twice as long to clean a floor these days. If they work for 10 hours a day, what percentage of their day, on average, is spent cleaning floors? **Answer:** It originally took the worker 6 minutes to clean a floor, but now it takes twice as long, so it now takes 6 * 2 = 12 minutes per floor. With 150 floors to clean, it will take the worker 150 * 12 = 1800 minutes total. Since there are 60 minutes in an hour, this is equal to 1800 / 60 = 30 hours of work. They have 6 days to get the work done, so they will work 30 / 6 = 5 hours per day. They work 10 hours a day, so the percentage of their day spent cleaning is (5 / 10) * 100% = 50%. The answer is $\boxed{50}$.

Overall Quality: excellent

The reasoning chain correctly calculates the time spent cleaning per floor, the total time required, the average time spent per day over the 6 days, and finally determines the correct percentage of the workday spent cleaning. All arithmetic operations are correct.

✓ No hallucinations detected

Question #19

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A class of 230 students has various hobbies. 5 like to dance, 8 like to play chess, 13 like to swim, 32 like to play volleyball, and the rest like to either play video games or play music. What percentage of the students like to play video games if the number of the students that like to play music is 7 less than two times the number that prefer playing volleyball? **Answer:** 1. **Students with other hobbies:** The total number of students with hobbies other than video games or music is 5 + 8 + 13 + 32 = 58. 2. **Students playing music:** The number of students playing music is 2 * 32 - 7 = 57. 3. **Students playing video games or music:** The total number of students in the class is 230. Subtracting the students with other hobbies leaves 230 - 58 = 172 students who play video games or play music. 4. **Students playing video games:** Subtracting the number of students playing music from those playing either video games or music leaves 172 - 57 = 115 students who play video games. 5. **Percentage of students playing video games:** The percentage of students who play video games is (115 / 230) * 100 = 50%. The answer is $\boxed{50}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the problem description. All calculations are correct.

✓ No hallucinations detected

Question #121

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Deshawn picks 142 pears on Saturday. Then he picks 172 pears on Sunday. On Monday, he picks triple the number of pears he did on Saturday. On Tuesday, he picks half the amount of what he picked in the past 3 days combined. On Wednesday, DeShawn is going to sell pears in boxes of 15 pears each. He is going to sell each box for $14. How much is DeShawn going to make? **Answer:** * **Saturday:** Deshawn picked 142 pears. * **Sunday:** Deshawn picked 172 pears. * **Monday:** Deshawn picked 142 * 3 = 426 pears. * **Total for first 3 days:** 142 + 172 + 426 = 740 pears. * **Tuesday:** Deshawn picked 740 / 2 = 370 pears. * **Total Pears:** 740 + 370 = 1110 pears. * **Boxes:** 1110 / 15 = 74 boxes. * **Total Earnings:** 74 * $14 = $1036. Final Answer: $\boxed{1036}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem description correctly. All calculations are accurate.

✓ No hallucinations detected

Question #40

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ravi has 10 square yards of banana field. There are 36 bananas per four-fifths of a square yard. Ravi can harvest his bananas every 4 months. In addition, Ravi owns a 13-square yard apricot field that produces 12 apricots per square yard. The apricots can be harvested every 4 months. In the span of two years, how many more bananas does Ravi harvest than apricots? **Answer:** First, let's figure out how many bananas Ravi harvests per square yard. Since there are 36 bananas per four-fifths of a square yard, there are 36 / (4/5) = 36 * (5/4) = 45 bananas per square yard. Since Ravi has 10 square yards of banana field, he harvests 45 * 10 = 450 bananas per harvest. Now, let's calculate how many apricots Ravi harvests. He has a 13-square yard apricot field that produces 12 apricots per square yard, so he harvests 13 * 12 = 156 apricots per harvest. Both the bananas and apricots can be harvested every 4 months / 4 months. There are 12 months in a year, so in two years (24 months), there are 24 / 4 = 6 harvests. Over two years, Ravi harvests 450 bananas per harvest * 6 harvests = 2700 bananas. He also harvests 156 apricots per harvest * 6 harvests = 936 apricots. The difference in the number of bananas and apricots harvested is 2700 - 936 = 1764. Final Answer: The final answer is $\boxed{1764}$

Overall Quality: excellent

The reasoning chain correctly calculates the yield per harvest for both bananas and apricots, correctly determines the number of harvests in two years (6), calculates the total yield over two years, and finds the correct difference. All arithmetic and logical steps align with the problem statement and ground truth.

✓ No hallucinations detected

Question #41

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Thiago has 25 square yards of orange field. There are 23 oranges per one-fourth of a square yard. Thiago can harvest his oranges every 12 months. In addition, Thiago owns a 9-square yard grape field that produces 13 grapes per square yard. The grapes can be harvested every 4 months. In the span of two years, how many more oranges does Thiago harvest than grapes? **Answer:** Thiago harvests oranges every 12 months, so in two years (24 months), he harvests 24/12 = 2 times. He has 25 square yards of orange field, and there are 23 oranges per 1/4 square yard. This means there are 23 * 4 = 92 oranges per square yard. So each harvest yields 25 * 92 = 2300 oranges. Over two years, he harvests 2 * 2300 = 4600 oranges. Thiago harvests grapes every 4 months. In two years (24 months), he harvests 24/4 = 6 times. He has 9 square yards of grape field, and each square yard produces 13 grapes. So each harvest yields 9 * 13 = 117 grapes. Over two years, he harvests 6 * 117 = 702 grapes. The difference between the number of oranges and grapes harvested is 4600 - 702 = 3898. The answer is $\boxed{3898}$.

Overall Quality: excellent

The reasoning chain correctly interprets all constraints of the problem, performs all calculations accurately, and arrives at the correct final answer.

✓ No hallucinations detected

Question #32

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Gabrielle makes tea using teaspoons of sugar and cups of water in a ratio of 54:12. She also uses 7 tablespoons of milk for every 2 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 240 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use? **Answer:** Let 's' be the number of teaspoons of sugar, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. From the ratio of sugar to water (54:12), we can simplify it to 9:2. So, s = (9/2)w. w = (2/9)s From the ratio of milk to water (7 tablespoons milk : 2 cups water), we get m = (7/2)w. Substituting w = (2/9)s into this equation gives us m = (7/2) * (2/9)s = (7/9)s. From the ratio of cream to sugar (2 tablespoons cream : 1 teaspoon sugar), we have c = 2s. We are given that the total quantity of ingredients is 240. Thus, s + w + m + c = 240. Substituting the expressions for w, m, and c in terms of 's': s + (2/9)s + (7/9)s + 2s = 240 (9/9)s + (2/9)s + (7/9)s + (18/9)s = 240 (36/9)s = 240 4s = 240 s = 60 Therefore, Gabrielle used \boxed{60} teaspoons of sugar.

Overall Quality: excellent

The reasoning chain correctly sets up the relationships between the variables based on the given ratios and solves the resulting linear equation accurately. The final answer matches the ground truth.

