question string | solution string | eval_internal_cot string | eval_solution string | judge_correct bool | judge_reasoning string | eval_prompt list | eval_steps list | steps_word_count int64 | trace_word_count int64 | word_count_diff int64 | 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 | metadata_answers_correct sequence | metadata_answers_correct_judge_data list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
8274 x 3529
Think step by step. | 29198946 | Okay, so I need to multiply 8274 by 3529. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this step by step. I remember that long multiplication involves breaking down the numbers by each digit and then adding up the results. Let me try to recall the exact process.
First, I should w... | The solution to the long multiplication equation \(8274 \times 3529\) is calculated as follows:
1. **Break down the multiplication by each digit of 3529:**
- **Ones place (9):**
\(8274 \times 9 = 74{,}466\)
- **Tens place (2, shifted one position left):**
\(8274 \times 2 = 16{,}548 \rightarrow 165{... | true | The solution accurately follows the steps of long multiplication and correctly sums the partial products to arrive at the final answer. The calculated answer matches the ground truth solution of 29198946. | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "Okay, so I need to multiply 8274 by 3529. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this step by step. I remember that long multiplication involves breaking down the numbers by each digit and then adding up the results. ... | 1,216 | 1,216 | 0 | gpt-4o-mini | 1. Proposal: "Therefore, 8274 multiplied by 3529 equals 29,198,946." This is a clear final answer proposal. 2. Verification: "Wait, let me verify this with another method to be sure." This indicates a verification process is about to happen. 3. Verification: "Let me recheck the partial products:" This is a continuation... | 5 | [
"29,198,946",
"29,198,946",
"29,198,946",
"29,198,946",
"29,198,946"
] | [
true,
true,
true,
true,
false
] | [
{
"correct": true,
"reasoning": "To evaluate the correctness of the provided solution for the multiplication of 8274 and 3529, we first calculate the product step by step:\n\nWe can multiply 8274 by 3529 using long multiplication:\n\n1. Write 8274 and 3529 for multiplication:\n \n \n 8274\n x 3529\n... | |
"What is the solution to the long multiplication equation below?\n\n9341 x 4130\n\nThink step by ste(...TRUNCATED) | 38578330 | "Okay, so I need to solve 9341 multiplied by 4130. Hmm, let me think about how to approach this. I r(...TRUNCATED) | "The solution to the long multiplication equation 9341 × 4130 is calculated as follows:\n\n1. **Bre(...TRUNCATED) | true | "The calculations presented in the solution are accurate, and the final result matches the ground tr(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to solve 9341 multiplied by 4130. Hmm, le(...TRUNCATED) | 929 | 936 | 7 | gpt-4o-mini | "1. Proposal: \"So the total of 9341 x 413 is 3,857,833.\" This is a final answer for the multiplica(...TRUNCATED) | 5 | [
"3,857,833",
"38,578,330",
"38,578,330",
"38,578,330",
"38,578,330"
] | [
false,
false,
false,
false,
false
] | [{"correct":false,"reasoning":"To evaluate the solution for the multiplication of 9341 x 4130, we sh(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n6637 x 5510\n\nThink step by ste(...TRUNCATED) | 36569870 | "Okay, so I need to multiply 6637 by 5510. Hmm, let's see. I remember that long multiplication invol(...TRUNCATED) | "To solve the long multiplication equation \\(6637 \\times 5510\\), we can break down the process in(...TRUNCATED) | true | "The solution provided calculates the product of 6637 and 5510 accurately by breaking down the multi(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 6637 by 5510. Hmm, let's see.(...TRUNCATED) | 878 | 1,300 | 422 | gpt-4o-mini | "1. Proposal: 'Therefore, the answer should be 36,569,870.' This is a clear final answer proposal. 2(...TRUNCATED) | 6 | [
"36,569,870",
"36,569,870",
"36,569,870",
"36,569,870",
"36,569,870",
"36,569,870"
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false,
false,
true,
true,
true,
true
] | [{"correct":false,"reasoning":"To verify the solution, we need to properly multiply 6637 by 5510. Th(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n5086 x 6642\n\nThink step by ste(...TRUNCATED) | 33781212 | "Okay, so I need to multiply 5086 by 6642. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(5086 \\times 6642\\), we break down the multiplication(...TRUNCATED) | true | "The provided solution correctly implements the long multiplication method. Each step of the multipl(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 5086 by 6642. Hmm, that's a p(...TRUNCATED) | 1,623 | 2,657 | 1,034 | gpt-4o-mini | "1. Proposal: The model states, \"So 5086 x 2 = 10172.\" This is a final answer for the first multip(...TRUNCATED) | 10 | ["10172","10172","203440","203440","3051600","3051600","30516000","30516000","33781212","33781212","(...TRUNCATED) | [
false,
false,
false,
false,
false,
false,
false,
false,
true,
true,
false,
true,
true,
true,
true
