question string | solution string | eval_prompt string | eval_internal_cot string | eval_solution string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | model_name string | measurement_answer_verification_reasoning string | measurement_answer_verification_final_count int64 | measurement_answer_verification_metadata sequence | measurement_answer_verification_raw_response string | extracted_answer_values sequence | measurement_answer_verification_final_recount int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | 2893883677558701 | What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | Okay, so I need to multiply 97,511,989 by 29,677,209. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts can make the multiplication easier. Maybe using the distributive property, like splitting each number i... | To solve the long multiplication equation \(97,511,989 \times 29,677,209\), we can break down each number into smaller parts and use the distributive property. Here are the key steps:
1. **Break down the numbers:**
- \(97,511,989 = 97,000,000 + 511,989\)
- \(29,677,209 = 29,000,000 + 677,209\)
2. **Use the dist... | What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | true | The solution provided correctly follows the steps of multiplication using the distributive property, and the final result matches the ground truth solution. | gpt-4o-mini | 1. Proposal of final answer: 'Therefore, the solution to 97,511,989 multiplied by 29,677,209 is 2,893,883,677,558,701.' This is a clear conclusion of the entire reasoning process. 2. Verification of the final answer: 'But let me check that addition again.' This indicates a desire to confirm the accuracy of the final an... | 8 | [
"Final answer proposed: 2,893,883,677,558,701",
"Verification steps taken: 7",
"Total instances of proposals and verifications: 8"
] | [
"2,893,883,677,558,701"
] | 1 | |
What is the solution to the long multiplication equation below?
39634656 x 65995812
Think step by step. | 2615721306060672 | What is the solution to the long multiplication equation below?
39634656 x 65995812
Think step by step. | Okay, so I need to multiply these two big numbers: 39,634,656 and 65,995,812. Hmm, that's a huge multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. But doing this manually... | To solve the long multiplication equation \(39,634,656 \times 65,995,812\), we can break down the problem using the distributive property and verify the result through multiple methods.
1. **Approximation and Adjustment**:
- Recognize that \(65,995,812\) is close to \(66,000,000\).
- Express \(65,995,812\) as \... | What is the solution to the long multiplication equation below?
39634656 x 65995812
Think step by step. | true | The solution provided accurately follows the steps for long multiplication using the distributive property, and the final result matches the ground truth solution exactly. | gpt-4o-mini | 1. Proposal of final answer: 'Therefore, 2,615,722,296,000,000 - 165,989,939,328 = 2,615,722,305,060,672' - This is a clear proposal of the final answer after performing the calculations. 2. Verification of final answer: 'Wait, let me check that subtraction again. Maybe I made a mistake here.' - This indicates a verifi... | 10 | [
"Final answer proposed: 2,615,722,305,060,672",
"Verification steps taken to confirm the final answer",
"Final answer confirmed after verification",
"Multiple checks on subtraction accuracy",
"Final answer restated after verification",
"Final answer proposed: 2,615,721,306,060,672",
"Verification steps ... | [
"2,615,722,305,060,672",
"2,615,721,306,060,672",
"2,615,721,306,060,672"
] | 3 | |
What is the solution to the long multiplication equation below?
24755057 x 57601784
Think step by step. | 1425935446221688 | What is the solution to the long multiplication equation below?
24755057 x 57601784
Think step by step. | Okay, so I need to multiply 24,755,057 by 57,601,784. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts might help. Maybe using the distributive property? Like, split each number into parts that are easier t... | To solve the long multiplication equation \(24755057 \times 57601784\), we can break down each number into smaller parts and use the distributive property \((a + b)(c + d) = ac + ad + bc + bd\).
1. **Split the numbers:**
- \(24755057 = 24000000 + 755057\)
- \(57601784 = 57000000 + 601784\)
2. **Compute each par... | What is the solution to the long multiplication equation below?