✓ No hallucinations detected

Question #34

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Reformatted Question: Kimia makes coffee using teaspoons of sugar and cups of water in a ratio of 55:44. She also uses 6 tablespoons of milk for every 24 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 240 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use? Answer: Let 's' be the number of teaspoons of sugar, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. From the ratio of sugar to water, we have s/w = 55/44. Simplifying, we get w = (44/55)s = (4/5)s . From the ratio of milk to water, we have m/w = 6/24 = 1/4. So, m = (1/4)w . Substituting into , we get m = (1/4) * (4/5)s = (1/5)s . From the ratio of cream to sugar, we have c/s = 2/1. So, c = 2s . We are given that the total quantity of ingredients is 240. Thus, s + w + m + c = 240. Substituting , , and into the total quantity equation, we get: s + (4/5)s + (1/5)s + 2s = 240 (5/5)s + (4/5)s + (1/5)s + (10/5)s = 240 (20/5)s = 240 4s = 240 s = 240/4 s = 60 Therefore, Kimia used 60 teaspoons of sugar. Final Answer: The final answer is $\boxed{60}$

Overall Quality: excellent

The reasoning chain correctly interprets all ratios, sets up the algebraic equation based on the total quantity constraint, and performs all arithmetic operations correctly, leading to the correct answer.

✓ No hallucinations detected

Question #123

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**Reformatted Question:** Luis picks 55 grapes on Friday. Then he picks 170 grapes on Saturday. On Sunday, he picks quintuple the number of grapes he did on Friday. On Monday, he picks half the amount of what he picked in the past 3 days combined. On Tuesday, Luis is going to sell grapes in boxes of 15 grapes each. He is going to sell each box for $10. How much is Luis going to make? **Answer:** On Friday, Luis picked 55 grapes. On Saturday, Luis picked 170 grapes. On Sunday, Luis picked 55 * 5 = 275 grapes. The total number of grapes picked from Friday to Sunday is 55 + 170 + 275 = 500 grapes. On Monday, Luis picked 500 / 2 = 250 grapes. The total number of grapes picked from Friday to Monday is 500 + 250 = 750 grapes. The number of boxes Luis can make is 750 / 15 = 50 boxes. The total amount Luis will make is 50 * $10 = $500. The answer is $\boxed{500}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps outlined in the problem description, and all arithmetic calculations are accurate. The final answer matches the ground truth.

✓ No hallucinations detected

Question #125

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**Reformatted Question:** Umar picks 147 apples on Sunday. Then he picks 99 apples on Monday. On Tuesday, he picks double the number of apples he did on Sunday. On Wednesday, he picks half the amount of what he picked in the past 3 days combined. On Thursday, Umar is going to sell apples in boxes of 27 apples each. He is going to sell each box for $11. How much is Umar going to make? **Answer:** On Sunday, Umar picked 147 apples. On Monday, Umar picked 99 apples. On Tuesday, Umar picked 147 * 2 = 294 apples. The total number of apples picked from Sunday to Tuesday is 147 + 99 + 294 = 540 apples. On Wednesday, Umar picked 540 / 2 = 270 apples. The total number of apples Umar picked is 540 + 270 = 810 apples. The number of boxes Umar can make is 810 / 27 = 30 boxes. Umar will make 30 * $11 = $330. The answer is $\boxed{330}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps correctly. All calculations are verified as correct.

✓ No hallucinations detected

Question #277

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**Reformatted Question:** Greenville High School is holding graduation in its Convention Center this year, which has space for 7700 people. After accounting for the 550 seats for graduates, 450 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally? **Answer:** First, we calculate the total number of seats occupied by graduates, faculty, and staff: 550 + 450 + 100 = 1100 seats. Next, we subtract the occupied seats from the total capacity of the Convention Center to find the number of seats remaining for friends and family: 7700 - 1100 = 6600 seats. Finally, we divide the remaining seats by the number of graduates to find out how many tickets each graduate receives: 6600 / 550 = 12 tickets per graduate. The answer is $\boxed{12}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the requirements of the problem. All calculations are correct.

✓ No hallucinations detected

Question #279

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**Reformatted Question:** Greenville High School is holding graduation in its Convention Center this year, which has space for 3900 people. After accounting for the 1150 seats for graduates, 400 seats for the faculty attending, and reserving 50 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally? **Answer:** The total number of seats available is 3900. Seats taken by graduates: 1150 Seats taken by faculty: 400 Seats taken by staff: 50 The total number of seats taken by graduates, faculty, and staff is 1150 + 400 + 50 = 1600. The remaining seats are available for friends and family: 3900 - 1600 = 2300. Since there are 1150 graduates and the 2300 tickets are split equally (split equally) among them (each graduate), each graduate receives 2300 / 1150 = 2 tickets. Final Answer: The final answer is $\boxed{2}$

Overall Quality: excellent

The reasoning chain correctly identifies the steps: summing the reserved seats, subtracting this total from the overall capacity, and then dividing the remaining seats by the number of graduates. All arithmetic operations are performed correctly.

✓ No hallucinations detected

Question #31

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**Reformatted Question:** Olga makes coffee using teaspoons of sugar and cups of water in a ratio of 48:10. She also uses 6 tablespoons of milk for every 10 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 210 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use? **Answer:** Let 's' be the number of teaspoons of sugar, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. We are given that the ratio of sugar to water is 48:10. This means s/w = 48/10. We are also given that the ratio of milk to water is 6:10, so m/w = 6/10. And, the ratio of cream to sugar is 2:1, so c/s = 2/1 or c = 2s. The total number of ingredients used is 210, thus s + w + m + c = 210. Since s/w = 48/10, we can write w = (10/48)s = (5/24)s. Since m/w = 6/10, and w = (5/24)s, then m = (6/10) * (5/24)s = (1/8)s. We also know c = 2s. Now, substitute these values of w, m, and c in terms of 's' into the equation s + w + m + c = 210: s + (5/24)s + (1/8)s + 2s = 210 Multiply the entire equation by 24 to get rid of the fractions: 24s + 5s + 3s + 48s = 5040 Combine like terms: 70s = 5040 Divide both sides by 80: s = 5040 / 80 s = 72 So, she used 72 teaspoons of sugar. Final Answer: The final answer is $\boxed{72}$

Overall Quality: poor

The model correctly set up the algebraic relationships based on the ratios. However, there is a critical calculation error when summing the coefficients of 's' (stating 70s instead of 80s), leading to an incorrect final answer (72 instead of 63). The subsequent division step is also inconsistent with the erroneous line above it.

✓ No hallucinations detected

Question #122

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**Reformatted Question:** Leon picks 80 apples on Thursday. Then he picks 50 apples on Friday. On Saturday, he picks triple the number of apples he did on Thursday. On Sunday, he picks half the amount of what he picked in the past 3 days combined. On Monday, Leon is going to sell apples in boxes of 15 apples each. He is going to sell each box for $12. How much is Leon going to make? **Answer:** * **Saturday's Apples:** Leon picked triple the amount he picked on Thursday, which is 80 apples * 3 = 240 apples. * **Total Apples Thursday-Saturday:** From Thursday to Saturday, he picked 80 + 50 + 240 = 370 apples. * **Sunday's Apples:** On Sunday, he picked half the amount of 370 apples, which is 370 / 2 = 185 apples. * **Total Apples:** In total, Leon picked 370 + 185 = 555 apples. * **Number of Boxes:** He can make 555 apples / 15 apples/box = 37 boxes. * **Total Earnings:** Leon will make 37 boxes * $12/box = $\boxed{444}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the problem steps correctly. All calculations match the ground truth.

