question string | solution string | model_responses list | is_model_response_correct__correctness_reasoning list | is_model_response_correct__final_answer list | is_model_response_correct__correctness_prompt list | is_model_response_correct list | args list |
|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
94 x 74
Think step by step. | 6956 | [
"To solve the long multiplication problem \\( 94 \\times 74 \\), follow these steps:\n\n1. **Calculate the product of the rightmost digits (units place) of both numbers:**\n \\[\n 4 \\times 4 = 16\n \\]\n Write down the 6 and carry over the 1 to the next column.\n\n2. **Calculate the product of the rightmos... | [
"The solution provided states that the answer to 94 multiplied by 74 is 6956, but the detailed calculation in the model output concludes with 6996. The model's detailed steps and the final boxed answer both indicate 6996, which matches the calculation. Therefore, the final answer in the solution (6956) does not mat... | [
"6956",
"",
"6996",
"6996",
"6596",
"1226"
] | [
"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,
true,
true,
false,
false
] | [
"74",
"94"
] |
What is the solution to the long multiplication equation below?
31 x 41
Think step by step. | 1271 | [
"To solve the long multiplication of 31 x 41, break it down into aquadogmatic territory:\n\n1. Multiply units: \\(1 \\times 1 = 1\\)\n2. Next, consider tens in both numbers and add an imagined zero: \n - Tens in 31 is 30,\n - Tens in 41 is 40.\n - Now multiply them imaginatively: \\(30 \\times 40 = 1200\\)\n3... | [
"The output provides a step-by-step calculation that concludes with the answer 1201. The solution states the correct answer as 1271, so the output's final answer does not match the solution. Therefore, the output is incorrect.",
"The model output contains a boxed number '1201', which appears to be the final answe... | [
"1201",
"1201",
"71",
"1271",
"1271",
"1571"
] | [
"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
] | [
"31",
"41"
] |
What is the solution to the long multiplication equation below?
41 x 31
Think step by step. | 1271 | [
"To solve the long multiplication problem: \\(41 \\times 31\\), we follow these steps:\n\n1. Multiply the top number (41) by the tens digit of the bottom number (1x10): \\(41 \\times 10 = 410\\).\n2. Multiply the top number by the ones digit of the bottom number (the non-zero digit, since we're dealing with a \"1\"... | [
"The model output concludes that the answer is 533, based on the steps it described. However, the solution provided for the multiplication of 41 and 31 is 1271, which is the correct answer. Therefore, the model's final answer does not match the solution.",
"The model output does not provide a final answer; it onl... | [
"533",
"Hold on, let me verify this answer.",
"1271",
"1271",
"533",
""
] | [
"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,
true,
true,
false,
false
] | [
"31",
"41"
] |
What is the solution to the long multiplication equation below?
48 x 64
Think step by step. | 3072 | [
"To solve the long multiplication equation 48 x 64, let's break it down step by step:\n\n1) First, write the numbers vertically:\n```\n 48\nx 64\n```\n\n2) Multiply 48 by 4 (the ones place of 64):\n ```\n 192\n ```\n Put this number inside the box below 48.\n\n3) Multiply 48 by 6 (the tens place of 64). ... | [
"The solution provided in the solution section is 3072, but the model output concludes the answer is 2352. The model's reasoning shows the calculation steps leading to 2352, which matches the correct multiplication of 48 and 64. Therefore, the model output's final answer is 2352, which does not match the solution's... | [
"2352",
"2352",
"2072",
"30,240",
"2352",
"2352"
] | [
"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,
false,
false
] | [
"48",
"64"
] |
What is the solution to the long multiplication equation below?
48 x 64
Think step by step. | 3072 | [
"To solve the long multiplication equation 48 x 64, let's break it down step by step:\n\n1) First, write the numbers vertically:\n```\n 48\nx 64\n```\n\n2) Multiply 48 by 4 (the ones place of 64):\n ```\n 192\n ```\n Put this number inside the box below 48.\n\n3) Multiply 48 by 6 (the tens place of 64). ... | [
"The solution provided in the solution section is 3072, but the model output concludes the answer is 2352. The model's reasoning involves multiplying 48 by 4 to get 192, and then multiplying 48 by 6 to get 288, which, when shifted appropriately, results in 2480. Adding 192 and 2480 gives 2672, not 2352. Therefore, ... | [
"2352",
"2352",
"2072",
"30,240",
"2352",
"2352"
] | [
"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,
false,
false
] | [
"48",
"64"
] |
What is the solution to the long multiplication equation below?
69 x 66
Think step by step. | 4554 | [
"To solve the long multiplication of 69 x 66, we follow these steps:\n\nStep 1: Multiply 69 by 6 and then add the result to another 69.\n\n69 x 6 = 414\n\nNow, we add this to 69 another time.\n\n414 + 69 = 483\n\nSo, the solution to the long multiplication equation 69 x 66 is 483.",
"But according to another sour... | [
"The model output states that the solution to 69 x 66 is 483, which differs from the provided solution of 4554. The model's reasoning involves multiplying 69 by 6 to get 414, then adding 69 to get 483, which is incorrect for the original multiplication problem.",
"The model output discusses alternative solutions ... | [
"483",
"483",
"4614",
"4314",
"",
"483"
] | [
"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
] | [
"66",
"69"
] |
What is the solution to the long multiplication equation below?
58 x 13
Think step by step. | 754 | [
"To solve the multiplication equation \\(58 \\times 13\\), we can break the problem down into two simpler steps:\n\n1. Multiply 58 by 3 (the ones place of 13).\n \\[\n 58 \\times 3 = 174\n \\]\n\n2. Multiply 58 by 10 (the tens place of 13, which is the same as moving the 10 to the front of the result).\n \\... | [
"The output states that the solution to 58 x 13 is 754, which matches the provided solution. The reasoning in the output correctly breaks down the multiplication into two steps: multiplying 58 by 3 to get 174, and multiplying 58 by 10 to get 580, then adding these to get 754. The final answer quoted is '754', which... | [
"754",
"638",
"-754",
"1804",
"754",
"(No numerical answer provided)"
] | [
"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,
true,
false
] | [
"13",
"58"
] |
What is the solution to the long multiplication equation below?
20 x 80
Think step by step. | 1600 | [
"To solve the long multiplication equation \\(20 \\times 80\\), let's break it down step by step:\n\n1. Write down the numbers to be multiplied on a vertical basis:\n \\[\n \\begin{array}{c@{}c}\n & 20 \\\\\n & \\times 80 \\\\\n \\end{array}\n \\]\n\n2. Multiply 20 by 0 (the units digit of 80):\n \\[\... | [
"The model output provides a detailed step-by-step explanation of multiplying 20 by 80, including partial calculations and the final answer. It concludes with 'Thus, the solution to the equation 20 x 80 is 1600,' which matches the solution provided. The final answer extracted from the output is '1600,' which aligns... | [
"1600",
"1600",
"1600",
"1600",
"",
"1600"
] | [
"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,
false,
true
] | [
"20",
"80"
] |
What is the solution to the long multiplication equation below?
80 x 20
Think step by step. | 1600 | [
"To solve the long multiplication equation \\(80 \\times 20\\), let's break it down step by step:\n\n1. **Understand the problem**: We need to multiply 80 by 20.\n \n2. **Long multiplication concept**: When you multiply two numbers, you can line them up vertically and multiply each digit place in one number by ea... | [
"The output states that the solution to 80 x 20 is 160, which matches the provided solution. The reasoning in the output correctly explains the multiplication process, including breaking down the multiplication and combining the results.",
"The model output states that the answer is 160, which matches the solutio... | [
"160",
"160",
"The output does not contain a final answer; it only discusses the multiplication process.",
"160",
"160",
"1600"
] | [
"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,
false,
false,
true
] | [
"20",
"80"
] |
What is the solution to the long multiplication equation below?
66 x 97
Think step by step. | 6402 | [
"To solve the multiplication equation \\( 66 \\times 97 \\), you can follow these steps:\n\n1. **Multiply 66 by the units digit of 97**: \n - 66 x 7 = 462\n\n2. **Multiply 66 by the tens digit of 97**: \n - 66 x 9 = 594\n - Since 97 has one '0' in the tens place, this is equivalent to multiplying 660 by 7, wh... | [
"The model output concludes that the product of 66 and 97 is 5082, based on the step-by-step calculation provided. The solution given is 6402, which does not match the model's computed answer. Therefore, the model's final answer is incorrect with respect to the solution.",
"The model output provides a detailed lo... | [
"5082",
"6022",
"6422",
"5082",
"6462",
"6402"
] | [
"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,
false,
true
] | [
"66",
"97"
] |
What is the solution to the long multiplication equation below?
97 x 66
Think step by step. | 6402 | [
"Step 1: Multiply the units digits\n97 × 6 = 582\n\nStep 2: Multiply the tens digit of the first number by the hundreds digit of the second number\n9 × 66 = 594\n\nStep 3: TAM (That's a_match) the digits\n582\n+594\n-------\n 654\n\nSo, 97 × 66 = 654",
"Wait, this result is too large. Let'scheck our work.\n\nStep... | [
"The model output provides a step-by-step calculation resulting in 654, which does not match the solution 6402. The steps and calculations are inconsistent and incorrect for the multiplication of 97 by 66.",
"The model output concludes with '97 × 66 = 654', which is the final answer provided in the output. The so... | [
"654",
"654",
"6540",
"654",
"654",
"654"
] | [
"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,
false,
false
] | [
"66",
"97"
] |
What is the solution to the long multiplication equation below?
45 x 65
Think step by step. | 2925 | [
"\\boxed{2925}",
"Wait, how? The long multiplication step by step:\n\n 1. Multiply 45 by 5 (the ones digit of the second number): 45 x 5 = 225.\n 2. Multiply 45 by 60 (the tens digit of the second number). You can either break this down further to 45 x 6 x 10, which gives 270 x 10 = 2700, or multiply 45 by 6 an... | [
"The model output is '\boxed{2925}', which directly presents the answer. The solution provided is 2925, matching the model output. Since the output is a boxed version of the number 2925, and the solution is 2925, the answer appears correct.",
"The output provides a detailed step-by-step explanation of the long mu... | [
"2925",
"2925",
"2925",
"2925",
"2925",
"79"
] | [
"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
] | [
"45",
"65"
] |
What is the solution to the long multiplication equation below?
