question string | solution string | model_responses sequence | is_model_response_correct__correctness_reasoning sequence | is_model_response_correct__final_answer sequence | is_model_response_correct__correctness_prompt sequence | is_model_response_correct sequence | args sequence |
|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
95 x 10
Think step by step. | 950 | [
"To solve the long multiplication equation \\(95 \\times 10\\), follow these steps:\n\n1. **Write down the numbers:** Place \\(95\\) at the top and \\(10\\) below it, aligning the digits as shown.\n2. **Multiply each digit of the bottom number by each digit of the top number one at a time.**\n - Multiply \\(10\\)... | [
"The model output provides a detailed step-by-step explanation of multiplying 95 by 10, including the partial calculations and the final answer. It concludes with 'So, 95 × 10 = 950,' which matches the solution provided. The reasoning aligns with standard multiplication procedures and confirms the correctness of th... | [
"950",
"950",
"950",
"",
"950",
"950"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
true,
true,
false,
true,
true
] | [
"10",
"95"
] |
What is the solution to the long multiplication equation below?
54 x 76
Think step by step. | 4104 | [
"To solve \\( 54 \\times 76 \\) using long multiplication, follow these steps:\n\n1. **Write the numbers:** Write 54 and 76 on top of each other to form a multiplication problem.\n\n2. **Multiply 54 by 6 (tens place of 76):**\n - Multiply 54 by 6.\n - 54 × 6 = 324\n\n Write the result (324) under the top line... | [
"The model output attempts to explain the steps of long multiplication but contains inaccuracies. It states that 54 × 6 = 324, which is correct, but then it says 54 × 7 = 378, which is also correct. However, it then mentions adding a 'left-over' from the previous step and combining results in a confusing manner, le... | [
"4064",
"4064",
"4064",
"4104",
"4064",
""
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
false,
false,
false,
true,
false,
false
] | [
"54",
"76"
] |
What is the solution to the long multiplication equation below?
76 x 65
Think step by step. | 4940 | [
"Step 1: Set up the multiplication\n - Multiply the units place of the bottom number by the number in the top row.\n\n 1. 76 (bottom)\n\n x 65 (top)\n ----\n\n Step 2: Multiply the tens place of the bottom number by the number in the top row.\n - Flip the number 65 to 56 and then multiply it b... | [
"The output's final answer is '8360', which is obtained after multiplying 76 by 65, but the solution provided states the answer as '4940'. Since the output's answer does not match the solution, the correctness depends on whether the output's calculation is correct. The output's calculation appears to be incorrect b... | [
"8360",
"",
"8360",
"4860",
"4940",
"4940"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
false,
false,
false,
false,
true,
true
] | [
"65",
"76"
] |
What is the solution to the long multiplication equation below?
81 x 33
Think step by step. | 2673 | [
"Certainly! We can break down the long multiplication process for \\( 81 \\times 33 \\) step by step:\n\n1. **Multiply 33 by 1 (the units place of 81):**\n \\[\n 33 \\times 1 = 33\n \\]\n\n2. **Multiply 33 by 8 (the tens place of 81 and place it in the tens place of the answer because we're multiplying by a t... | [
"The model output states that the solution to 81 x 33 is 297, which is incorrect. The provided solution is 2673, which is the correct product of 81 and 33. The model's reasoning is flawed because it incorrectly sums 33 and 264 to get 297, which does not align with the actual multiplication process. Therefore, the f... | [
"297",
"486",
"297",
"2673",
"(No explicit final answer provided in the output)",
"297"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
false,
true,
false,
true,
false,
false
] | [
"33",
"81"
] |
What is the solution to the long multiplication equation below?
33 x 81
Think step by step. | 2673 | [
"To solve the long multiplication equation 33 x 81, we will break it down into simpler parts.\n\nStep 1: Break down 81 into 80 and 1.\n33 x (80 + 1)\n\nStep 2: Distribute 33 to both 80 and 1 in the equation.\n33 x 80 + 33 x 1\n\nStep 3: Calculate 33 x 80 and 33 x 1.\n33 x 80 = 2,640\n33 x 1 = 33\n\nStep 4: Add the ... | [
"The model output correctly breaks down the multiplication 33 x 81 into parts, calculates each part, and sums them to find the final answer. It explicitly states that 33 x 80 = 2,640 and 33 x 1 = 33, then adds these to get 2,673, which matches the solution provided. The final answer in the output is '2,673', which ... | [
"2,673",
"2,673",
"2673",
"2,673",
"2673",
""
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
true,
true,
true,
true,
false
] | [
"33",
"81"
] |
What is the solution to the long multiplication equation below?
