question stringclasses 5
values | solution stringclasses 5
values | eval_prompt stringclasses 5
values | eval_internal_cot stringclasses 1
value | eval_solution stringclasses 5
values | raw_eval_prompt stringclasses 5
values | judge_correct bool 1
class | judge_reasoning stringclasses 5
values | model_name stringclasses 1
value | measurement_answer_verification_reasoning stringclasses 5
values | measurement_answer_verification_final_count int64 1 5 | measurement_answer_verification_metadata sequencelengths 1 5 | measurement_answer_verification_raw_response stringclasses 1
value | extracted_answer_values sequencelengths 1 5 | measurement_answer_verification_final_recount int64 1 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | 43351525 | What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | To solve the long multiplication equation \( 5761 \times 7525 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7525)
We can express \( 7525 \) as \( 8000 - 475 \). This allows us to rewrite the multiplic... | What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | true | The solution accurately followed the steps of breaking down the multiplication using the distributive property, calculated the intermediate products correctly, and performed the final subtraction accurately. The format of the answer is consistent with the ground truth solution, confirming its correctness. | gpt-4o-mini | 1. Proposal of final answer: The model states, "Final Answer: \boxed{43,351,525}" which is a clear proposal of the final answer to the multiplication problem. This counts as the first instance. 2. Verification of final answer: After proposing the final answer, the model does not explicitly verify it in the trace. Howev... | 2 | [
"Final answer proposed: 43,351,525",
"Verification through calculation steps leading to the final answer."
] | [
"43,351,525"
] | 1 | ||
What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | 28275338 | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | To solve the long multiplication equation \(7826 \times 3613\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7826\) by each digit of \(3613\) (considering their place values) and then add the results together.
### Step 1: Break down t... | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | true | The solution provided correctly follows the procedure for long multiplication using the distributive property, and the calculations are accurate. The final result matches the ground truth solution. | gpt-4o-mini | 1. Proposal of final answer: The model states, "Final Answer: \[\boxed{28,275,338}\]" which is a clear proposal of the final answer. This counts as the first instance. 2. Verification of final answer: The model then verifies the answer using the standard long multiplication method, stating, "For additional clarity, let... | 3 | [
"Final answer proposed: 28,275,338",
"Verification method used: standard long multiplication",
"Total verifications: 2"
] | [
"28,275,338",
"28,275,338"
] | 2 | ||
What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | 56187703 | What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | To solve the multiplication problem \( 8767 \times 6409 \), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6409 \) as \( 6000 + 400 + 0 + 9 \). This allows us to multiply \( 8767 \) by each component separately a... | What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | true | The solution correctly performed long multiplication by breaking down the number 6409 and then computing each component. The addition of all partial results was accurately performed, resulting in the correct final product of 56187703. The boxed format is maintained properly. | gpt-4o-mini | The trace concludes with a clear final answer: 'Final result: 56,187,703'. This statement directly presents the solution to the multiplication problem, which counts as a proposal of a final answer. | 1 | [
"Final answer proposed: 56,187,703"
] | [
"56,187,703"
] | 1 | ||
What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | 19863352 | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall... | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | true | The solution provided by the judge correctly calculates the product of 5,266 and 3,772 and achieves the same result as the ground truth solution, which is 19,863,352. All steps of the multiplication, addition of partial results, and alternative methods were accurately executed. The final numerical representation was al... | gpt-4o-mini | 1. Proposal of final answer: 'the product of 5,266 and 3,772 is: \boxed{1.9863352 \times 10^7} or 19,863,352.' This is a clear conclusion of the entire reasoning process. 2. Verification of the final answer: 'This matches our previous result, confirming the accuracy of our calculation.' This checks the final answer aga... | 5 | [
"Final answer proposed: 19,863,352",
"First verification: matches previous result",
"Second verification: consistent with previous calculations",
"Third verification: confidence in final answer after multiple checks",
"Final answer reiterated at the end"
] | [
"19,863,352",
"19,863,352",
"19,863,352",
"19,863,352",
"19,863,352"
] | 5 | ||
What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | 28859852 | What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | To solve the long multiplication equation \( 8764 \times 3293 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8764 \) by each digit of \( 3293 \) (starting from the right) and then sum the results, taking into account the place value... | What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | true | The provided solution correctly computes the multiplication of 8764 and 3293 using the distributive property and confirms the result with long multiplication. The final answer matches the ground truth (28859852), albeit with formatting differences (commas vs. no commas). Thus, the answer is correct. | gpt-4o-mini | 1. Proposal of final answer: The model states, "The result matches, confirming the solution." This indicates that the final answer is being proposed as correct. 2. Verification of final answer: The model then states, "To ensure accuracy, let's verify using another method..." and proceeds to perform the verification ste... | 3 | [
"Final answer proposed: 28,859,852",
"First verification: using standard long multiplication",
"Second verification: confirming the solution matches"
] | [
"28,859,852",
"28,859,852",
"28,859,852"
] | 3 |
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