12 x 55
Think step by step. | 660 | [
"To solve the long multiplication equation 12 x 55, we can break it down into smaller steps.\n\nStep 1: Multiply 5 and 12.\n5 x 12 = 60\n\nStep 2: Multiply 50 and 12.\n50 x 12 = 600\n\nStep 3: Add the results from step 1 and step 2.\n60 + 600 = 660\n\nSo, the solution to the long multiplication equation 12 x 55 is ... | [
"The model output concludes with 'So, the solution to the long multiplication equation 12 x 55 is 660,' which matches the provided solution '660.' The reasoning steps provided are correct and lead to the same final answer.",
"The model output confirms the solution by performing the multiplication step-by-step and... | [
"660",
"660",
"720",
"660",
"660",
"660"
] | [
"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
] | [
"12",
"55"
] |
What is the solution to the long multiplication equation below?
16 x 83
Think step by step. | 1328 | [
"To solve \\( 16 \\times 83 \\), you can use the standard multiplication method:\n\n1. Multiply the units digits: \\( 6 \\times 3 = 18 \\).\n2. Multiply the second digit of the number you are multiplying by the first digit of the other number (including a zero for the place it's supposed to take): \\( 6 \\times 8 =... | [
"The solution states that the answer to 16 x 83 is 1328. The model output, however, concludes that 16 x 83 = 498, which does not match the solution. The model's reasoning involves multiplying 16 and 83 step by step, but the calculations provided are incorrect, leading to an incorrect final answer.",
"The model ou... | [
"498",
"1328",
"496",
"498",
"4988",
"1760"
] | [
"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,
false,
false,
false
] | [
"16",
"83"
] |
What is the solution to the long multiplication equation below?
62 x 80
Think step by step. | 4960 | [
"Step 1: Understand the multiplication\nTo solve the multiplication problem, we need to multiply the numbers given in the problem: 62 and 80.\n\nStep 2: Multiply the ones digit\n62 x 0 = 0\nExplanation: Any number multiplied by 0 equals 0.\n\nStep 3: Multiply the tens digit\n62 x 8 = 496\nExplanation: 62 x 8 = 496,... | [
"The output concludes that 62 x 80 = 4960, which matches the solution provided. The reasoning steps in the output correctly multiply 62 by 80, breaking it down into 62 x 0 and 62 x 8, then summing appropriately. The final answer quoted is '4960', which aligns with the solution.",
"The model output questions the c... | [
"4960",
"4960",
"4976",
"4960",
"4960",
""
] | [
"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,
false
] | [
"62",
"80"
] |
What is the solution to the long multiplication equation below?
80 x 62
Think step by step. | 4960 | [
"To solve this problem, we can use long multiplication, as shown below:\n\n **80** * **62**\n **1600** (80 * 2)\n**5600** (80 * 60, shifted one place to the left)\n\nTherefore, the product of **80 x 62** is **4960**.",
"Wait, let me try to break this down differently using actual numbers:\n\n- 80 times 2 is 160... | [
"The model output states that the product of 80 and 62 is 4960, which matches the solution provided. The reasoning in the output correctly performs the multiplication: 80 * 2 = 160, and 80 * 60 = 4800, then summing these gives 160 + 4800 = 4960.",
"The model output provides a detailed breakdown of the multiplicat... | [
"4960",
"4960",
"4960",
"3,360",
"7600",
"4960"
] | [
"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,
false,
true
] | [
"62",
"80"
] |
What is the solution to the long multiplication equation below?
80 x 62
Think step by step. | 4960 | [
"To solve this problem, we can use long multiplication, as shown below:\n\n **80** * **62**\n **1600** (80 * 2)\n**5600** (80 * 60, shifted one place to the left)\n\nTherefore, the product of **80 x 62** is **4960**.",
"Wait, let me try to break this down differently using actual numbers:\n\n- 80 times 2 is 160... | [
"The model output concludes that the product of 80 and 62 is 4960, which matches the solution provided. The reasoning steps include multiplying 80 by 2 to get 160, and 80 by 60 to get 4800, then summing these to get 4960.",
"The model output provides a detailed step-by-step calculation: 80 times 2 equals 160, and... | [
"4960",
"4960",
"4960",
"3,360",
"7600",
"4960"
] | [
"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,
false,
true
] | [
"62",
"80"
] |
What is the solution to the long multiplication equation below?
94 x 53
Think step by step. | 4982 | [
"To solve the long multiplication problem \\(94 \\times 53\\), we can break it down into a series of steps, specifically:\n\n1. **Multiply the number by the units place of the other number:**\n - Multiply 94 by 3:\n \\[\n 94 \\times 3 = 282\n \\]\n\n2. **Move to the tens place:**\n - Multiply 94 by ... | [
"The model output correctly performs the long multiplication step-by-step, arriving at the final answer of 4982, which matches the provided solution. The reasoning explicitly details the multiplication of 94 by 3 and 5, including the place value adjustments, and sums the partial products to get 4982.",
"The model... | [
"4982",
"",
"4982",
"4982",
"4982",
"5102"
] | [
"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
] | [
"53",
"94"
] |
What is the solution to the long multiplication equation below?
53 x 94
Think step by step. | 4982 | [
"To solve the long multiplication equation \\( 53 \\times 94 \\), we follow these steps:\n\n1. **Break down the multiplication using the distributive property**:\n \\[\n 53 \\times 94 = 53 \\times (90 + 4)\n \\]\n \n2. ** Distribute \\( 53 \\) to both terms inside the parentheses**:\n \\[\n 53 \\t... | [
"The model output correctly computes the multiplication step-by-step, breaking down 53 x 94 into 53 x (90 + 4), then calculating 53 x 90 as 4770 and 53 x 4 as 212, and finally adding these to get 4982. The final answer quoted is '4982', which matches the solution provided. Therefore, the output is correct.",
"The... | [
"4982",
"4982",
"4972",
"4982",
"4982",
""
] | [
"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,
false
] | [
"53",
"94"
] |
What is the solution to the long multiplication equation below?
70 x 33
Think step by step. | 2310 | [
"To solve the long multiplication equation 70 x 33, you can break it down into smaller parts or use the standard long multiplication method. Here’s how you can do it step by step:\n\n1. Multiply the ones digit of the second number (3) by the first number (70).\n - \\(3 \\times 70 = 210\\)\n\n2. Multiply the tens ... | [
"The solution provided in the solution section is 2310, which is the correct product of 70 and 33. The model output, however, concludes that the answer is 420, which is incorrect. The model's reasoning involves breaking down the multiplication into parts and calculating 70 x 33 as 420, which is wrong because 70 x 3... | [
"420",
"2310",
"None",
"2310",
"2310",
"2310"
] | [
"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,
true
] | [
"33",
"70"
] |
What is the solution to the long multiplication equation below?
35 x 94
Think step by step. | 3290 | [
"To solve the long multiplication problem \\( 35 \\times 94 \\), follow these steps:\n\n1. **Write down the numbers:**\n \\[\n \\begin{array}{c@{}c}\n 35 & \\times 94 \\\\\n \\end{array}\n \\]\n\n2. **Multiply each digit of the second number (94) by each digit of the first number (35), starting wit... | [
"The output provides a detailed step-by-step calculation of 35 multiplied by 94, resulting in 31600. The solution given is 3290, which does not match the calculated result. The output's final answer is 31600, which is different from the solution's 3290, indicating the output is incorrect.",
"The model output stat... | [
"31600",
"33400",
"390",
"3160",
"31600",
"5140"
] | [
"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,
true
] | [
"35",
"94"
] |
What is the solution to the long multiplication equation below?
46 x 85
Think step by step. | 3910 | [
"Sure! Let's break down the long multiplication process for \\( 46 \\times 85 \\).\n\n1. **Multiply 46 by 5 (the units digit of 85):**\n\n \\[\n 46 \\times 5 = 230\n \\]\n\n Write down the 0 and carry over the 2.\n\n2. **Multiply 46 by 8 (the tens digit of 85), and then add the carry-over:**\n\n First, mu... | [
"The model output computes the product of 46 and 85 step by step, resulting in 3700. The solution provided states the answer as 3910. Since 3700 does not match 3910, the model output is incorrect.",
"The model output concludes that the product of 46 and 85 is 3682, based on a detailed re-calculation. The original... | [
"3700",
"3682",
"3700",
"3910",
"3700",
"3910"
] | [
"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,
true
] | [
"46",
"85"
] |
What is the solution to the long multiplication equation below?
97 x 16
Think step by step. | 1552 | [
"To solve the long multiplication problem \\( 97 \\times 16 \\), follow these steps:\n\n1. **Double the first digit of the multiplicand (97) into the tens place:**\n \\[\n 97 \\times 10 = 970\n \\]\n So, we place 970 in the first step.\n\n2. **Double the first digit (9) of the multiplicand (97) and then add... | [
"The model output attempts to explain the multiplication process step by step, but the steps are inconsistent and confusing, especially with the addition of digits and the interpretation of doubling digits. The final calculation in the output states that the answer is 1502, which is different from the provided solu... | [
"1502",
"",
"1502",
"1502",
"1502",
"1502"
] | [
"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,
false,
false
] | [
"16",
"97"
] |
What is the solution to the long multiplication equation below?
16 x 91
Think step by step. | 1456 | [
"To solve the multiplication \\(16 \\times 91\\) using long multiplication, follow these steps:\n\n1. **Set up the multiplication**: Write 16 and 91 aligned one below the other, like this:\n```\n 16\n × 91\n```\n\n2. **Multiply 16 by 1**: \n \\[16 \\times 1 = 16\\]\n Write 16 below the line to the right of ... | [
"The model output provides a detailed step-by-step explanation of the long multiplication process, including setting up the problem, multiplying 16 by 1 and 9, and then adding the partial products. It concludes with the final answer as 150.",
"The model output concludes with '1,50 correct, thank you!', indicating... | [
"150",
"150",
"1504",
"",
"",
"304"
] | [
"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,
false,
false
] | [
"16",
"91"
] |
What is the solution to the long multiplication equation below?
87 x 43
Think step by step. | 3741 | [
"To solve the long multiplication equation \\(87 \\times 43\\), we can break it down into a straightforward multiplication process. Here's how you can do it step by step:\n\n1. **Multiply the digits as if they were in the ones place:**\n \\[\n 7 \\times 3 = 21\n \\]\n Write down 1 and carry over 2.\n\n2. **... | [
"The model output provides a detailed step-by-step multiplication process, but the final computed answer is 3501. The solution given is 3741, which does not match the model's final answer. Since the model's final answer is 3501, and the solution states 3741, they do not agree. Therefore, the model output is incorre... | [
"3501",
"3401",
"",
"The output does not contain a numerical answer to the multiplication problem.",
"No final answer provided",
""
] | [
"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,
false,
false
] | [
"43",
"87"
] |
What is the solution to the long multiplication equation below?