24755057 x 57601784
Think step by step. | true | The provided solution accurately follows the steps of long multiplication, correctly applying the distributive property to break down the numbers into manageable parts. Each calculation of the constituent parts is correct, leading to an accurate final sum that matches the ground truth solution. | gpt-4o-mini | 1. Proposal of final answer: "So the final result is 1,425,935,446,221,688." This is a clear conclusion of the calculation process. 2. Verification of final answer: "But let me check once more for any possible errors in the intermediate steps." This indicates a double-checking of the previously proposed answer. 3. Veri... | 6 | [
"Final answer proposed: 1,425,935,446,221,688",
"First verification: checking for errors in intermediate steps",
"Second verification: confirming correctness of the final answer",
"Third verification: checking formatting of the final answer",
"Reiteration of final answer: 1,425,935,446,221,688",
"Final co... | [
"1,425,935,446,221,688",
"1,425,935,446,221,688"
] | 2 | |
What is the solution to the long multiplication equation below?
53563670 x 33752847
Think step by step. | 1807926358268490 | What is the solution to the long multiplication equation below?
53563670 x 33752847
Think step by step. | Okay, so I need to multiply 53,563,670 by 33,752,847. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. Let me recall: when you have two numbers,... | The solution to the long multiplication equation \(53,\!563,\!670 \times 33,\!752,\!847\) is calculated by breaking down the numbers into manageable parts, using distributive properties, and verifying through multiple methods. Here's the step-by-step breakdown:
1. **Breakdown and Multiplication**:
- Split \(53,\!56... | What is the solution to the long multiplication equation below?
53563670 x 33752847
Think step by step. | true | The solution provided correctly follows a detailed breakdown of the long multiplication process, accurately computes each component, sums them correctly, and confirms the result through multiple methods. The final computed result matches the ground truth solution. | gpt-4o-mini | 1. Proposal of final answer: 'Therefore, the product of 53,563,670 and 33,752,847 is 1,807,926,358,268,490.' This is a clear conclusion stating the final answer. 2. Verification of the result: 'Wait, let me verify this result. Let me check the addition steps again to ensure there are no errors.' This indicates a verifi... | 5 | [
"Final answer proposed: 1,807,926,358,268,490",
"First verification of the answer",
"Second verification of the answer",
"Third verification of the answer",
"Final confirmation of the answer"
] | [
"1,807,926,358,268,490",
"1,807,926,358,268,490",
"1,807,926,358,268,490",
"1,807,926,358,268,490",
"1,807,926,358,268,490"
] | 5 | |
What is the solution to the long multiplication equation below?
81471995 x 26159399
Think step by step. | 2131258424531005 | What is the solution to the long multiplication equation below?
81471995 x 26159399
Think step by step. | Okay, so I need to multiply 81,471,995 by 26,159,399. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts might make it easier. Maybe using the distributive property? Like, splitting each number into parts tha... | The solution to the long multiplication equation \(81471995 \times 26159399\) is calculated by breaking down both numbers into smaller, manageable parts and using the distributive property (FOIL method). Here's the step-by-step breakdown:
1. **Split the numbers**:
- \(81471995 = 80000000 + 1471995\)
- \(26159399... | What is the solution to the long multiplication equation below?
81471995 x 26159399
Think step by step. | true | The original solution accurately follows the long multiplication process and performs the arithmetic correctly across each step, leading to a final result that matches the ground truth solution. | gpt-4o-mini | 1. Proposal of final answer: 'Therefore, 81,471,995 x 26,159,399 = 2,131,258,424,531,005.' This is a clear conclusion of the multiplication problem, marking the first count.
2. Verification of final answer: 'But wait, let me cross-verify this result to ensure I didn't make any arithmetic errors.' This indicates the mo... | 8 | [
"Final answer proposed: 2,131,258,424,531,005",
"First verification: cross-verify result",
"Second verification: confirming addition result",
"Third verification: modulo 9 check",
"Fourth verification: modulo 11 check",
"Final answer proposed: 2,131,258,424,531,005",
"Verification through modulo 11 chec... | [
"2,131,258,424,531,005",
"2,131,258,424,531,005"
] | 2 |
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