69 x 15
Think step by step. | 1035 | [
"To solve the long multiplication equation \\( 69 \\times 15 \\), follow these steps:\n\n1. **Set Up the Problem**: Write the numbers one below the other and align the digits by place value:\n\n\\[\n\\begin{array}{c@{}c}\n & 69 \\\\\n\\times & 15 \\\\\n\\end{array}\n\\]\n\n2. **Multiply 69 by 5**:\n - Write down ... | [
"The output provides a detailed step-by-step explanation of multiplying 69 by 15, including setting up the problem, multiplying by each digit, and adding partial products. It concludes with the final answer as 405. The solution states that the answer is 1035, which does not match the output's final answer. The outp... | [
"405",
"995",
"405",
"1035",
"1035",
"225"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
false,
true,
false,
true,
true,
false
] | [
"15",
"69"
] |
What is the solution to the long multiplication equation below?
15 x 69
Think step by step. | 1035 | [
"To solve the multiplication problem \\( 15 \\times 69 \\), we can follow these steps:\n\n1. **Break down the multiplication into simpler parts**:\n - First, break 69 into 60 + 9.\n - Now we have multiplication problems: \\( 15 \\times 60 \\) and \\( 15 \\times 9 \\).\n\n2. **Calculate each part separately**:\n... | [
"The model output correctly breaks down the multiplication into parts, calculates each part accurately, and sums them to get 1035, which matches the solution provided. The final answer extracted from the output is '1035', which matches the solution.",
"The output quotes the final answer as '1035' and states that ... | [
"1035",
"1035",
"10350",
"1035",
"1035",
"1035"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
true,
false,
true,
true,
true
] | [
"15",
"69"
] |
What is the solution to the long multiplication equation below?
85 x 58
Think step by step. | 4930 | [
"To solve the long multiplication of 85 x 58, let's break it down step by step:\n\n1. First, we will write 85 and 58 on top of each other.\n\n```\n 85\n x 58\n-------\n```\n\n2. Now we multiply each digit of 85 by 8. We start from the ones place (easier to do mentally initially).\n\n Multiply 5 by 8:\n 5 x... | [
"The model output provides a detailed step-by-step long multiplication process, ultimately arriving at the final answer '4930'. The solution given is also '4930'. Since the model's final answer matches the solution, and the reasoning aligns with the multiplication process, the output is correct.",
"The model outp... | [
"4930",
"7004",
"4930",
"148% of 85, which is 12730",
"5650",
"4930"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
false,
true,
false,
false,
true
] | [
"58",
"85"
] |
What is the solution to the long multiplication equation below?
32 x 35
Think step by step. | 1120 | [
"To solve the multiplication problem step by step:\n\n1. Break down the multiplication into simpler parts:\n 32 x 30 = 32 x 3+5x3\n Here, we add 5 to 3 both times because 5 is in the units (5) and in the tens (50) brackets beside 3.\n\n2. Calculate the first part:\n First 32 x 3 = 96\n Second 32 x (50) = 32... | [
"The output states that the solution to 32 x 35 is 1696, which does not match the provided solution of 1120. The reasoning in the output is flawed because it incorrectly calculates 32 x 50 as 1600 and then adds 96, resulting in 1696, which is incorrect. The correct calculation should be 32 x 35 = (30 + 5) x 32 = (3... | [
"1696",
"The output does not contain a clear, explicit final answer to the multiplication problem.",
"1696",
"1120",
"1120",
"70"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
false,
false,
false,
true,
true,
false
] | [
"32",
"35"
] |
What is the solution to the long multiplication equation below?
69 x 98
Think step by step. | 6762 | [
"Let’s solve 69 × 98 step by step:\n\n1. Break down 98 into 90 + 8.\n\n2. Multiply 69 by 8: \n $$69 \\times 8 = 552$$\n\n3. Multiply 69 by 90:\n $$69 \\times 90 = 6210$$\n\n4. Add the two results together.\n $$552 + 6210 = 6762$$\n\nSo, the solution to 69 × 98 is 6762.\n\n\\boxed{6762",
"Wait, how? 78 x 85 ... | [
"The model output provides a step-by-step calculation that correctly multiplies 69 by 98, resulting in 6762, which matches the solution provided. The final answer quoted in the output is '6762', which is the same as the solution.",
"The model output does not provide a clear answer to the question 'What is 69 x 98... | [
"6762",
"No answer provided",
"Hold on, let me verify this answer.",
"6762",
"6921",
"6762"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
false,
false,
true,
false,
true
] | [
"69",
"98"
] |
What is the solution to the long multiplication equation below?
98 x 69
Think step by step. | 6762 | [
"To solve the long multiplication of \\( 98 \\times 69 \\):\n\n1. **Break down the problem**:\n - \\( 98 \\) times the number formed by subtracting \\( 1 \\) from the ones digit of \\( 69 \\), i.e., \\( (69 - 1)\\) \n - \\( 98 \\times 68 \\)\n\n2. **Further break down**:\n - First, multiply \\( 98 \\) by the... | [
"The model output provides a detailed step-by-step calculation of 98 multiplied by 69, ultimately arriving at the answer 7448. The solution given is 6762, which does not match the model's final answer. Since the model's final answer is 7448, and the solution states 6762, the model's output is incorrect with respect... | [
"7448",
"",
"6622",
"6762",
"7448",
"Wait, how?"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
false,
false,
false,
true,
false,
false
] | [
"69",
"98"
] |
What is the solution to the long multiplication equation below?