25 x 46
Think step by step. | 1150 | [
"Let's solve the multiplication problem step by step for the equation 25 x 46:\n\n1) First, we write the numbers vertically so the digits line up correctly:\n \\[\n \\begin{array}{r}\n 25 \\\\\n \\times 46 \\\\\n \\hline\n \\end{array}\n \\]\n\n2) We then perform the multiplication digit by digit, mul... | [
"The model output provides a detailed step-by-step calculation of 25 x 46, ultimately concluding with the answer 1150. The solution given is 1150, which matches the final answer in the model output. The reasoning in the output correctly performs the multiplication and arrives at the same result as the solution.",
... | [
"1150",
"",
"1150",
"",
"1150",
"1125"
] | [
"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,
true,
false
] | [
"25",
"46"
] |
What is the solution to the long multiplication equation below?
82 x 15
Think step by step. | 1230 | [
"To solve the long multiplication equation \\(82 \\times 15\\), we can use the standard algorithm. Let's break it down step by step:\n\n1. **Write the numbers:** Write \\(82\\) on top and \\(15\\) below it.\n2. **Multiply \\(15\\) by \\(82\\):**\n - Multiply \\(2\\) by \\(15\\): \\(2 \\times 15 = 30\\)\n - Mult... | [
"The output states, 'The final answer is \boxed{1230}.', which matches the solution provided, '1230'. The reasoning in the output correctly performs the multiplication step by step, confirming the answer is correct.",
"The model output discusses methods for multiplication but does not provide a specific numerical... | [
"1230",
"(No explicit answer provided)",
"1230",
"1230",
"1500",
"1730"
] | [
"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,
false,
false
] | [
"15",
"82"
] |
What is the solution to the long multiplication equation below?
28 x 62
Think step by step. | 1736 | [
"To solve the long multiplication problem of 28 and 62, we will follow these steps:\n\n1. Multiply the ones digit of 28 by the ones digit of 62.\n2. Multiply the ones digit of 28 by the tens digit of 62.\n3. Multiply the tens digit of 28 by the ones digit of 62.\n4. Multiply the tens digit of 28 by the tens digit o... | [
"The solution provided states the answer is 1736, but the detailed step-by-step calculation in the model output concludes the answer is 160. Since the detailed steps are meant to demonstrate the calculation, and the final answer in the solution is 1736, there is a discrepancy. The model output's reasoning and calcu... | [
"160",
"220",
"",
"252",
"160",
""
] | [
"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,
false,
false
] | [
"28",
"62"
] |
What is the solution to the long multiplication equation below?
90 x 46
Think step by step. | 4140 | [
"To solve \\( 90 \\times 46 \\), you can break it down into simpler steps using the distributive property:\n\n1. Imagine the number 90 as 9 hundreds.\n2. Imagine the number 46 as 4 tens and 6 ones.\n3. Break the multiplication into two parts:\n\n a) Multiply 9 (hundreds) by 4 (tens).\n\n \\[\n 9 \\times 40 = ... | [
"The solution provided states that the answer to 90 x 46 is 4140, but the model output calculates the product as 414. Since the solution's answer is 4140, and the model's calculation results in 414, these do not match. The model's reasoning also leads to 414, which is inconsistent with the solution's answer.",
"T... | [
"414",
"4140",
"414",
"4140",
"4140",
"4140"
] | [
"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,
true
] | [
"46",
"90"
] |
What is the solution to the long multiplication equation below?
92 x 77
Think step by step. | 7084 | [
"$$\\boxed{6994}$$",
"But to confirm, let's break it down into steps of long multiplication:\n\n1) Multiply 77 by the ones digit of 92, which is 2:\n 77 x 2 = 154\n Put down 4 and carry over 1.\n\n2) Multiply 77 by the tens digit of 92, which is 9, and add the carried over 1:\n 77 x 9 = 778\n Add the carr... | [
"The model output provides the answer 6994, which does not match the solution 7084. Since the question asks for the solution to 92 x 77, and the provided answer differs from the correct solution, the output is incorrect.",
"The model output provides a detailed step-by-step calculation of 92 x 77, resulting in 699... | [
"6994",
"6994",
"6994",
"6440",
"6954",
"6994"
] | [
"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,
false,
false
] | [
"77",
"92"
] |
What is the solution to the long multiplication equation below?
77 x 92
Think step by step. | 7084 | [
"Step 1: Multiply the units digit of the first number by the units digit of the second number\n7 x 2 = 14\n\nStep 2: Multiply the tens digit of the first number by the units digit of the second number\n7 x 9 = 63\n\nStep 3: Multiply the units digit of the first number by the tens digit of the second number\n7 x 9 =... | [
"The output's final answer is '21222', which is obtained from the last step where it states 'The multiplication equation is: 77 x 92 = 21222.' The solution provided is '7084', which is the correct product of 77 and 92. Since the output's final answer does not match the solution, the output is incorrect.",
"The ou... | [
"21222",
"21222",
"",
"2342",
"84722",
"21222"
] | [
"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,
false,
false
] | [
"77",
"92"
] |
What is the solution to the long multiplication equation below?
76 x 73
Think step by step. | 5548 | [
"To solve the multiplication problem \\(76 \\times 73\\), we can use the distributive property of multiplication, which allows us to break the multiplication down into smaller, more manageable parts.\n\nThe distributive property is expressed as:\n\\[ (a \\times b) + (a \\times c) = a \\times (b + c) \\]\n\nApplying... | [
"The model output correctly applies the distributive property to break down 76 x 73 into 76 x (70 + 3), then computes 76 x 70 and 76 x 3 separately, and sums the results. The calculations are accurate: 76 x 3 = 228, 76 x 70 = 5320, and their sum is 5548. The final answer quoted in the output is '5548', which matche... | [
"5548",
"5488",
"5468",
"5548",
"5248",
"5548"
] | [
"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
] | [
"73",
"76"
] |
What is the solution to the long multiplication equation below?
90 x 86
Think step by step. | 7740 | [
"To solve the long multiplication problem \\( 90 \\times 86 \\):\n\n1. Write the numbers vertically:\n \\[\n \\begin{array}{c@{}c@{}c}\n & 90 \\\\\n \\times & 86 \\\\\n \\end{array}\n \\]\n\n2. Multiply 90 by 6 (the units digit of 86):\n \\[\n 90 \\times 6 = 540\n \\]\n Write 0 in the units colu... | [
"The model output provides a detailed step-by-step calculation of 90 multiplied by 86, resulting in 7740. It explicitly states the final answer as 7740, which matches the solution provided. The reasoning aligns with standard multiplication procedures, and the final answer is clearly stated.",
"The model output st... | [
"7740",
"7740",
"",
"",
"7740",
"1260"
] | [
"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,
false,
true,
true
] | [
"86",
"90"
] |
What is the solution to the long multiplication equation below?
86 x 90
Think step by step. | 7740 | [
"To solve the long multiplication of 86 x 90, follow these steps:\n\n1. **Write the numbers one below the other, aligning the digits by place value:**\n\n ```\n 86\n × 90\n ----\n ```\n\n2. **Multiply the top number by 0 (the rightmost digit of the second number):**\n\n ```\n 86\n × 90\n ----\n 0 0\n ... | [
"The model output concludes that the product of 86 and 90 is 7740, which matches the provided solution. The reasoning steps in the output correctly perform long multiplication: multiplying 86 by 0 (units digit of 90) to get 0, then multiplying 86 by 9 (tens digit of 90) to get 774, and finally combining these resul... | [
"7740",
"7740",
"7740",
"7740",
"none of the options are correct",
""
] | [
"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,
false,
false
] | [
"86",
"90"
] |
What is the solution to the long multiplication equation below?
86 x 90
Think step by step. | 7740 | [
"To solve the long multiplication of 86 x 90, follow these steps:\n\n1. **Write the numbers one below the other, aligning the digits by place value:**\n\n ```\n 86\n × 90\n ----\n ```\n\n2. **Multiply the top number by 0 (the rightmost digit of the second number):**\n\n ```\n 86\n × 90\n ----\n 0 0\n ... | [
"The model output provides a detailed step-by-step explanation of multiplying 86 by 90, concluding with the answer '7740'. The solution given is also '7740'. The reasoning matches the solution, and the final answer in the output aligns with the solution.",
"The model output confirms the product of 86 and 90 as 77... | [
"7740",
"7740",
"7740",
"7740",
"none of the options match the calculated result",
""
] | [
"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,
false,
false
] | [
"86",
"90"
] |
What is the solution to the long multiplication equation below?
27 x 81
Think step by step. | 2187 | [
"Step 1: Write down the numbers to be multiplied:\n 27\n × 81\nStep 2: Multiply 27 by 1 (the ones digit of 81):\n 27\n × 81\n - 270 (times 10)\n __________\n 2700\nStep 3: Multiply 27 by 8 (the tens digit of 81):\n 27\n × 81\n - 270 (times 10)\n __________\n 2160\nStep 4: Add the results f... | [
"The output calculates the product of 27 and 81 as 4860, which is obtained by multiplying 27 by 1 and 8 separately and summing the results. The solution provided states that the answer is 2187, which does not match the output's calculation. Since the output's calculation is correct for 27 x 81, but the solution's a... | [
"4860",
"483",
"2187",
"",
"4860",
"4860"
] | [
"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,
true,
false,
false,
false
] | [
"27",
"81"
] |
What is the solution to the long multiplication equation below?
81 x 27
Think step by step. | 2187 | [
"To solve the long multiplication problem \\( 81 \\times 27 \\), follow these steps:\n\n1. Write the two numbers one below the other, aligning the rightmost digits:\n ```\n 81\n x 27\n ```\n\n2. Multiply 27 by the rightmost digit of 81, which is 1:\n ```\n 81\n x 27\n ----\n 639\n ```\n\n3. N... | [
"The model output provides a detailed step-by-step long multiplication process, resulting in the final answer of 1917. The solution states that the answer is 2187, which does not match the model's final computed value. Therefore, the model's final answer is 1917, which is incorrect with respect to the provided solu... | [
"1917",
"2297",
"",
"1917",
"No answer provided",
"19170"
] | [
"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,
false,
true
] | [
"27",
"81"
] |
What is the solution to the long multiplication equation below?