✓ No hallucinations detected

Question #21

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**Reformatted Question:** A group of 150 students has various hobbies. 27 like to play music, 8 like to play chess, 13 like to swim, 9 like to play football, and the rest like to either paint or play video games. What percentage of the students like to paint if the number of the students that like to play video games is 3 less than two times the number that prefer playing football? **Answer:** First, let's find the number of students who like to play video games. Two times the number of students who like football is 2 * 9 = 18. Three less than this is 18 - 3 = 15 students. So, 15 students like to play video games. Next, let's find the total number of students engaged in hobbies other than painting and video games. This sum is 27 + 8 + 13 + 9 = 57 students. Now, let's find the number of students who like to paint or play video games. We know there are a total of 150 students, so 150 - 57 = 93 students either paint or play video games. Since 15 students like to play video games, the number of students who like to paint is 93 - 15 = 78. Finally, to find the percentage of students who like to paint, we calculate (78 / 150) * 100% = 52%. The answer is $\boxed{52}$.

Overall Quality: excellent

The reasoning chain correctly calculates the number of students who like video games, correctly sums the known hobbies, correctly deduces the number of students who paint, and correctly calculates the final percentage. All arithmetic and logic steps are sound.

✓ No hallucinations detected

Question #36

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**Reformatted Question:** Hiroshi has 20 hectares of apricot field. There are 28 apricots per two-fourths of a hectare. Hiroshi can harvest his apricots every 6 months. In addition, Hiroshi owns a 12-hectare grape field that produces 14 grapes per hectare. The grapes can be harvested every 4 months. In the span of two years, how many more apricots does Hiroshi harvest than grapes? **Answer:** First, calculate the number of apricots harvested per hectare. Since two-fourths is equal to one-half, there are 28 apricots per half a hectare. This means there are 28 * 2 = 56 apricots per hectare. Next, find the total number of apricots Hiroshi harvests from his 20 hectares. He harvests 56 apricots per hectare * 20 hectares = 1120 apricots per harvest. Over two years (24 months), Hiroshi can harvest apricots 24 months / 6 months per harvest = 4 times. This means he harvests a total of 1120 apricots * 4 harvests = 4480 apricots. Now, calculate the number of grapes Hiroshi harvests. He harvests 14 grapes per hectare from his 12-hectare grape field, for a total of 14 grapes per hectare * 12 hectares = 168 grapes per harvest. Over two years (24 months), Hiroshi can harvest grapes 24 months / 4 months per harvest = 6 times. This means he harvests a total of 168 grapes * 6 harvests = 1008 grapes. Finally, find the difference in the number of apricots and grapes harvested. Hiroshi harvests 4480 apricots and 1008 grapes over two years. The difference is 4480 - 1008 = 3472. The answer is $\boxed{3472}$.

Overall Quality: excellent

The reasoning chain correctly interprets all parts of the problem, performs all necessary calculations accurately, and arrives at the correct final answer.

✓ No hallucinations detected

Question #30

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Reformatted Question: Olivia makes tea using teaspoons of sugar and cups of water in a ratio of 51:5. She also uses 7 tablespoons of milk for every 5 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 220 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use? Answer: Let 's' be the number of teaspoons of sugar, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. From the ratio of sugar to water (51:5), we have s/w = 51/5. From the ratio of milk to water (7 tablespoons milk : 5 cups water), we have m/w = 7/5. From the ratio of cream to sugar (2 tablespoons cream : 1 teaspoon sugar), we have c/s = 2/1 or c = 2s. We are given that s + w + m + c = 220. Since s/w = 51/5, we have w = (5/51)s. Since m/w = 7/5, we have m = (7/5)w = (7/5) * (5/51)s = (7/51)s. We also know c = 2s. Substituting w, m, and c in terms of 's' into the equation s + w + m + c = 220: s + (5/51)s + (7/51)s + 2s = 220 (51/51)s + (5/51)s + (7/51)s + (102/51)s = 220 (165/51)s = 220 s = (220 * 51) / 165 s = (220 * 51) / 165 = (20 * 51)/15 = (4 * 51)/3 = 4 * 17 = 68 Therefore, Olivia used 68 teaspoons of sugar. Final Answer: The final answer is $\boxed{68}$

Overall Quality: excellent

The reasoning chain correctly sets up the system of equations based on the given ratios and the total constraint, and all algebraic manipulations and arithmetic calculations are correct, leading to the correct answer.

✓ No hallucinations detected

Question #33

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**Reformatted Question:** Mia makes coffee using teaspoons of sugar and cups of water in a ratio of 48:7. She also uses 9 tablespoons of milk for every 7 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 170 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use? **Answer:** Let 's' be the number of teaspoons of sugar, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. We are given that the ratio of sugar to water is 48:7. So, s/w = 48/7. This can be rewritten as w = (7/48)s. Equation 1 We are also given that she uses 9 tablespoons of milk for every 7 cups of water. So, m/w = 9/7. Since w = (7/48)s from Equation 1, we can substitute this into the milk equation: m = (9/7) * (7/48)s = (9/48)s = (3/16)s. Equation 2 She uses 2 tablespoons of heavy cream for every teaspoon of sugar. So, c/s = 2/1, or c = 2s. Equation 3 We are given that the total amount of ingredients used is 170. Therefore, s + w + m + c = 170. Now we substitute the expressions for w, m, and c from Equation 1, Equation 2, and Equation 3 into the total equation: s + (7/48)s + (3/16)s + 2s = 170 To simplify, we can find a common denominator (which is 48): (48/48)s + (7/48)s + (9/48)s + (96/48)s = 170 (48s + 7s + 9s + 96s)/48 = 170 (160/48)s = 170 s = (170 * 48) / 160 s = (17 * 48) / 16 s = (17 * 3) / 1 = 51. Teaspoons of Sugar Final Answer: The final answer is $\boxed{51}$

Overall Quality: excellent

The reasoning chain correctly sets up the proportional relationships between the ingredients based on the given ratios and the total constraint. All algebraic manipulations and arithmetic calculations are correct, leading to the correct final answer.

✓ No hallucinations detected

Question #62

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Reformatted Question: To make a call from a hotel room phone, you must pay €0.4 for each minute of your call. After 15 minutes, the price drops to €0.3 per minute. After 35 minutes from the start of the call, the price drops even more to €0.2 per two minutes. If your total bill is more than €15, you get a 10% discount on your total bill. How much would a 115-minute call cost? Answer: The first 15 minutes cost 15 * €0.4 = €6. The next 20 minutes (from minute 15 to minute 35) cost 20 * €0.3 = €6. The remaining 115 - 35 = 80 minutes are charged at €0.2 per two minutes. This means there are 80/2 = 40 two-minute intervals. So the cost for this portion is 40 * €0.2 = €8. The total cost before any discount is €6 + €6 + €8 = €20. Since €20 is more than €15, a 10% discount applies. The discount amount is €20 * 0.1 = €2. The final cost is €20 - €2 = €18. The answer is \boxed{18}.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all steps required by the problem description. All calculations are correct.

✓ No hallucinations detected

Question #64

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Reformatted Question: To make a call from a hotel room phone, you must pay ₺0.6 for each minute of your call. After 10 minutes, the price drops to ₺0.4 per minute. After 35 minutes from the start of the call, the price drops even more to ₺0.1 per two minutes. If your total bill is more than ₺15, you get a 15% discount on your total bill. How much would a 115-minute call cost? Answer: The 115-minute call can be broken down into three parts: * **Part 1:** The first 10 minutes cost 10 minutes * ₺0.6/minute = ₺6. * **Part 2:** From minute 11 to minute 35 (25 minutes in total) cost (35 - 10) minutes * ₺0.4/minute = ₺10. * **Part 3:** From minute 36 to minute 115 (80 minutes in total) cost (115 - 35) minutes * ₺0.1/2 minutes = 80 minutes / 2 * ₺0.1 = ₺4. The total cost before discount is ₺6 + ₺10 + ₺4 = ₺20. Since ₺20 is more than ₺15, a 15% discount applies. The discount amount is ₺20 * 0.15 = ₺3. The final cost is ₺20 - ₺3 = ₺17. The answer is \boxed{17}.