78 x 30
Think step by step. | 2340 | [
"To solve the long multiplication equation \\(78 \\times 30\\) step by step:\n\n1. **Multiply 78 by 0 (the units place of 30):**\n \\[\n 78 \\times 0 = 0\n \\]\n This is because any number multiplied by 0 equals 0.\n\n2. **Multiply 78 by 3 (the tens place of 30):**\n \\[\n 78 \\times 3 = 234\n \\]\n ... | [
"The model output correctly performs the multiplication step by step: multiplying 78 by 0 to get 0, then multiplying 78 by 3 to get 234, and then adjusting for the place value (tens) to get 2340. It then adds these results to arrive at 2340, which matches the solution provided. The final answer quoted in the output... | [
"2340",
"The model output does not provide a final answer.",
"2340",
"2340",
"2340",
"2340"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
false,
true,
true,
true,
true
] | [
"30",
"78"
] |
What is the solution to the long multiplication equation below?
78 x 30
Think step by step. | 2340 | [
"To solve the long multiplication equation \\(78 \\times 30\\) step by step:\n\n1. **Multiply 78 by 0 (the units place of 30):**\n \\[\n 78 \\times 0 = 0\n \\]\n This is because any number multiplied by 0 equals 0.\n\n2. **Multiply 78 by 3 (the tens place of 30):**\n \\[\n 78 \\times 3 = 234\n \\]\n ... | [
"The model output correctly performs the multiplication step by step: multiplying 78 by 0 to get 0, then multiplying 78 by 3 to get 234, and then adjusting for the place value (tens) to get 2340. It then adds these results to arrive at 2340, which matches the solution provided. The final answer quoted in the output... | [
"2340",
"The model output does not provide a final answer.",
"2340",
"2340",
"2340",
"2340"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
false,
true,
true,
true,
true
] | [
"30",
"78"
] |
What is the solution to the long multiplication equation below?
49 x 11
Think step by step. | 539 | [
"To solve the multiplication equation \\( 49 \\times 11 \\), we can use the standard algorithm for long multiplication. Here are the steps:\n\n1. **Write the numbers in a grid:**\n ```\n 49\n x11\n ----\n ```\n\n2. **Multiply 49 by 1:**\n \\[\n 49 \\times 1 = 49\n \\]\n Write 49 below the line, al... | [
"The output provides a detailed step-by-step explanation of multiplying 49 by 11, including intermediate calculations and the final addition, concluding with the answer 539. The solution given is 539, which matches the final answer in the output. The reasoning aligns with the solution, and the final answer in the o... | [
"539",
"539",
"539",
"",
"539",
"539"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
true,
true,
false,
true,
true
] | [
"11",
"49"
] |
What is the solution to the long multiplication equation below?
11 x 49
Think step by step. | 539 | [
"To solve the long multiplication equation \\(11 \\times 49\\), we can break it down into simpler steps.\n\nFirst, consider \\(11 \\times 49\\) as:\n\\[11 \\times (50 - 1)\\]\n\nThis is a distributive property of multiplication over addition (or subtraction):\n\\[11 \\times 50 - 11 \\times 1\\]\n\nLet's calculate e... | [
"The model output correctly computes the multiplication step-by-step, breaking down 11 x 49 into 11 x (50 - 1), calculating 11 x 50 as 550, and subtracting 11 to get 539. The final answer quoted is '539', which matches the solution provided. Therefore, the output is correct.",
"The output states 'Final answer: 53... | [
"539",
"539",
"539",
"539",
"539",
"539"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
true,
true,
true,
true,
true
] | [
"11",
"49"
] |
What is the solution to the long multiplication equation below?
36 x 46
Think step by step. | 1656 | [
"To solve the multiplication problem \\(36 \\times 46\\), we can break it down into smaller steps for better understanding and accuracy. Here's the step-by-step process:\n\n1. **Write the numbers in a horizontal manner**: Instead of multiplying them vertically, we can easily break them into smaller numbers and solv... | [
"The output provides a detailed step-by-step solution to the multiplication problem, breaking down 36 x 46 into 36 x 40 + 36 x 6, calculating each part, and summing them to get 1656. The final answer quoted is '1656', which matches the solution provided. Therefore, the output correctly solves the problem and the fi... | [
"1656",
"1656",
"2116",
"1656",
"1656",
"1656"
] | [
"You are given a question, a solution, and a model output. For the current output, reason step by step about whether it is correct with respect to the solution. Quote the relevant parts of the output and explain your reasoning. Parse the final answers value and then return a boolean field 'is_correct' (True if the ... | [
true,
true,
false,
true,
true,
true
] | [
"36",
"46"
] |
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