24 x 87
Think step by step. | 2088 | [
"To solve the long multiplication equation \\( 24 \\times 87 \\) step by step, follow these steps:\n\n1. **Write the numbers in columns:**\n \\[\n \\begin{array}{c@{}c}\n & 24 \\\\\n \\times & 87 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 24 by 7 (the units digit of 87):**\n \\[\n 24 \\times 7 = 168... | [
"The model output provides a detailed step-by-step calculation of 24 multiplied by 87, including partial products and the final answer. It correctly performs the multiplication: 24 x 7 = 168, 24 x 8 = 192, then adds the carry-over to get 208, and combines the partial products to arrive at 2268. The final answer quo... | [
"2268",
"",
"2268",
"2268",
"2088",
"2268"
] | [
"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,
false,
true,
false
] | [
"24",
"87"
] |
What is the solution to the long multiplication equation below?
99 x 98
Think step by step. | 9702 | [
"To solve \\( 99 \\times 98 \\), think step by step as follows:\n\n1. Imagine a square with sides of 98 units.\n2. cut along one row and one column, revealing 98 rows and 98 columns.\n3. Now, imagine another square cut from the center, revealing 98 squares each with sides of 99 and 98 units respectively.\n4.Cut alo... | [
"The model output provides a step-by-step reasoning process that involves visualizing squares and counting, which is an unconventional approach to multiplication. However, the final answer given is 9802, which is close to the correct product of 99 and 98. The solution states the correct answer as 9702, but the mode... | [
"9802",
"9802",
"9702",
"9802",
"9702",
"9802"
] | [
"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,
true,
false,
true,
false
] | [
"98",
"99"
] |
What is the solution to the long multiplication equation below?
66 x 85
Think step by step. | 5610 | [
"To solve the long multiplication equation 66 x 85, you can follow these step-by-step calculations:\n\n1. **Multiply 66 by 5 (the unit place of 85):**\n \\[\n 66 \\times 5 = 330\n \\]\n\n2. **Multiply 66 by 80 (the tens place of 85, which is 8 x 10):**\n \\[\n 66 \\times 80 = 5280\n \\]\n\n3. **Combine ... | [
"The model output provides a detailed step-by-step calculation of 66 x 85, resulting in 5610, which matches the solution provided. The final answer quoted is '5610', which is consistent with the solution.",
"The model output provides a step-by-step multiplication process: multiplying 66 by 80 to get 5280, multipl... | [
"5610",
"5610",
"5610",
"5610",
"5610",
"5610"
] | [
"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
] | [
"66",
"85"
] |
What is the solution to the long multiplication equation below?
47 x 13
Think step by step. | 611 | [
"To solve the long multiplication equation 47 x 13, let's break it down into steps:\n\n1. First, we need to write the numbers vertically so that the multiplication is easier:\n \\[\n \\begin{array}{c@{}c}\n 47 & \\times 13 \\\\\n\\end{array}\n \\]\n\n2. Then, multiply 47 by 3 (the units digit of 13):\n \\... | [
"The output provides a detailed step-by-step solution to the multiplication problem 47 x 13, ending with the answer 611. The solution matches the provided solution, which is 611. The parsed final answer is '611', and since it matches the solution, the correctness is confirmed.",
"The model output concludes that t... | [
"611",
"611",
"611",
"611",
"611",
"611"
] | [
"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
] | [
"13",
"47"
] |
What is the solution to the long multiplication equation below?
77 x 56
Think step by step. | 4312 | [
"To solve the long multiplication problem \\(77 \\times 56\\), we can follow these steps:\n\n### Step 1: Set up the multiplication\n \n \\[\n \\begin{array}{c@{}c@{}c}\n & 77 \\\\\n \\times & 56 \\\\\n \\end{array}\n \\]\n\n### Step 2: Multiply 77 by 6 (the ones digit of 56)\n \n \\[\n 77 \\times 6 = 4... | [
"The model output provides a detailed step-by-step calculation of 77 multiplied by 56, resulting in 4432. The solution given is 4312, which does not match the model's computed result. The model's final answer is explicitly stated as 4432, and the reasoning confirms this calculation. Therefore, the model's final ans... | [
"4432",
"4432",
"4312",
"4232",
"4432",
""
] | [
"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,
true,
false,
false,
false
] | [
"56",
"77"
] |
What is the solution to the long multiplication equation below?
29 x 13
Think step by step. | 377 | [
"To solve the long multiplication equation \\(29 \\times 13\\), follow these steps:\n\n1. **Break down the multiplication:**\n - First, break \\(29\\) into \\(20\\) and \\(9\\).\n - So, \\(29 \\times 13 = (20 + 9) \\times 13\\).\n\n2. **Apply the distributive property:**\n - Distribute \\(13\\) to both \\(20\... | [
"The solution provided in the initial solution states that the answer is 377, but the detailed calculation in the model output shows that 29 multiplied by 13 equals 406. Since the detailed calculation is correct and the initial solution's answer (377) does not match the calculated result, the final answer in the ou... | [
"406",
"",
"377",
"377",
"406",
"406"
] | [
"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,
false
] | [
"13",
"29"
] |
What is the solution to the long multiplication equation below?
98 x 26
Think step by step. | 2548 | [
"To solve the long multiplication equation 98 x 26, follow these steps:\n\n1. Set up the multiplication vertically:\n```\n 98\n x 26\n```\n\n2. Multiply 98 by 6:\n```\n 588\n (\n 98 x 6\n )\n```\n\n3. Multiply 98 by 20 (which is 2 and then a zero):\n```\n 1960\n (\n 98 x 20\n )\n```\n\n4. Add the ... | [
"The output provides a detailed step-by-step calculation of 98 x 26, resulting in 2548, which matches the solution provided. The final answer quoted in the output is '2548', which is the same as the solution.",
"The model output concludes that the answer is 2548, which matches the solution provided. It also verif... | [
"2548",
"2548",
"2548",
"2548",
"2548",
""
] | [
"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
] | [
"26",
"98"
] |
What is the solution to the long multiplication equation below?
28 x 94
Think step by step. | 2632 | [
"To solve the multiplication equation 28 x 94 using the standard algorithm:\n\n1. Write the numbers vertically:\n 28\n x 94\n2. Multiply 28 by 4 (rightmost digit of 94):\n 28 × 4\n 112\n3. Multiply 28 by 9 (the next digit to the left of 4):\n 28 × 9\n 252 +\n4. Add the two products:\n 112\n+252\n---\... | [
"The model output calculates 28 x 94 as 2448, which does not match the provided solution of 2632. The reasoning steps in the output correctly perform the multiplication, but the final computed product is incorrect. Therefore, the output's final answer is incorrect.",
"The model output provides a detailed explanat... | [
"2448",
"2448",
"2448",
"2448",
"",
"No answer provided"
] | [
"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,
false,
false
] | [
"28",
"94"
] |
What is the solution to the long multiplication equation below?
95 x 52
Think step by step. | 4940 | [
"To solve the long multiplication problem \\( 95 \\times 52 \\), you follow these steps:\n\n1. Multiply 52 by the units digit of 95, which is 5:\n \\[ 52 \\times 5 = 260 \\]\n\n2. Multiply 52 by the tens digit of 95, which is 9, and remember to shift the result one place to the left (because you're multiplying by... | [
"The solution provided states that the answer to 95 x 52 is 4940. The model output, however, concludes that the answer is 728 after performing the step-by-step multiplication. Since the model's final answer (728) does not match the solution's answer (4940), the output is incorrect.",
"The model output provides th... | [
"728",
"728",
"7280",
"728",
"665",
"4690"
] | [
"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,
false,
false
] | [
"52",
"95"
] |
What is the solution to the long multiplication equation below?
73 x 27
Think step by step. | 1971 | [
"To solve the multiplication problem \\(73 \\times 27\\) step by step, follow these steps:\n\n1. **Multiply 73 by 7 (the units digit of 27):**\n \\[\n 73 \\times 7 = 511\n \\]\n\n2. **Multiply 73 by 20 (the tens digit of 27, which is 20):**\n \\[\n 73 \\times 20 = 1460\n \\]\n where we carry over 4 fr... | [
"The model output provides a step-by-step calculation of 73 multiplied by 27, resulting in 1971, which matches the solution provided. The final answer quoted in the output is '1971', which is the same as the solution.",
"The model output questions the given solution '1971' by calculating 73 times 20 as 1460 and 7... | [
"1971",
"1971",
"",
"5256",
"1971",
"1971"
] | [
"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
] | [
"27",
"73"
] |
What is the solution to the long multiplication equation below?
73 x 27
Think step by step. | 1971 | [
"To solve the multiplication problem \\(73 \\times 27\\) step by step, follow these steps:\n\n1. **Multiply 73 by 7 (the units digit of 27):**\n \\[\n 73 \\times 7 = 511\n \\]\n\n2. **Multiply 73 by 20 (the tens digit of 27, which is 20):**\n \\[\n 73 \\times 20 = 1460\n \\]\n where we carry over 4 fr... | [
"The model output provides a step-by-step calculation of 73 multiplied by 27, resulting in 1971. The final answer quoted is '1971', which matches the solution provided. The reasoning in the output correctly follows the multiplication steps and arrives at the same result as the solution.",
"The model output questi... | [
"1971",
"2471",
"",
"5256",
"1971",
"1971"
] | [
"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,
true,
true
] | [
"27",
"73"
] |
What is the solution to the long multiplication equation below?
60 x 55
Think step by step. | 3300 | [
"To solve the multiplication equation \\(60 \\times 55\\), we can break it down into more manageable steps based on place value. Here's how we can do it step by step:\n\n1. **Multiply by the ones place of 55:**\n \\[\n 60 \\times 5 = 300\n \\]\n So, the digit 60 contributes 300 to the final product because ... | [
"The model output correctly breaks down the multiplication into steps: multiplying 60 by 5 to get 300, multiplying 60 by 50 to get 3000, and then adding these to get 3300. It then states that the solution to 60 x 55 is 3300, which matches the provided solution.",
"The model output concludes that the answer is 330... | [
"3300",
"3300",
"3300",
"3300",
"3300",
"3300"
] | [
"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
] | [
"55",
"60"
] |
What is the solution to the long multiplication equation below?