Overall Quality: excellent

The reasoning chain correctly breaks down the call duration based on the tiered pricing structure, performs all arithmetic calculations accurately, and correctly applies the discount logic. The final answer matches the ground truth.

✓ No hallucinations detected

Question #65

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**Reformatted Question:** To make a call from a hotel room phone, you must pay ¥0.9 for each minute of your call. After 10 minutes, the price drops to ¥0.6 per minute. After 35 minutes from the start of the call, the price drops even more to ¥0.4 per two minutes. If your total bill is more than ¥15, you get a 20% discount on your total bill. How much would a 65-minute call cost? **Answer:** * **Cost for the first 10 minutes:** ¥0.9/minute * 10 minutes = ¥9 * **Cost for minutes 11-35:** ¥0.6/minute * (35-10) minutes = ¥0.6/minute * 25 minutes = ¥15 * **Cost for minutes 36-65:** This is 65-35 = 30 minutes. Since the rate is ¥0.4 per two minutes, we calculate the cost as ¥0.4 * (30 minutes / 2 minutes/unit) = ¥6 * **Total cost before discount:** ¥9 + ¥15 + ¥6 = ¥30 * **Check for discount:** Since ¥30 is greater than ¥15, a discount applies. * **Discount amount:** ¥30 * 20% = ¥6 * **Final cost:** ¥30 - ¥6 = ¥24 The 65-minute call would cost \boxed{24}.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows all steps required by the problem description. All calculations are correct.

✓ No hallucinations detected

Question #35

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**Reformatted Question:** Uma makes tea using teaspoons of sugar and cups of water in a ratio of 45:5. She also uses 8 tablespoons of milk for every 4 cups of water, and uses 2 tablespoons of heavy cream for every teaspoon of sugar. She used a total of 210 teaspoons of sugar, cups of water, tablespoons of cream, and tablespoons of milk. How many teaspoons of sugar did she use? **Answer:** Let 's' be the number of teaspoons of sugar Uma used, 'w' be the number of cups of water, 'm' be the number of tablespoons of milk, and 'c' be the number of tablespoons of cream. From the ratio of sugar to water (45:5), we can simplify it to 9:1. This means for every 9 teaspoons of sugar, Uma uses 1 cup of water. So, w = s/9. w = s/9 From the ratio of milk to water (8 tablespoons milk : 4 cups water), we can simplify it to 2:1. This means for every cup of water, Uma uses 2 tablespoons of milk. So, m = 2w. Substituting w = s/9 into this equation gives us m = 2 * (s/9) = 2s/9. m = 2s/9 From the ratio of cream to sugar (2 tablespoons cream : 1 teaspoon sugar), we know that c = 2s. c = 2s We are given that the total quantity of ingredients used is 210. Therefore, s + w + m + c = 210. Substituting , , and into this equation gives us: s + (s/9) + (2s/9) + 2s = 210 Multiplying both sides by 9 to eliminate the fractions: 9s + s + 2s + 18s = 1890 Combining like terms: 30s = 1890 Dividing both sides by 30: s = 1890 / 30 s = 63 Therefore, Uma used 63 teaspoons of sugar. Final Answer: The final answer is $\boxed{63}$

Overall Quality: excellent

The reasoning correctly sets up the proportional relationships between the ingredients based on the given ratios and solves the resulting linear equation accurately to find the amount of sugar used. The final answer matches the ground truth.

✓ No hallucinations detected

Question #61

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Reformatted Question: To make a call from a phone booth, you must pay ₺0.9 for each minute of your call. After 10 minutes, the price drops to ₺0.6 per minute. After 35 minutes from the start of the call, the price drops even more to ₺0.4 per two minutes. If your total bill is more than ₺25, you get a 20% discount on your total bill. How much would a 115-minute call cost? Answer: The call can be broken down into three segments based on the pricing structure: * **Segment 1:** The first 10 minutes cost ₺0.9 per minute. This totals to 10 * 0.9 = ₺9. * **Segment 2:** From minute 11 to minute 35 (25 minutes total), the cost is ₺0.6 per minute. This totals to 25 * 0.6 = ₺15. * **Segment 3:** From minute 36 to minute 115 (80 minutes total) which is 80/2 = 40 two-minute blocks. So it costs 40 * ₺0.4 = ₺16. The total cost before any discount is 9 + 15 + 16 = ₺40. Since ₺40 is greater than ₺25, a 20% discount applies. The discount amount is 40 * 0.2 = ₺8. The final cost of the 115-minute call is 40 - 8 = ₺32. Final Answer: The final answer is $\boxed{32}$

Overall Quality: excellent

The reasoning chain correctly breaks down the call duration based on the tiered pricing structure, calculates the cost for each segment accurately, sums them up, applies the discount correctly, and arrives at the correct final cost. All arithmetic and logic are sound.

✓ No hallucinations detected

Question #63

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Reformatted Question: To make a call from a phone booth, you must pay ₺0.8 for each minute of your call. After 10 minutes, the price drops to ₺0.7 per minute. After 30 minutes from the start of the call, the price drops even more to ₺0.4 per two minutes. If your total bill is more than ₺15, you get a 15% discount on your total bill. How much would a 120-minute call cost? Answer: The cost for the first 10 minutes is ₺0.8/minute * 10 minutes = ₺8. The cost for the next 20 minutes (from minute 10 to minute 30) is ₺0.7/minute * 20 minutes = ₺14. The remaining time is 120 minutes - 30 minutes = 90 minutes. The cost for these 90 minutes is ₺0.4/2 minutes * 90 minutes = ₺18. The total cost before any discount is ₺8 + ₺14 + ₺18 = ₺40. Since ₺40 is more than ₺15, a 15% discount applies. The discount amount is ₺40 * 0.15 = ₺6. The final cost of the 120-minute call is ₺40 - ₺6 = ₺34. The answer is $\boxed{34}$.

Overall Quality: excellent

✓ No hallucinations detected

Question #18

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**Reformatted Question:** A group of 290 students has various hobbies. 12 like to paint, 8 like to play chess, 13 like to swim, 39 like to play cricket, and the rest like to either play video games or hike. What percentage of the students like to play video games if the number of the students that like to hike is 5 less than two times the number that prefer playing cricket? **Answer:** First, we calculate the total number of students engaged in hobbies other than video games or hiking. This includes painting, chess, swimming, and cricket: 12 + 8 + 13 + 39 = 72 students. Next, we find the number of students who like to hike. We're told it is 5 less than twice the number of cricket players. Twice the number of cricket players is 2 * 39 = 78. Five less than this is 78 - 5 = 73 students who like to hike. The total number of students involved in hobbies besides video games is 72 (other hobbies) + 73 (hiking) = 145 students. The total number of students is 290. Subtracting the students engaged in other hobbies gives us the number of students who like to play video games: 290 - 145 = 145 students. Finally, we calculate the percentage of students who like to play video games: (145 / 290) * 100 = 50%. The answer is $\boxed{50}$.

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem statement. All arithmetic calculations are accurate, and the logic used to derive the number of video game players and the final percentage is sound.