] | [{"correct":false,"reasoning":"To evaluate the correctness of the provided solution, we need to perf(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n8996 x 8373\n\nThink step by ste(...TRUNCATED) | 75323508 | "Okay, so I need to multiply 8996 by 8373. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(8996 \\times 8373\\), we break down the multiplication(...TRUNCATED) | true | "The solution correctly calculates the product of 8996 and 8373 using both the long multiplication m(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 8996 by 8373. Hmm, that's a p(...TRUNCATED) | 1,005 | 1,302 | 297 | gpt-4o-mini | "1. Proposal: 'So the final result is 75,323,508.' - This is a clear final answer proposal. 2. Verif(...TRUNCATED) | 6 | [
"75,323,508",
"75,323,508",
"75,323,508",
"75,323,508",
"75,323,508",
"75,323,508"
] | [
false,
true,
false,
true,
false,
true
] | [{"correct":false,"reasoning":"The solution provided, 75,323,508, includes a comma which makes it fo(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n9275 x 6116\n\nThink step by ste(...TRUNCATED) | 56725900 | "Okay, so I need to multiply 9275 by 6116. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(9275 \\times 6116\\), we can break down the multiplier(...TRUNCATED) | true | "The solution correctly breaks down the multiplication of 9275 by each part of 6116, calculates each(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 9275 by 6116. Hmm, that's a p(...TRUNCATED) | 1,177 | 1,617 | 440 | gpt-4o-mini | "1. Proposal: The model states, \"So, the total is 56,725,900. That matches the previous result. So,(...TRUNCATED) | 5 | [
"56,725,900",
"56,725,900",
"56,725,900",
"56,725,900",
"56,725,900"
] | [
true,
false,
true,
true,
false
] | [{"correct":true,"reasoning":"The provided solution of 56,725,900 and the ground truth solution of 5(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n1556 x 1996\n\nThink step by ste(...TRUNCATED) | 3105776 | "Okay, so I need to multiply 1556 by 1996. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(1556 \\times 1996\\), we can use the distributive prop(...TRUNCATED) | true | "The solution correctly applies the distributive property to simplify the multiplication, accurately(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 1556 by 1996. Hmm, that's a p(...TRUNCATED) | 961 | 1,026 | 65 | gpt-4o-mini | "1. Proposal: 'So, the result of 1556 × 1996 is 3,105,776.' - This is a clear final answer proposal(...TRUNCATED) | 5 | [
"3105776",
"3105776",
"3105776",
"3105776",
"3105776"
] | [
true,
true,
true,
true,
true
] | [{"correct":true,"reasoning":"To check the correctness of the solution, we can perform the long mult(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n3622 x 5165\n\nThink step by ste(...TRUNCATED) | 18707630 | "Okay, so I need to multiply 3622 by 5165. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(3622 \\times 5165\\), we can break down the multiplier(...TRUNCATED) | true | "The provided solution correctly performs the long multiplication of 3622 and 5165 by breaking down (...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 3622 by 5165. Hmm, that's a p(...TRUNCATED) | 875 | 1,636 | 761 | gpt-4o-mini | "1. Proposal: \"So the total is 18,707,630.\" This is a clear final answer proposal. 2. Verification(...TRUNCATED) | 5 | [
"18707630",
"18707630",
"18707630",
"18707630",
"18707630"
] | [
true,
true,
true,
true,
true
] | [{"correct":true,"reasoning":"To verify the solution to the multiplication of 3622 by 5165, we can p(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n6624 x 7409\n\nThink step by ste(...TRUNCATED) | 49077216 | "Okay, so I need to multiply 6624 by 7409. Hmm, that's a pretty big multiplication. Let me think abo(...TRUNCATED) | "To solve the long multiplication equation \\(6624 \\times 7409\\), we break down the multiplication(...TRUNCATED) | true | "The breakdown of the multiplication is accurately executed, and the final sum of the products yield(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 6624 by 7409. Hmm, that's a p(...TRUNCATED) | 1,346 | 2,091 | 745 | gpt-4o-mini | "1. Proposal of final answer: \"So, putting it all together, 6624 x 7409 = 49,077,216.\" This is a c(...TRUNCATED) | 5 | [
"49,077,216",
"49,077,216",
"49,077,216",
"49,077,216",
"49,077,216"
] | [
true,
true,
true,
true,
false
] | [{"correct":true,"reasoning":"To verify the multiplication, we multiply 6624 by 7409 step by step. W(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n2861 x 2656\n\nThink step by ste(...TRUNCATED) | 7598816 | "Okay, so I need to multiply 2861 by 2656. Hmm, that's a pretty big multiplication problem. Let me t(...TRUNCATED) | "To solve the long multiplication equation \\(2861 \\times 2656\\), we break down the multiplication(...TRUNCATED) | true | "The solution correctly breaks down the long multiplication into manageable parts, accurately calcul(...TRUNCATED) | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | [{"contains_final_answer":false,"content":"Okay, so I need to multiply 2861 by 2656. Hmm, that's a p(...TRUNCATED) | 921 | 1,466 | 545 | gpt-4o-mini | "1. Proposal of final answer: \"So, the total sum is 7,598,816.\" This is a clear proposal of the fi(...TRUNCATED) | 5 | [
"7598816",
"7598816",
"7598816",
"7598816",
"7598816"
] | [
true,
true,
true,
true,
true
] | [{"correct":true,"reasoning":"To evaluate the correctness of the provided solution, we compare it wi(...TRUNCATED) |
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