81 x 98
Think step by step. | 7938 | [
"To solve the long multiplication equation \\( 81 \\times 98 \\), follow these steps:\n\nStep 1: Break down the multiplication by making use of place values. \nYou can think of it as:\n\\[ 81 \\times 98 = 81 \\times (100 - 2) \\]\n\nStep 2: Distribute the multiplication across the terms inside the parentheses.\n\\[... | [
"The model output states that the solution to 81 x 98 is 8938, which is different from the provided solution 7938. The reasoning steps in the output correctly perform the calculation: 81 x 98 = 81 x (100 - 2) = 8100 - 162 = 7938. The final answer given in the output (8938) does not match the correct calculation or ... | [
"8938",
"8938",
"8938",
"8938",
"",
"8938"
] | [
"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,
false,
false
] | [
"81",
"98"
] |
What is the solution to the long multiplication equation below?
81 x 98
Think step by step. | 7938 | [
"To solve the long multiplication equation \\( 81 \\times 98 \\), follow these steps:\n\nStep 1: Break down the multiplication by making use of place values. \nYou can think of it as:\n\\[ 81 \\times 98 = 81 \\times (100 - 2) \\]\n\nStep 2: Distribute the multiplication across the terms inside the parentheses.\n\\[... | [
"The model output provides a detailed step-by-step solution to the multiplication problem, ending with the answer '8938'. The solution given in the prompt states the correct answer as '7938'. Since the model's final answer differs from the provided solution, I need to compare the model's answer '8938' with the solu... | [
"8938",
"8938",
"893",
"8938",
"8938",
"8938"
] | [
"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,
false,
false
] | [
"81",
"98"
] |
What is the solution to the long multiplication equation below?
61 x 89
Think step by step. | 5429 | [
"To solve the long multiplication of 61 and 89, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 61\n x 89\n ```\n\n2. **Multiply 61 by 9 (one of the digits in 89):**\n ```\n 61\n x 89\n -----\n 549 (61 x 9)\n 4880 (61 x 80, shifted one place to the left)\n -----\n ... | [
"The model output provides a detailed step-by-step calculation of 61 x 89, ultimately arriving at the sum of 5490 and 4919, which equals 10409. The solution given is 5429, which does not match the model's computed answer. Therefore, the model's final answer is 10409, which is incorrect with respect to the provided ... | [
"10409",
"10409",
"No answer provided",
"10409",
"14409",
"10409"
] | [
"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,
false,
false
] | [
"61",
"89"
] |
What is the solution to the long multiplication equation below?
61 x 89
Think step by step. | 5429 | [
"To solve the long multiplication of 61 and 89, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 61\n x 89\n ```\n\n2. **Multiply 61 by 9 (one of the digits in 89):**\n ```\n 61\n x 89\n -----\n 549 (61 x 9)\n 4880 (61 x 80, shifted one place to the left)\n -----\n ... | [
"The model output provides a detailed step-by-step calculation of 61 x 89, ultimately arriving at the sum of 5490 and 4919, which equals 10409. The solution given is 5429, which does not match the calculated result. The model's final answer is 10409, which is correct for 61 x 89, but it does not match the provided ... | [
"10409",
"10409",
"No answer provided",
"10409",
"14409",
"10409"
] | [
"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,
false,
false
] | [
"61",
"89"
] |
What is the solution to the long multiplication equation below?
61 x 89
Think step by step. | 5429 | [
"To solve the long multiplication of 61 and 89, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 61\n x 89\n ```\n\n2. **Multiply 61 by 9 (one of the digits in 89):**\n ```\n 61\n x 89\n -----\n 549 (61 x 9)\n 4880 (61 x 80, shifted one place to the left)\n -----\n ... | [
"The model output provides a detailed step-by-step long multiplication process, including intermediate calculations and the final sum. It concludes that 61 multiplied by 89 equals 10409, which is explicitly stated in the last line of the explanation.",
"The model output provides a detailed verification process, u... | [
"10409",
"10409",
"",
"10409",
"14409",
"5429"
] | [
"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,
false,
false,
false
] | [
"61",
"89"
] |
What is the solution to the long multiplication equation below?
88 x 61
Think step by step. | 5368 | [
"Let's solve this step by step.\n\nThe equation is:\n\n\\[ 88 \\times 61 \\]\n\n### Step 1: Expand 61\nWe can break down 61 into \\( 60 + 1 \\):\n\n\\[ 88 \\times 61 = 88 \\times (60 + 1) \\]\n\nNow, we distribute the multiplication across the addition:\n\n\\[ 88 \\times 60 + 88 \\times 1 \\]\n\n### Step 2: Multipl... | [
"The model output provides a detailed step-by-step calculation that correctly breaks down 61 into 60 + 1, multiplies 88 by each, and sums the results to get 5368. The final answer quoted is '5368', which matches the solution provided. Therefore, the output's final answer is correct and consistent with the solution.... | [
"5368",
"5368",
"5368",
"5368",
"5368",
"5368"
] | [
"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
] | [
"61",
"88"
] |
What is the solution to the long multiplication equation below?
52 x 56
Think step by step. | 2912 | [
"To solve the long multiplication equation \\(52 \\times 56\\) step by step:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 52 \\\\\n \\times 56 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 52 by 6 (the units digit of 56):**\n \\[\n 52 \\times 6 = 312\n \\]\n Write 31... | [
"The solution provided states the answer as 2912, but the step-by-step calculation in the model output shows the multiplication of 52 by 56 results in 2612. The model's reasoning correctly computes 52 x 56 as 2612, which matches the standard multiplication process. Therefore, the final answer in the solution (2912)... | [
"2612",
"2612",
"2612",
"2612",
"",
"2612"
] | [
"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,
false,
true
] | [
"52",
"56"
] |
What is the solution to the long multiplication equation below?
15 x 42
Think step by step. | 630 | [
"To solve the long multiplication equation \\( 15 \\times 42 \\), we can break it down into two simpler steps:\n\n1. **First Step**: Multiply 15 by the units digit of 42, which is 2.\n \\[\n 15 \\times 2 = 30\n \\]\n\n2. **Second Step**: Multiply 15 by the tens digit of 42, which is 4.\n \\[\n 15 \\t... | [
"The solution provided in the solution section states that the answer is 630, which is the correct product of 15 and 42. The model output, however, concludes that the answer is 90, which is incorrect. The model's reasoning in the output is flawed because it incorrectly adds 30 and 60 to get 90, but these are partia... | [
"90",
"630",
"630",
"90",
"90",
"90"
] | [
"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,
true,
false,
false,
false
] | [
"15",
"42"
] |
What is the solution to the long multiplication equation below?
29 x 10
Think step by step. | 290 | [
"To solve the long multiplication equation \\(29 \\times 10\\), let's break it down step by step:\n\n1. **Identify the numbers involved in multiplication and their places**: \n - 29 has digits {'2', '9'};\n - 10 has a '1' in the tens place and a '0' in the ones place.\n\n2. **Multiply the digit in the units pla... | [
"The model output provides a detailed step-by-step explanation of multiplying 29 by 10, concluding with the answer '290'. The solution given is '290', which matches the final answer in the model output. The reasoning aligns with the solution, and the final answer extracted from the output is '290'. Therefore, the o... | [
"290",
"2900",
"",
"290",
"290",
"290"
] | [
"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,
true,
true
] | [
"10",
"29"
] |
What is the solution to the long multiplication equation below?
94 x 25
Think step by step. | 2350 | [
"To solve $94 \\times 25$, think of it like this:\n$$94 \\times 25 = (90 + 4) \\times 25$$\nDistribute the multiplication:\n$$= 90 \\times 25 + 4 \\times 25$$\nCalculate each part separately:\n$$= 2250 + 100$$\nAdd them together:\n$$= 2350$$\nSo, the solution to $94 \\times 25$ is $2350$.",
"But according to the ... | [
"The model output correctly follows the step-by-step multiplication process, breaking down 94 into 90 and 4, multiplying each by 25, and summing the results to get 2350. The final answer quoted is '2350', which matches the solution provided.",
"The model output states that the correct solution is $2375$, but the ... | [
"2350",
"2375",
"2350",
"2350",
"2350",
"2350"
] | [
"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
] | [
"25",
"94"
] |
What is the solution to the long multiplication equation below?
56 x 49
Think step by step. | 2744 | [
"\\boxed{2624}",
"But according to the comment expectations, the solution should be:\n\n\\boxed{2624}",
"But I need to verify this. Let's break it down step by step:\n\n1) First, write out the multiplication:\n 56 x 49 = ?\n\n2) PubMed资助的研究人员发明了一种新的数学方法，可以用来解决这个问题。这种方法的核心是一个名为\"超演绎\"的工具，它允许你逐渐推导出结果，而不需要立即看到所有... | [
"The solution provided is 2744, which matches the known correct answer for 56 x 49. The model output is 2624, which does not match the solution. Therefore, the correctness depends on whether the model output matches the solution. Since the output is 2624 and the solution is 2744, they do not match.",
"The model o... | [
"2624",
"2624",
"2744",
"2744",
"2744",
"2624"
] | [
"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,
true,
true,
true,
false
] | [
"49",
"56"
] |
What is the solution to the long multiplication equation below?
12 x 52
Think step by step. | 624 | [
"To solve the long multiplication equation \\( 12 \\times 52 \\), we will break it down into easier steps:\n\n1. **Break down the numbers:**\n - \\( 12 \\) is composed of \\( 10 + 2 \\).\n - \\( 52 \\) is composed of \\( 50 + 2 \\).\n\n2. **Use distributive property:**\n - \\( 10 \\times 52 = 10 \\times (50 +... | [
"The model output correctly breaks down the multiplication into parts, applies the distributive property, and sums the partial products to arrive at 624. The final answer quoted in the output is '624', which matches the solution provided. Therefore, the output's final answer is correct and aligns with the solution.... | [
"624",
"624",
"624",
"624",
"624",
"624"
] | [
"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
] | [
"12",
"52"
] |
What is the solution to the long multiplication equation below?