✓ No hallucinations detected

Question #60

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Reformatted Question: To make a call from a phone booth, you must pay $0.7 for each minute of your call. After 10 minutes, the price drops to $0.5 per minute. After 30 minutes from the start of the call, the price drops even more to $0.1 per two minutes. If your total bill is more than $15, you get a 15% discount on your total bill. How much would a 90-minute call cost? Answer: Cost for the first 10 minutes: $0.7/minute * 10 minutes = $7 Cost for the next 20 minutes (30 minutes total - 10 minutes): $0.5/minute * 20 minutes = $10 Remaining minutes: 90 minutes - 30 minutes = 60 minutes Number of 2-minute blocks in remaining minutes: 60 minutes / 2 = 30 blocks Cost for the remaining 60 minutes: 30 blocks * $0.1/2 minutes = $3 Total cost before discount: $7 + $10 + $3 = $20 Since $20 > $15, a 15% discount applies. Discount amount: $20 * 0.15 = $3 Final cost after discount: $20 - $3 = $17 The 90-minute call would cost $\boxed{17}$.

Overall Quality: excellent

The reasoning chain correctly calculates the cost for each segment of the 90-minute call based on the tiered pricing structure, correctly applies the discount, and arrives at the correct final cost. All arithmetic operations are correct.

✓ No hallucinations detected

Question #238

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Reformatted Question: A cleaner has to clean a hospital with 90 floors. They have 10 days to get it done. It takes them 10 minutes per floor. However, due to a recent injury, the cleaner has become slower and it will take them twice as long to clean a floor these days. If they work for 15 hours a day, what percentage of their day, on average, is spent cleaning floors? Answer: It takes the cleaner twice as long as 10 minutes which is 10 * 2 = 20 minutes per floor. To clean all 90 floors, it will take the cleaner 90 * 20 = 1800 minutes. There are 10 days to clean, so the cleaner will spend 1800 / 10 = 180 minutes cleaning each day. 15 hours is equal to 15 * 60 = 900 minutes. The percentage of the day spent cleaning is (180 / 900) * 100 = 20%. The answer is $\boxed{20}$.

Overall Quality: excellent

The reasoning chain is mathematically sound and logically follows the steps required to solve the problem, correctly calculating the daily cleaning time and comparing it to the total daily working time.

✓ No hallucinations detected

Question #278

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Generated Answer

**Reformatted Question:** Riverside Academy is holding graduation in its Gymnasium this year which has space for 7800 people. After accounting for the 1050 seats for graduates, 350 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally? **Answer:** First, we calculate the total number of seats occupied by graduates, faculty, and staff: 1050 + 350 + 100 = 1500 seats. Next, we subtract the occupied seats from the total gymnasium capacity to find the number of seats remaining for friends and family: 7800 - 1500 = 6300 seats. Finally, we divide the remaining seats by the number of graduates to find out how many tickets each graduate receives: 6300 / 1050 = 6 tickets per graduate. The answer is $\boxed{6}$.

Overall Quality: excellent

The reasoning chain correctly follows the required steps: summing the reserved seats (graduates, faculty, staff), subtracting this total from the capacity, and then dividing the remainder by the number of graduates. All arithmetic operations are correct.

✓ No hallucinations detected

Question #280

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Riverside Academy is holding graduation in its Gymnasium this year which has space for 8900 people. After accounting for the 1050 seats for graduates, 400 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally? **Answer:** The total number of seats available is 8900. Subtract the seats reserved for graduates (1050), faculty (400), and staff (100) to find the remaining seats: 8900 - 1050 - 400 - 100 = 7350 seats. There are 1050 graduates. Divide the remaining 7350 seats equally among the 1050 graduates: 7350 / 1050 = 7 tickets per graduate. Thus, each graduate would receive \boxed{7} tickets.

Overall Quality: excellent

The reasoning chain correctly identifies the steps needed: summing the reserved seats, subtracting this sum from the total capacity, and then dividing the remaining seats by the number of graduates. All arithmetic operations performed are correct.

✓ No hallucinations detected

Question #236

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A janitor has to clean a building with 135 floors. They have 3 days to get it done. It takes them 5 minutes per floor. However, due to a recent injury, the janitor has become slower and it will take them twice as long to clean a floor these days. If they work for 15 hours a day, what percentage of their day, on average, is spent cleaning floors? **Answer:** It takes the janitor 5 minutes * 2 = 10 minutes to clean one floor now. To clean all 135 floors, it will take 10 minutes/floor * 135 floors = 1350 minutes. Converting this to hours, we have 1350 minutes / 60 minutes/hour = 22.5 hours. The janitor has 3 days to work, so they'll spend an average of 22.5 hours / 3 days = 7.5 hours/day cleaning. The janitor works 15 hours per day. The percentage of their day spent cleaning is (7.5 hours / 15 hours) * 100% = 50%. The answer is $\boxed{50}$.

Overall Quality: excellent

The reasoning chain correctly calculates the time spent cleaning per day and the resulting percentage of the workday, matching the ground truth.

✓ No hallucinations detected

Question #281

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Riverside Academy is holding graduation in its Gymnasium this year which has space for 7300 people. After accounting for the 700 seats for graduates, 200 seats for the faculty attending, and reserving 100 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally? **Answer:** First, we calculate the total number of seats occupied by the graduates, faculty, and staff: 700 + 200 + 100 = 1000 seats. Next, we subtract the occupied seats from the total gymnasium capacity to find the number of seats remaining for friends and family: 7300 - 1000 = 6300 seats. Finally, we divide the remaining seats by the number of graduates to determine how many tickets each graduate receives: 6300 / 700 = 9 tickets/graduate. The answer is $\boxed{9}$.

Overall Quality: excellent

The reasoning chain correctly identifies the steps needed: summing the fixed attendees (graduates, faculty, staff), subtracting this total from the capacity, and then dividing the remainder by the number of graduates. All arithmetic operations are performed correctly, leading to the correct final answer.

✓ No hallucinations detected

Question #239

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: A cleaner has to clean a hospital with 135 floors. They have 5 days to get it done. It takes them 5 minutes per floor. However, due to a recent injury, the cleaner has become slower and it will take them twice as long to clean a floor these days. If they work for 9 hours a day, what percentage of their day, on average, is spent cleaning floors? Answer: It takes the cleaner 5 * 2 = 10 minutes to clean each floor now. To clean all 135 floors, it will take them 135 * 10 minutes/floor = 1350 minutes. There are 9 hours * 60 minutes/hour = 540 minutes in a workday. The percentage of their day spent cleaning is (1350 minutes / (5 days * 540 minutes/day)) * 100% = (1350 / 2700) * 100% = 0.5 * 100% = 50%. The answer is $\boxed{50}$.

Overall Quality: excellent

The reasoning chain is mathematically correct and logically sound. It correctly calculates the total time required for cleaning and compares it to the total time available over the 5 days to determine the average percentage of the day spent cleaning.

✓ No hallucinations detected

Question #276

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Sunnyside High is holding graduation in its Sports Arena this year, which has space for 7500 people. After accounting for the 600 seats for graduates, 250 seats for the faculty attending, and reserving 50 seats for the event's staff, how many tickets would each graduate receive to give to their friends and family if the tickets are split equally? **Answer:** First, we calculate the total number of seats taken by graduates, faculty, and staff: 600 + 250 + 50 = 900 seats. Next, we subtract the occupied seats from the total capacity of the arena: 7500 - 900 = 6600 available seats. Finally, since the tickets are distributed equally among the graduates, we divide the available seats by the number of graduates: 6600 / 600 = 11 tickets per graduate. Therefore, each graduate would receive $\boxed{11}$ tickets.

Overall Quality: excellent

The reasoning chain correctly identifies the steps: summing all reserved seats, subtracting this sum from the total capacity, and then dividing the remaining seats by the number of graduates. All arithmetic operations are performed correctly.

✓ No hallucinations detected

Question #237

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A cleaner has to clean a hospital with 60 floors. They have 3 days to get it done. It takes them 6 minutes per floor. However, due to a recent injury, the cleaner has become slower and it will take them twice as long to clean a floor these days. If they work for 8 hours a day, what percentage of their day, on average, is spent cleaning floors? **Answer:** It originally took the cleaner 6 minutes to clean a floor, but now takes twice as long, so it now takes 6 * 2 = 12 minutes per floor. To clean all 60 floors, it will take 12 minutes/floor * 60 floors = 720 minutes. Since there are 60 minutes in an hour, this is equivalent to 720 minutes / 60 minutes/hour = 12 hours of cleaning. They have 3 days to complete this cleaning, so they will spend 12 hours / 3 days = 4 hours cleaning per day. Since they work 8 hours each day, the percentage of their day spent cleaning is (4/8) * 100% = 50%. The answer is $\boxed{50}$.

Overall Quality: excellent

The reasoning chain correctly calculates the time spent cleaning per day and the resulting percentage of the workday, matching the ground truth.

✓ No hallucinations detected

Question #95

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Deshawn's dog has 146 puppies, 28 of which have spots. Mohammed's dog has 43 puppies, 12 of which have spots. Hiroshi has 51 dogs, each having 11 puppies with spots. After a visit to the vet, DeShawn discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots? **Answer:** 1. **Deshawn's spotted puppies after the vet visit:** Deshawn initially had 28 spotted puppies. He had 146 - 28 = 118 unspotted puppies. Half of those, or 118 / 2 = 59 puppies, were discovered to have spots. So, Deshawn now has 28 + 59 = 87 spotted puppies. 2. **Total number of Deshawn's puppies:** Deshawn still has 146 puppies in total. 3. **Mohammed's spotted puppies:** Mohammed has 12 spotted puppies. 4. **Total number of Mohammed's puppies:** Mohammed has 43 puppies. 5. **Hiroshi's spotted puppies:** Hiroshi has 51 dogs * 11 spotted puppies per dog = 561 spotted puppies. 6. **Total number of Hiroshi's puppies:** Hiroshi has 51 dogs * 11 puppies per dog = 561 puppies (all of his puppies have spots, according to the question). This was actually not necessary to calculate to answer the question, but just included for completeness. 7. **Total spotted puppies:** 87 + 12 + 561 = 660 spotted puppies. 8. **Total puppies:** 146 + 43 + 561 = 750 total puppies. 9. **Percentage of spotted puppies:** (660 / 750) * 100% = 88%. Final Answer: \boxed{88}

Overall Quality: excellent

The reasoning chain correctly follows all steps required by the problem. All calculations are accurate, and the logic for updating the spotted puppy count based on the vet visit is sound.

✓ No hallucinations detected

Question #234

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A janitor has to clean a building with 80 rooms. They have 4 days to get it done. It takes them 6 minutes per room. However, due to a recent injury, the janitor has become slower and it will take them twice as long to clean a room these days. If they work for 10 hours a day, what percentage of their day, on average, is spent cleaning rooms? **Answer:** It now takes the janitor 6 minutes * 2 = 12 minutes to clean each room. To clean all 80 rooms, it will take 12 minutes/room * 80 rooms = 960 minutes. 960 minutes is equivalent to 960 minutes / 60 minutes/hour = 16 hours. Since the janitor works for 4 days, they spend 16 hours / 4 days = 4 hours/day cleaning. Since their workday is 10 hours long, the percentage of their day spent cleaning is (4 hours / 10 hours) * 100% = 40%. The answer is $\boxed{40}$.

Overall Quality: excellent

The reasoning chain correctly calculates the time spent cleaning per day and the resulting percentage of the workday, matching the ground truth steps.

✓ No hallucinations detected

Question #6

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A fog bank rolls in from the ocean to cover a city. It takes 30 minutes to cover every 3 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 72 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover a quarter of the city? **Answer:** The fog initially covers 3 miles in 30 minutes, meaning its speed is 3 miles / 30 minutes = 0.1 miles/minute . A quarter of the city is 72 miles * (1/4) = 18 miles . Since the wind speed is halved in one hour (60 minutes), we need to determine if the time to cover a quarter of the city (18 miles) is less than or greater than 60 minutes. If it's less than 60 minutes, the initial speed applies. At the initial speed of 0.1 miles/minute, it would take 18 miles / 0.1 miles/minute = 180 minutes to cover 18 miles. Since 180 minutes is greater than 60 minutes, the wind speed will change before the fog covers a quarter of the city. However, the question asks for the time to cover a quarter (18 miles) of the city. We'll use the initial speed because the question says the wind speed *will be halved* in an hour, not that it *is* halved. So, it will take 18 miles / 0.1 miles/minute = 180 minutes to cover 18 miles (a quarter of the city). The answer is $\boxed{180}$.

Overall Quality: poor

The model correctly calculates the target distance (18 miles) and the initial speed (0.1 miles/minute). However, it makes a critical logical error by ignoring the speed change that occurs at 60 minutes, despite calculating that the total time required (180 minutes) exceeds 60 minutes. This leads to an incorrect final answer (180 vs 300).

Detected Issues (1)

calculation_error low

Statement

The fog initially covers 3 miles in 30 minutes, meaning its speed is 3 miles / 30 minutes = 0.1 miles/minute .

Explanation

The calculation 3 / 30 = 0.1 is mathematically correct, but the unit conversion used in the ground truth implies the speed should be calculated in miles per minute based on the rate given (3 miles per 30 minutes). However, the ground truth uses a different interpretation of the rate: 60/30*3 miles in 1 hour, which implies a speed of 6 miles per hour, or 0.1 miles/minute. Let's re-examine the initial rate: 3 miles in 30 minutes. This is equivalent to 6 miles in 60 minutes (1 hour). So the initial speed is 6 miles/hour, or 6/60 = 0.1 miles/minute. The calculation 3/30 = 0.1 is mathematically correct.

Answer Span:

3 miles / 30 minutes = 0.1 miles/minute

Reference/Question Span:

It takes 30 minutes to cover every 3 miles

Question #22

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A class of 100 students has various hobbies. 14 like to hike, 8 like to play chess, 13 like to swim, 2 like to play cricket, and the rest like to either dance or play music. What percentage of the students like to dance if the number of the students that like to play music is 5 less than ten times the number that prefer playing cricket? **Answer:** First, we calculate the number of students who like to play music. Since 2 students like to play cricket, and the number of students who play music is 5 less than 10 times this number, there are (10 * 2) - 5 = 15 students who like to play music. This is equal to 15 students. Next, we calculate the number of students who like to hike, play chess, or swim. This is 14 + 8 + 13 = 35 students. This is equal to 35 students. We know there are 100 students total. We have accounted for 35 students (hike, chess, swim) and 15 students (music), and 2 students who like to play cricket. This sums to 35 + 15 + 2 = 52 students. This is equal to 52 students.. The remaining students like to dance, so there are 100 - 52 = 48 students who like to dance. This is equal to 48 students. Finally, we express this number as a percentage of the total number of students. The percentage of students who like to dance is (48/100) * 100% = 48%. The answer is $\boxed{48}$.