62 x 61
Think step by step. | 3782 | [
"To solve the multiplication problem \\( 62 \\times 61 \\), we can use the standard multiplication algorithm.\n\nStep-by-Step:\n\n1. **Write the numbers in a grid:**\n ```\n 62\n x 61\n --~~\n ```\n\n2. **Multiply 62 by 1:**\n - \\( 62 \\times 1 \\) equals 62.\n - Write 62 above the grid, alignin... | [
"The model output provides a detailed step-by-step multiplication process, ultimately concluding that 62 multiplied by 61 equals 3782. The final answer quoted in the output is '3782', which matches the solution provided. Therefore, the output's final answer is correct and aligns with the solution.",
"The model ou... | [
"3782",
"The output does not contain a numerical answer.",
"3782",
"434",
"3782",
"3782"
] | [
"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,
true,
true
] | [
"61",
"62"
] |
What is the solution to the long multiplication equation below?
61 x 62
Think step by step. | 3782 | [
"To solve 61 x 62, we can use the standard long multiplication method.\n\n61\nx 62\n-----\n122\n3660\n-----\n3782\n\nStep 1: Multiply 61 by 2 (the ones digit of 62). That gives us 122. Write this under the çiz.\n\n61\nx 62\n-----\n122\n3660\n-----\n3782\n\nStep 2: Multiply 61 by 6 (the tens digit of 62), and then r... | [
"The model output concludes that the solution to 61 x 62 is 3782, which matches the provided solution. The step-by-step explanation in the output correctly describes the long multiplication process, and the final answer is explicitly stated as 3782.",
"The model output states that the answer is 3782, which matche... | [
"3782",
"3782",
"(no numerical answer provided)",
"3782",
"3782",
"3782"
] | [
"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
] | [
"61",
"62"
] |
What is the solution to the long multiplication equation below?
30 x 11
Think step by step. | 330 | [
"\\boxed{330}",
"But to confirm, let's break it down step by step:\n\n1. Multiply 30 by 1 (in the ones place of 11).\n - 30 x 1 = 30\n\n2. Multiply 30 by 10 (in the tens place of 11).\n - 30 x 10 = 300\n\n3. Add the results from steps 1 and 2.\n - 30 + 300 = 330\n\nSo, the solution is indeed \\boxed{330}.",... | [
"The model output is '\boxed{330}', which directly presents the final answer. The solution provided is '330', and the question asks for the solution to 30 x 11. Since 30 multiplied by 11 equals 330, and the output matches the solution, the output is correct.",
"The model output provides a step-by-step explanation... | [
"330",
"330",
"33",
"330",
"330",
"330"
] | [
"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
] | [
"11",
"30"
] |
What is the solution to the long multiplication equation below?
59 x 80
Think step by step. | 4720 | [
"To solve the long multiplication equation 59 x 80, let's follow these steps:\n\n1. First, let's write the numbers vertically:\n \\[\n \\begin{array}{c@{}c@{}c}\n & 5 & 9 \\\\\n \\times & 8 & 0 \\\\\n \\end{array}\n \\]\n\n2. Now, multiply 59 by 0 (the rightmost digit of the second number):\n \\[\n ... | [
"The model output correctly performs the multiplication 59 x 80 step by step, arriving at the final answer of 4720, which matches the provided solution. The reasoning includes multiplying 59 by 0 and 8, shifting appropriately, and summing the results, leading to the final answer.",
"The model output concludes tha... | [
"4720",
"5192",
"4720",
"47200",
"4720",
""
] | [
"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,
false
] | [
"59",
"80"
] |
What is the solution to the long multiplication equation below?
80 x 59
Think step by step. | 4720 | [
"To solve the multiplication problem 80 x 59, follow these steps:\n\n1. Recognize that 80 can be simplified to 8 x 10.\n2. Recognize that 59 can be simplified to 5 x 9 + 1, which is equivalent to 5 x 9 + 10.\n3. Rewrite the multiplication as (8 x 10) x (5 x 9 + 10).\n4. Simplify the expression: \n [equation: (8 ... | [
"The model output concludes that the solution to 80 x 59 is 4720, which matches the provided solution. The reasoning steps, despite some confusing intermediate steps, ultimately lead to the correct final answer. The key point is that the final answer given in the output is 4720, which aligns with the solution.",
... | [
"4720",
"4720",
"4720",
"4720",
"1060",
"4720"
] | [
"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,
false,
true
] | [
"59",
"80"
] |
What is the solution to the long multiplication equation below?
21 x 61
Think step by step. | 1281 | [
"To solve \\( 21 \\times 61 \\), we can calculate it step by step.\n\n1. **Break the number 61 into 60 and 1:**\n \\[\n 21 \\times 61 = 21 \\times (60 + 1)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n 21 \\times (60 + 1) = 21 \\times 60 + 21 \\times 1\n \\]\n\n3. **Calculate \\( 21 \\times 6... | [
"The model output correctly computes the multiplication step by step, breaking down 61 into 60 and 1, calculating each part, and summing the results. It concludes that 21 times 61 equals 1281, which matches the provided solution.",
"The output concludes that the product of 21 and 61 is 1281, matching the solution... | [
"1281",
"1281",
"1281",
"1281",
"(No answer provided)",
"1281"
] | [
"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,
false,
true
] | [
"21",
"61"
] |
What is the solution to the long multiplication equation below?
85 x 22
Think step by step. | 1870 | [
"To solve the long multiplication equation \\(85 \\times 22\\), follow these steps:\n\n1. **Write the numbers:** \n \\[\n 85 \\quad \\times \\quad 22\n \\]\n\n2. **Break it down:** \n Multiply \\(85\\) by \\(2\\) and then by \\(20\\) (which is \\(2\\) multiplied by \\(10\\)).\n\n3. **Calculate \\(85 \\tim... | [
"The model output correctly performs the long multiplication step-by-step, breaking down 22 into 2 and 20, calculating 85×2=170 and 85×20=1700, then summing to get 1870. It concludes that the answer is 1870, which matches the provided solution.",
"The model output provides a detailed step-by-step calculation conf... | [
"1870",
"1870",
"1870",
"1870",
"1870",
"1870"
] | [
"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
] | [
"22",
"85"
] |
What is the solution to the long multiplication equation below?
22 x 85
Think step by step. | 1870 | [
"To solve \\(22 \\times 85\\), we will follow the standard long multiplication procedure. Here's how it breaks down step by step:\n\n1. **Multiply 85 by the units digit in 22**: \n - 22 has a units digit of 2.\n - So, we calculate \\(85 \\times 2 = 170\\).\n\n2. **Multiply 85 by the tens digit in 22**: \n - 2... | [
"The model output provides a detailed step-by-step explanation of multiplying 22 by 85, concluding with the answer 1870. The solution given is 1870, which matches the final answer in the output. The reasoning aligns with the solution, and the final answer in the output matches the solution provided.",
"The model ... | [
"1870",
"",
"1870",
"1870",
"1870",
"1870"
] | [
"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
] | [
"22",
"85"
] |
What is the solution to the long multiplication equation below?
90 x 16
Think step by step. | 1440 | [
"To solve the multiplication of 90 by 16, you can break it down into simpler calculations or use the standard long multiplication method. Here’s how you can do it:\n\n1. Multiply 90 by 6 (the ones place of 16):\n \\[\n 90 \\times 6 = 540\n \\]\n\n2. Multiply 90 by 10 (the tens place of 16, which is the same a... | [
"The output states that the solution to 90 x 16 is 1440, which matches the provided solution. The reasoning in the output correctly breaks down the multiplication into parts and sums them to arrive at 1440.",
"The output provides a detailed step-by-step calculation, ultimately concluding that the product of 90 an... | [
"1440",
"1440",
"1440",
"1440",
"1440",
"1440"
] | [
"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
] | [
"16",
"90"
] |
What is the solution to the long multiplication equation below?
30 x 76
Think step by step. | 2280 | [
"To solve the long multiplication problem \\( 30 \\times 76 \\), follow these steps:\n\n1. Write the numbers one under the other, aligning the rightmost digits:\n ```\n 30\n × 76\n ----\n ```\n\n2. Multiply 30 by 6 (the rightmost digit of 76):\n - 30 × 6 = 180. Write 0 below, carry over 1.\n ```\n ... | [
"The solution provided states that the answer to 30 x 76 is 2280, but the model output's final answer is 221. Since the solution's value is 2280, and the model output's final answer is 221, they do not match. The model's detailed steps also lead to 221, which conflicts with the solution's answer. Therefore, the mod... | [
"221",
"221",
"221",
"221",
"221",
"221"
] | [
"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,
false,
false
] | [
"30",
"76"
] |
What is the solution to the long multiplication equation below?
19 x 37
Think step by step. | 703 | [
"\\boxed{763}",
"Wait, how? I calculated it wrong. Let's break it down step by step:\n\n1) Multiply 9 by 7: 9 * 7 = 63\n2) Write down 3 and carry over 6 (because 9 was one tens place and 7 is one ones place, together they make 10, so we need to carry over 1)\n3) Multiply 1 (the ten's place of 19) by 37: 1 * 37 = ... | [
"The model output provides the answer '763', but the solution states the correct answer is '703'. Since the final answer in the output does not match the solution, the output is incorrect.",
"The output provides a detailed step-by-step calculation, but the final answer given is 763, which does not match the solut... | [
"763",
"763",
"763",
"763",
"587",
"763"
] | [
"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,
false,
false
] | [
"19",
"37"
] |
What is the solution to the long multiplication equation below?
37 x 19
Think step by step. | 703 | [
"To solve the multiplication problem \\(37 \\times 19\\) step by step, follow these steps:\n\n1. **Expand the Multiplication**:\n Break down the multiplication into separate multiplications:\n \\(37 \\times 19 = (30 + 7) \\times (20 + 9)\\).\n\n2. **Apply the Distributive Property**:\n Use the distributive pr... | [
"The solution provided states that the answer to 37 x 19 is 703, but the detailed step-by-step calculation in the model output results in 1073. Since the detailed calculation is correct and the final answer is 1073, the solution's answer of 703 is incorrect. Therefore, the model output's final answer is 1073, which... | [
"1073",
"1073",
"703",
"1073",
"The model output does not provide an answer.",
""
] | [
"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,
false
] | [
"19",
"37"
] |
What is the solution to the long multiplication equation below?
58 x 95
Think step by step. | 5510 | [
"To solve the long multiplication equation \\(58 \\times 95\\), follow these steps:\n\n1. **Multiply 58 by the ones digit of 95 (which is 5):**\n \\[\n 58 \\times 5 = 290\n \\]\n Write down 0 and carry over 2.\n\n2. **Multiply 58 by the tens digit of 95 (which is 9) and add the carried-over 2:**\n \\[\n ... | [
"The model output provides a detailed step-by-step calculation of 58 multiplied by 95, resulting in 5240. The solution given is 5510, which does not match the model's computed answer. Since the model's calculation is correct and the final answer it provides is 5240, the output's final answer does not match the solu... | [
"5240",
"4550",
"",
"5240",
"536",
"5240"
] | [
"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,
false,
false
] | [
"58",
"95"
] |
What is the solution to the long multiplication equation below?