Overall Quality: excellent

The reasoning chain correctly calculates the number of students who play music, correctly sums the known groups, correctly finds the number of students who dance by subtraction from the total, and correctly converts this number to a percentage. All arithmetic and logic steps align with the problem statement and ground truth.

✓ No hallucinations detected

Question #90

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: Mateo's dog has 149 puppies, 25 of which have spots. Mohammed's dog has 49 puppies, 12 of which have spots. Ibrahim has 54 dogs, each having 13 puppies with spots. After a visit to the vet, Mateo discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots? Answer: Mateo initially had 25 puppies with spots. He had 149 - 25 = 124 puppies without spots. After the vet visit, half of the 124 unspotted puppies, which is 124/2 = 62 puppies, were found to have spots. So now, Mateo has 25 + 62 = 87 puppies with spots. Mohammed has 12 puppies with spots. Ibrahim has 54 dogs * 13 puppies with spots per dog = 702 puppies with spots. The total number of puppies with spots is 87 + 12 + 702 = 801. The total number of puppies is 149 + 49 + (54 * 13) = 149 + 49 + 702 = 899 + 1 = 900. The percentage of puppies with spots is (801/900) * 100% = 89%. Final Answer: The final answer is $\boxed{89}$

Overall Quality: excellent

The reasoning chain is mathematically sound and follows the logic derived from the problem statement correctly. All calculations are accurate.

✓ No hallucinations detected

Question #93

1 issue

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Pavel's dog has 100 puppies, 22 of which have spots. Hiroshi's dog has 40 puppies, 15 of which have spots. Santiago has 55 dogs, each having 12 puppies with spots. After a visit to the vet, Pavel discovered that half of his unspotted puppies actually have spots that were not visible before. What percentage of all the puppies have spots? **Answer:** 1. **Pavel's spotted puppies after the vet visit:** Pavel initially had 22 spotted puppies. He had 100 - 22 = 78 unspotted puppies. Half of these unspotted puppies were found to have spots: 78 / 2 = 39 puppies. So, Pavel now has 22 + 39 = 61 spotted puppies. 2. **Hiroshi's spotted puppies:** Hiroshi has 15 spotted puppies. 3. **Santiago's spotted puppies:** Santiago has 55 dogs * 12 spotted puppies/dog = 660 spotted puppies. 4. **Total spotted puppies:** The total number of spotted puppies is 61 + 15 + 660 = 736 spotted puppies. 5. **Total puppies:** Pavel has 100 puppies, Hiroshi has 40 puppies, and Santiago has 55 dogs * 12 puppies/dog + 55 dogs * (12 unspotted puppies implied/dog )= 660 + 660 = 1320 puppies, for a total of 100 + 40 + 1320 = 1460 puppies. 6. **Percentage of spotted puppies:** The percentage of spotted puppies is (736 / 1460) * 100% = 50.41% (approximately). Final Answer: \boxed{50.41}

Overall Quality: poor

The model correctly calculated the spotted puppies (736). However, it made a significant logical error in Step 5 by assuming Santiago's dogs had 12 spotted puppies AND 12 unspotted puppies each, leading to an inflated total puppy count (1460 instead of 800) and an incorrect final percentage (50.41% instead of 92%).

Detected Issues (1)

logical_error high

Statement

Santiago has 55 dogs * 12 spotted puppies/dog + 55 dogs * (12 unspotted puppies implied/dog )= 660 + 660 = 1320 puppies

Explanation

The problem states Santiago has 55 dogs, each having 12 puppies *with spots*. It does not state that each dog also has 12 unspotted puppies. The total number of puppies for Santiago should be 55 * 12 = 660 puppies, all of which are spotted according to the initial description for Santiago.

Answer Span:

Santiago has 55 dogs * 12 spotted puppies/dog + 55 dogs * (12 unspotted puppies implied/dog )= 660 + 660 = 1320 puppies

Reference/Question Span:

Santiago has 55 dogs, each having 12 puppies with spots.

Question #291

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Ava can peel 5 zucchinis a minute and saute 20 zucchinis in 6 minutes. How many minutes will it take her to peel and saute 140 zucchinis if it takes 24 seconds to wash each zucchini before peeling it? Note that Ava can't work in parallel and needs to take a 15-minute break after peeling the zucchinis before she can start sautéing them. **Answer:** First, let's calculate the time it takes Ava to peel 140 zucchinis. Since she peels 5 zucchinis per minute, it will take her 140 / 5 = 28 minutes to peel all the zucchinis. Next, let's calculate the time it takes to wash 140 zucchinis. Since washing takes 24 seconds per zucchini, it will take 140 * 24 seconds = 3360 seconds. Converting this to minutes, we get 3360 seconds / 60 seconds/minute = 56 minutes. Now, let's calculate the time it takes to saute 140 zucchinis. Since she can saute 20 zucchinis in 6 minutes, it will take her (140 / 20) * 6 = 42 minutes to saute all the zucchinis. Since Ava can't work in parallel (), we need to add the washing time, peeling time, the break time (), and the sauteing time to get the total time. Total time = 56 minutes + 28 minutes + 15 minutes + 42 minutes = 141 minutes. Therefore, it will take Ava \boxed{141} minutes to peel and saute 140 zucchinis.

Overall Quality: excellent

The reasoning chain correctly calculates all components (peeling time, washing time, sauteing time) and correctly sums them up, respecting the sequential nature of the tasks and the break time, leading to the correct final answer.

✓ No hallucinations detected

Question #11

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A fog bank rolls in from the ocean to cover a city. It takes 90 minutes to cover every 3 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 78 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover a third of the city? **Answer:** The fog bank covers 3 miles in 90 minutes. This means its speed is 3 miles / 90 minutes = 1/30 miles per minute . We want to know how long it takes to cover a third of the city. Given that the city is 78 miles across, a third of the city is 78 miles / 3 = 26 miles . Since the wind speed is halved in one hour (60 minutes), the new speed after 60 minutes will be (1/30 miles per minute) / 2 = 1/60 miles per minute . We need to determine how long it takes to cover the first 26 miles. The fog travels at the initial speed (1/30 miles per minute) for the first 60 minutes. In this time it covers (1/30 miles/minute) * 60 minutes = 2 miles . This leaves 26 miles - 2 miles = 24 miles to be covered at the reduced speed of 1/60 miles per minute . The time it takes to cover these remaining 24 miles at the reduced speed is 24 miles / (1/60 miles/minute) = 24 * 60 = 1440 minutes . The total time is the initial 60 minutes plus the additional 1440 minutes: 60 minutes + 1440 minutes = 1500 minutes . Therefore, it will take $\boxed{1500}$ minutes for the fog bank to cover a third of the city.

Overall Quality: excellent

The reasoning chain correctly calculates the required distance, determines the initial speed, calculates the distance covered in the first hour, determines the remaining distance, calculates the time needed for the remaining distance using the halved speed, and sums the times correctly. All arithmetic and logic align with the ground truth.