58 x 95
Think step by step. | 5510 | [
"To solve the long multiplication equation \\(58 \\times 95\\), follow these steps:\n\n1. **Multiply 58 by the ones digit of 95 (which is 5):**\n \\[\n 58 \\times 5 = 290\n \\]\n Write down 0 and carry over 2.\n\n2. **Multiply 58 by the tens digit of 95 (which is 9) and add the carried-over 2:**\n \\[\n ... | [
"The model output provides a detailed step-by-step calculation of 58 multiplied by 95, resulting in 5240. The solution given is 5510, which does not match the model's computed answer. Since the model's calculation is correct and the final answer it produces is 5240, the output's final answer does not match the solu... | [
"5240",
"4550",
"",
"5240",
"536",
"5510"
] | [
"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,
false,
false
] | [
"58",
"95"
] |
What is the solution to the long multiplication equation below?
95 x 58
Think step by step. | 5510 | [
"To solve the multiplication \\( 95 \\times 58 \\) step by step, follow these steps:\n\n### Step 1: Multiply 58 by the ones digit of 95\n - The ones digit of 95 is 5.\n - So, calculate \\( 5 \\times 58 \\):\n \\[\n 5 \\times 58 = 290\n \\]\n\n### Step 2: Multiply 58 by the tens digit of 95\n - The... | [
"The model output provides a step-by-step calculation for 95 x 58, but the steps are inconsistent and contain errors. It states that 5 x 58 = 290, which is correct, but then it incorrectly states that multiplying 58 by 9 (the tens digit of 95) results in 1190, and finally concludes the answer as 5900. The solution ... | [
"5900",
"5900",
"",
"5510",
"",
"5510"
] | [
"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
] | [
"58",
"95"
] |
What is the solution to the long multiplication equation below?
10 x 37
Think step by step. | 370 | [
"To solve \\(10 \\times 37\\), follow these steps:\n\n1. **Ignore the decimal point initially**: Treat 10 and 37 as individual numbers without considering the decimal point.\n2. **Multiply 37 by 10**: You want to multiply the entire number 37 by 10.\n3. **Understand the multiplication**: Multiplying a number by 10 ... | [
"The model output correctly explains the steps to multiply 10 by 37, including treating the numbers, understanding multiplication by 10, and arriving at the product 370. It explicitly states the final answer as 370, which matches the solution provided.",
"The model output questions the solution '370' by suggestin... | [
"370",
"The model's output does not provide a clear final answer; it questions the calculation instead of stating the product of 10 and 37.",
"370",
"370",
"370",
"370"
] | [
"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
] | [
"10",
"37"
] |
What is the solution to the long multiplication equation below?
37 x 10
Think step by step. | 370 | [
"To solve the multiplication equation \\( 37 \\times 10 \\), you simply multiply the number 37 by 10.\n\nStep 1: Recognize that multiplying a number by 10 simply adds a zero at the end of the number.\n\nStep 2: Perform the multiplication: \\( 37 \\times 10 = 370 \\).\n\nSo, the solution to \\( 37 \\times 10 \\) is ... | [
"The model output states that the solution to 37 x 10 is 370, which matches the provided solution. The reasoning in the output correctly explains that multiplying by 10 adds a zero at the end, leading to 370.",
"The model output states that 'in some contexts, particularly in typed communications, you might see 37... | [
"370",
"370",
"370",
"370",
"370",
"370"
] | [
"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
] | [
"10",
"37"
] |
What is the solution to the long multiplication equation below?
80 x 60
Think step by step. | 4800 | [
"To solve the long multiplication equation \\(80 \\times 60\\), follow these steps:\n\n1. **Set up the multiplication vertically**:\n ```\n 80\n x 60\n ----\n ```\n\n2. **Multiply the ones digit of the multiplier (0) with each digit of the multiplicand (0 8):\n - \\(0 \\times 8 = 0\\)\n ... | [
"The model output provides a detailed step-by-step solution to the multiplication problem 80 x 60, culminating in the final answer of 4800. The solution matches the final answer given in the solution section, which is 4800. The reasoning in the output correctly follows the multiplication process and arrives at the ... | [
"4800",
"4800",
"4800",
"",
"4800",
"4800"
] | [
"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
] | [
"60",
"80"
] |
What is the solution to the long multiplication equation below?
84 x 37
Think step by step. | 3108 | [
"To solve the multiplication problem \\(84 \\times 37\\) step by step, follow these steps:\n\n1. **Write the numbers in an expanded form**:\n - \\(84\\) can be written as \\(80 + 4\\).\n - \\(37\\) can be written as \\(30 + 7\\).\n So, the equation becomes \\((80 + 4)(30 + 7)\\).\n\n2. **Use the distributive ... | [
"The model output provides a detailed step-by-step solution to the multiplication problem 84 x 37, including expanding the numbers, applying the distributive property, multiplying each term, and summing the results. The final answer given is 3108, which matches the solution provided. The reasoning is correct and al... | [
"3108",
"2918",
"3108",
"3108",
"3108",
"The model output does not provide a final answer; it only mentions verifying the answer."
] | [
"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,
false
] | [
"37",
"84"
] |
What is the solution to the long multiplication equation below?
22 x 90
Think step by step. | 1980 | [
"To solve the long multiplication equation 22 x 90, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 22\n x 90\n ```\n\n2. **Multiply 22 by 0 (the units digit of 90):**\n ```\n 22\n x 90\n -----\n 000\n ```\n Why did't we change the 2 to a 20? Here, we have a '0', so we... | [
"The model output correctly performs the long multiplication step-by-step, multiplying 22 by 0 and then by 9, and combining the results to get 1980. It concludes that 22 x 90 = 1980, which matches the provided solution.",
"The model output concludes that 22 x 90 = 1980, which matches the provided solution. The re... | [
"1980",
"1980",
"1980",
"1980",
"1980",
"1980"
] | [
"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
] | [
"22",
"90"
] |
What is the solution to the long multiplication equation below?
22 x 90
Think step by step. | 1980 | [
"To solve the long multiplication equation 22 x 90, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 22\n x 90\n ```\n\n2. **Multiply 22 by 0 (the units digit of 90):**\n ```\n 22\n x 90\n -----\n 000\n ```\n Why did't we change the 2 to a 20? Here, we have a '0', so we... | [
"The model output correctly performs the long multiplication step-by-step, multiplying 22 by 0 and then by 9, and combining the results to get 1980. It concludes that 22 x 90 = 1980, which matches the provided solution.",
"The model output provides a detailed step-by-step calculation, ultimately concluding that 2... | [
"1980",
"1980",
"1980",
"1980",
"1980",
"1980"
] | [
"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
] | [
"22",
"90"
] |
What is the solution to the long multiplication equation below?
68 x 43
Think step by step. | 2924 | [
"To solve the long multiplication equation \\(68 \\times 43\\), we can break it down into simpler steps:\n\n1. First, multiply 68 by 3:\n \\[\n 68 \\times 3 = 204\n \\]\n2. Next, multiply 68 by 40 (which is the same as 4 times 10, so we are multiplying by 4 and then adding a zero at the end):\n \\[\n 68 \... | [
"The model output correctly performs the long multiplication step-by-step: multiplying 68 by 3 to get 204, multiplying 68 by 40 to get 2720, and then adding these results to obtain 2924. The final answer quoted is '2924', which matches the solution provided. Therefore, the output is correct.",
"The model output s... | [
"2924",
"2924",
"2924",
"",
"27404",
"2924"
] | [
"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,
false,
true
] | [
"43",
"68"
] |
What is the solution to the long multiplication equation below?
17 x 46
Think step by step. | 782 | [
"To solve the long multiplication problem \\(17 \\times 46\\), let's break it down into a step-by-step process:\n\n### Step 1: Set up the problem\nThe multiplication is \\(17 \\times 46\\).\n\n### Step 2: Break down 46 into its tens and ones digit\n- 46 can be written as 40 + 6.\n \n Therefore, the multiplication... | [
"The model output provides a detailed step-by-step solution to the multiplication problem 17 x 46, ending with the final answer '782'. The solution matches the answer provided in the solution section, which is also 782. Therefore, the model output correctly solves the problem and arrives at the correct final answer... | [
"782",
"782",
"782",
"782",
"782",
"782"
] | [
"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
] | [
"17",
"46"
] |
What is the solution to the long multiplication equation below?
46 x 17
Think step by step. | 782 | [
"To solve the long multiplication equation \\( 46 \\times 17 \\), we can use the standard method called the \"long multiplication\" or \"grid method\" for smaller numbers. Here, we will present a step-by-step approach using the grid method for convenience.\n\n### Step-by-Step Solution:\n\n1. **Break Down the Multip... | [
"The model output concludes that the answer is 782, which matches the provided solution. The reasoning process in the output is somewhat convoluted and contains some inaccuracies in the step-by-step explanation, but the final answer aligns with the solution. Since the final answer extracted from the output is 782, ... | [
"782",
"782",
"",
"782",
"782",
""
] | [
"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,
false
] | [
"17",
"46"
] |
What is the solution to the long multiplication equation below?
32 x 36
Think step by step. | 1152 | [
"To solve the long multiplication equation \\( 32 \\times 36 \\), we follow these steps:\n\nStep 1: Multiply 32 by 6 (the units digit of 36).\n32 × 6 = 192\n\nStep 2: Multiply 32 by 30 (the tens digit of 36, written as 30).\n32 × 30 = 960\n\nStep 3: Add the results from the previous steps.\n192 + 960 = 1152\n\nSo, ... | [
"The model output correctly follows the steps of long multiplication: multiplying 32 by 6 to get 192, multiplying 32 by 30 to get 960, and then adding these results to obtain 1152. The final answer quoted is '1152', which matches the solution provided. Therefore, the output is correct.",
"The model output conclud... | [
"1152",
"1152",
"1152",
"1152",
"1152",
""
] | [
"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
] | [
"32",
"36"
] |
What is the solution to the long multiplication equation below?