✓ No hallucinations detected

Question #37

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** Oliver has 15 hectares of grape field. There are 15 grapes per 1/3 of a hectare. Oliver can harvest his grapes every 4 months. In addition, Oliver owns a 9-hectare apple field that produces 16 apples per hectare. The apples can be harvested every 4 months. In the span of two years, how many more grapes does Oliver harvest than apples? **Answer:** First, calculate the number of grapes harvested per hectare. Since there are 15 grapes per 1/3 hectare, there are 15 * 3 = 45 grapes per hectare. Next, calculate the total number of grapes Oliver can harvest from his 15-hectare field. He harvests 45 grapes/hectare * 15 hectares = 675 grapes per harvest. Since there are 12 months in a year, two years is 24 months. Because Oliver can harvest his grapes every 4 months, in two years, he harvests 24 months / 4 months/harvest = 6 times. Therefore, in two years Oliver harvests a total of 675 grapes * 6 harvests = 4050 grapes. Now calculate the total number of apples Oliver can harvest from his 9-hectare field. He harvests 16 apples/hectare * 9 hectares = 144 apples per harvest. Since Oliver harvests apples every 4 months, in two years (24 months), he harvests 24 months / 4 months/harvest = 6 times. So, in two years Oliver harvests a total of 144 apples * 6 harvests = 864 apples. Finally, the difference between the number of grapes and apples harvested is 4050 grapes - 864 apples = 3186. Final Answer: The final answer is $\boxed{3186}$

Overall Quality: excellent

The reasoning chain correctly calculates the yield for both grapes and apples over two years and finds the correct difference. All arithmetic operations are correct, and the logic follows the problem constraints.

✓ No hallucinations detected

Question #7

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A fog bank rolls in from the ocean to cover a city. It takes 75 minutes to cover every 10 miles of the city. However, we know that the wind speed is going to be halved in one hour (60 minutes). If the city is 72 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/4 of the city? **Answer:** First, we need to determine how far the fog bank needs to travel to cover 1/4 of the city. The city is 72 miles across, so 1/4 of the city is (1/4) * 72 miles = 18 miles. Next, we calculate the initial speed of the fog bank. It takes 75 minutes to cover 10 miles, so the initial speed is 10 miles / 75 minutes = 2/15 miles per minute. Since the wind speed halves after 60 minutes, the new speed will be (2/15 miles per minute) / 2 = 1/15 miles per minute. Now, we know the fog bank travels the first 10 miles at the initial speed. This takes 75 minutes. The remaining distance to cover 1/4 of the city (18 miles) is 18 miles - 10 miles = 8 miles. It will take 8 miles / (1/15 miles per minute) = 120 minutes to cover the remaining distance. Therefore, the total time to cover 1/4 of the city is the initial 75 minutes + 120 minutes = 195 minutes. Final Answer: The final answer is $\boxed{195}$

Overall Quality: poor

The reasoning contains a critical logical error by assuming the first 10 miles are covered entirely at the initial rate, ignoring the constraint that the speed halves after exactly 60 minutes. This leads to an incorrect total time calculation.

✓ No hallucinations detected

Question #8

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A fog bank rolls in from the ocean to cover a city. It takes 60 minutes to cover every 3 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 54 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/3 of the city? **Answer:** The city is 54 miles across, so 1/3 of the city is (54 * 1/3) = 18 miles. Initially, the fog covers 3 miles in 60 minutes. This means the fog's speed is (3 miles / 60 minutes) = 0.05 miles per minute. After one hour (60 minutes), the wind speed is halved. This means the fog's speed is reduced to (0.05/2) = 0.025 miles per minute. Since we are calculating the time it takes for the fog to cover 18 miles and the wind speed changes after the first hour, we need to consider the time it takes to cover the first 3 miles and then the remaining 15 miles. The time to cover the first 3 miles is given as 60 minutes. Now, the fog needs to cover an additional (18 - 3) = 15 miles. At the reduced speed of 0.025 miles per minute, the time to cover 15 miles is (15 miles / 0.025 miles/minute) = 600 minutes. The total time to cover 18 miles is the sum of the time to cover the first 3 miles and the remaining 15 miles, which is 60 minutes + 600 minutes = 660 minutes. Final Answer: The final answer is $\boxed{660}$

Overall Quality: excellent

The reasoning chain correctly calculates the required distance, determines the initial speed, correctly calculates the reduced speed after one hour, correctly separates the time taken for the first 3 miles (at the initial speed) and the remaining 15 miles (at the reduced speed), and sums these times to reach the correct total time of 660 minutes. All calculations are arithmetically sound and the logic follows the problem constraints.

✓ No hallucinations detected

Question #9

Clean

Full Question

Ground Truth Answer

Generated Answer

**Reformatted Question:** A fog bank rolls in from the ocean to cover a city. It takes 60 minutes to cover every 6 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 72 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/3 of the city? **Answer:** The fog bank covers 6 miles in 60 minutes, so its initial speed is 6 miles / 60 minutes = 0.1 miles per minute. We want to find the time it takes to cover 1/3 of the city. Since the city is 72 miles across, 1/3 of the city is (1/3) * 72 miles = 24 miles. Since the wind speed is halved in one hour (60 minutes), and the initial speed is 0.1 miles per minute, the new speed after 60 minutes will be 0.1 / 2 = 0.05 miles per minute. Since we're looking at the time to cover 24 miles, and the fog bank's initial speed is 0.1 miles/minute, it will take 24 miles / 0.1 miles/minute = 240 minutes. However, the speed changes to 0.05 miles/minute after 60 minutes. Let's see how far the fog has travelled in the first 60 minutes: 0.1 miles/minute * 60 minutes = 6 miles. The remaining distance to cover is 24 miles - 6 miles = 18 miles. At the new speed of 0.05 miles/minute, it will take 18 miles / 0.05 miles/minute = 360 minutes to cover the remaining 18 miles. So the total time to cover 24 miles is the initial 60 minutes + 360 minutes = 420 minutes. Final Answer: The final answer is $\boxed{420}$

Overall Quality: excellent

The reasoning chain correctly identifies the required distance, calculates the initial speed, correctly models the speed reduction after one hour, calculates the distance covered in the first hour, determines the remaining distance, calculates the time needed for the remaining distance at the reduced speed, and sums the times correctly. The final answer matches the ground truth.

✓ No hallucinations detected

Question #10

Clean

Full Question

Ground Truth Answer

Generated Answer

Reformatted Question: A fog bank rolls in from the ocean to cover a city. It takes 25 minutes to cover every 5 miles of the city. However, we know that the wind speed is going to be halved in one hour. If the city is 54 miles across from the oceanfront to the opposite inland edge, how many minutes will it take for the fog bank to cover 1/2 of the city? Answer: The fog initially covers 5 miles in 25 minutes. This means the fog travels at a speed of 5/25 = 0.2 miles per minute . Half the city is 54 * 1/2 = 27 miles . Since the wind speed changes after one hour (60 minutes), we need to calculate how far the fog travels in the first hour. In 60 minutes, the fog travels 0.2 miles/minute * 60 minutes = 12 miles . After 1 hour, the wind speed is halved. The new speed is 0.2 miles/minute / 2 = 0.1 miles/minute . The remaining distance to cover half the city is 27 miles - 12 miles = 15 miles . At the new speed, it will take 15 miles / 0.1 miles/minute = 150 minutes to cover the remaining distance. The total time to cover half the city is the initial 60 minutes plus the additional 150 minutes, which is 60 + 150 = 210 minutes . Final Answer: The final answer is $\boxed{210}$

Overall Quality: excellent

The reasoning chain correctly calculates the initial speed, the distance covered in the first hour, the remaining distance, the reduced speed, the time taken for the remaining distance, and the total time. All arithmetic operations are correct, and the logic follows the problem constraints perfectly.

✓ No hallucinations detected

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Detected Issues (1)

Detected Issues (1)