36 x 32
Think step by step. | 1152 | [
"Step 1: \nFirst, we need to multiply the units digits of both numbers. 6 x 2 = 12. We write down 2 and carry the 1.\n\nStep 2: \nNext, we need to multiply the tens digits of both numbers and add the carried digit. (3 - 1) x 2 + 1 = 5 x 2 + 1 = 10 + 1 = 11. We write down 1 and carry the 1.\n\nStep 3: \nNow, we n... | [
"The solution states that the product of 36 and 32 is 1152, which matches the final answer provided in the model output ('Theboxed{1152}'). The model's step-by-step reasoning, despite some inaccuracies in the intermediate steps, concludes correctly with the final answer 1152. The parsed final answer is '1152', whic... | [
"1152",
"2135",
"1152",
"1152",
"1152",
""
] | [
"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,
false
] | [
"32",
"36"
] |
What is the solution to the long multiplication equation below?
15 x 17
Think step by step. | 255 | [
"To solve the long multiplication of 15 and 17, follow these steps:\n\n1. Write the numbers one below the other, aligning the digits by place value.\n \\[\n \\begin{array}{c@{}c}\n 15 & \\\\\n \\times 17 & \\\\\n \\end{array}\n \\]\n\n2. Multiply each digit of 17 by 1 (the first digit of 15), and writ... | [
"The output provides a detailed step-by-step explanation of multiplying 15 by 17, but the final answer given is 67. The solution states that the correct answer is 255, which is the actual product of 15 and 17. Therefore, the output's final answer (67) does not match the solution's answer (255).",
"The model outpu... | [
"67",
"255",
"",
"",
"255",
"255"
] | [
"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,
false,
true,
true
] | [
"15",
"17"
] |
What is the solution to the long multiplication equation below?
81 x 48
Think step by step. | 3888 | [
"Certainly! Let's break down the multiplication of 81 by 48 step by step:\n\n1. **First, let's write down the numbers and align them by place value:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 4 & 8 \\\\\n \\times & 8 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **First, multiply 81 by 8 (the units... | [
"The model output provides a detailed step-by-step calculation of 81 multiplied by 48, including partial products and their sum, resulting in 3888. The solution given is 3888, which matches the final answer in the model output. Therefore, the model's final answer is correct and aligns with the provided solution.",
... | [
"3888",
"3888",
"3888",
"3888",
"",
"3321"
] | [
"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,
false,
false
] | [
"48",
"81"
] |
What is the solution to the long multiplication equation below?
81 x 48
Think step by step. | 3888 | [
"Certainly! Let's break down the multiplication of 81 by 48 step by step:\n\n1. **First, let's write down the numbers and align them by place value:**\n \\[\n \\begin{array}{c@{}c@{}c@{}c}\n & 4 & 8 \\\\\n \\times & 8 & 1 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **First, multiply 81 by 8 (the units... | [
"The model output provides a detailed step-by-step calculation of 81 multiplied by 48, resulting in 3888. The solution given is 3888, which matches the final answer in the model output. The reasoning in the output correctly performs the multiplication and arrives at the same result as the solution.",
"The model o... | [
"3888",
"3888",
"3888",
"3888",
"",
"3321"
] | [
"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,
false,
false
] | [
"48",
"81"
] |
What is the solution to the long multiplication equation below?
48 x 81
Think step by step. | 3888 | [
"To solve the long multiplication equation 48 x 81, you can break it down into simpler parts. Here's how you do it step by step:\n\n1. First, let's write the multiplication as follows, breaking it into easier parts:\n (40 + 8) x (80 + 1)\n\n2. Now apply the distributive property (also known as the FOIL method for... | [
"The solution provided in the output is 3988, which is obtained by breaking down 48 x 81 into parts and summing their products. The original solution states the answer as 3888, which does not match the output's calculated answer. Since the output's calculation results in 3988, and the solution's answer is 3888, the... | [
"3988",
"3888",
"3988",
"3988",
"3888",
"3988"
] | [
"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,
false,
true,
false
] | [
"48",
"81"
] |
What is the solution to the long multiplication equation below?
90 x 60
Think step by step. | 5400 | [
"To solve the long multiplication equation \\( 90 \\times 60 \\), we can follow these steps:\n\n1. **Break down the numbers:**\n \\[\n 90 = 9 \\times 10\n \\]\n \\[\n 60 = 6 \\times 10\n \\]\n\n2. **Multiply the numbers:**\n \\[\n 9 \\times 6 = 54\n \\]\n\n3. **Multiply the result by 10:**\n \\[... | [
"The solution provided in the original solution is 5400, but the model output concludes the answer is 540. The model's reasoning shows that 90 x 60 equals 540, which matches the calculation 9 x 6 x 10 = 540. Therefore, the model output's final answer is 540, which does not match the solution's answer of 5400.",
"... | [
"540",
"5400",
"540",
"540",
"540",
"540"
] | [
"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,
false,
false,
false
] | [
"60",
"90"
] |
What is the solution to the long multiplication equation below?
60 x 90
Think step by step. | 5400 | [
"Let's solve the is multiplication problem step by step.\n\n1. First, write down the numbers to be multiplied:\n \\[\n \\begin{array}{c@{}c@{}c}\n & 6 & 0 \\\\\n \\times & 9 & 0 \\\\\n \\end{array}\n \\]\n\n2. Multiply 60 by 0 (the units digit of the multiplier):\n \\[\n 60 \\times 0 = 0\n \\]\n... | [
"The solution provided is 5400, which is the correct product of 60 and 90. The model output's step-by-step calculation, however, concludes with 540, which is incorrect. The model's reasoning shows multiplying 60 by 0 to get 0, and 60 by 9 to get 540, then adding these to get 540. But this is a misinterpretation of ... | [
"540",
"600",
"540",
"540",
"5400",
"5400"
] | [
"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
] | [
"60",
"90"
] |
What is the solution to the long multiplication equation below?
22 x 13
Think step by step. | 286 | [
"To solve \\(22 \\times 13\\), we can use the long multiplication method. Here's how it works step by step:\n\n1. Multiply the ones digit of the multiplier (1) by each digit in the multiplicand (22).\n\n \\(1 \\times 2 = 2\\)\n \\(1 \\times 2 = 2\\)\n\n2. Write these products one below the other, aligning them ... | [
"The solution provided states that 22 multiplied by 13 equals 286, but the detailed step-by-step explanation concludes that 22 times 13 equals 82. Since the detailed steps are consistent with the final answer of 82, the solution's stated answer of 286 is incorrect. The model output's final answer is 82, which match... | [
"82",
"226",
"286",
"266",
"124",
"82"
] | [
"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,
true,
false
] | [
"13",
"22"
] |
What is the solution to the long multiplication equation below?
13 x 22
Think step by step. | 286 | [
"To solve the long multiplication of 13 x 22, we can break it down into smaller steps.\n\n1. Multiply the units place of both numbers: 3 x 2 = 6\n2. Multiply the tens place of the first number by the units place of the second number: 1 x 2 = 2\n3.ей add these results together: 6 + 2 = 8\n\nSo, the solution is 86.\n... | [
"The model output concludes that the answer is 86, which is different from the provided solution of 286. The reasoning steps in the output are flawed, as they do not correctly perform the long multiplication of 13 x 22, and the final answer does not match the actual product.",
"The model output concludes with the... | [
"86",
"86",
"The model output does not state the answer; it only asks for an explanation.",
"286",
"266",
"866"
] | [
"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
] | [
"13",
"22"
] |
What is the solution to the long multiplication equation below?
60 x 75
Think step by step. | 4500 | [
"To solve the long multiplication equation 60 x 75, we can break it down into smaller, manageable steps. Let's use the standard multiplication method:\n\n1. Multiply 60 by 5 (the units digit of 75): \n \\[ 60 \\times 5 = 300 \\]\n\n2. Multiply 60 by 70 (the tens digit of 75), then add a zero at the end:\n \\[ 60 ... | [
"The model output concludes that the solution to 60 x 75 is 4500, which matches the provided solution. The reasoning steps provided in the output correctly break down the multiplication into parts and sum them to arrive at 4500.",
"The model output provides a step-by-step multiplication process and concludes with... | [
"4500",
"4500",
"4500",
"420",
"",
""
] | [
"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,
false,
false
] | [
"60",
"75"
] |
What is the solution to the long multiplication equation below?
62 x 97
Think step by step. | 6014 | [
"To solve the long multiplication problem 62 x 97, follow these step-by-step calculations:\n\n1) Break down 97 into 90 + 7:\n 62 x (90 + 7) = 62 x 90 + 62 x 7\n\n2) Calculate 62 x 90:\n 62 x 90 = 5580\n\n3) Calculate 62 x 7:\n 62 x 7 = 434\n\n4) Add the two results from step 2 and step 3:\n 5580 + 434 = 601... | [
"The output provides a detailed step-by-step calculation of 62 x 97, resulting in 6014, which matches the solution provided. The final answer quoted in the output is '6014', which is the same as the solution.",
"The model output concludes with 'The final answer is: 6014' and provides a detailed step-by-step calcu... | [
"6014",
"6014",
"6014",
"6014",
"6014",
"6014"
] | [
"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
] | [
"62",
"97"
] |
What is the solution to the long multiplication equation below?
38 x 83
Think step by step. | 3154 | [
"\\boxed{3074}",
"Wait, how? Let's break it down step by step:\n\n1) First, let's consider the multiplication of the two \"8's\". Imagine theivy walls supporting these giants:\n\n 8 8\n x3 3\n\n 64 24\n\n 72 48 (7 * 8 = 56, carry 5; 5 * 8 = 40, add the carry, making it 45)\n\n2) Moving to th... | [
"The solution provided is 3154, but the model output states 3074. Since the solution is 3154, the model output does not match the solution. Therefore, the correctness depends on whether the output matches the solution. The output is \boxed{3074}, which does not match 3154, so it is incorrect.",
"The model output ... | [
"3074",
"3074",
"3074",
"3064",
"3074",
"B"
] | [
"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,
false,
false
] | [
"38",
"83"
] |
What is the solution to the long multiplication equation below?
38 x 83
Think step by step. | 3154 | [
"\\boxed{3074}",
"Wait, how? Let's break it down step by step:\n\n1) First, let's consider the multiplication of the two \"8's\". Imagine theivy walls supporting these giants:\n\n 8 8\n x3 3\n\n 64 24\n\n 72 48 (7 * 8 = 56, carry 5; 5 * 8 = 40, add the carry, making it 45)\n\n2) Moving to th... | [
"The solution provided is 3154, but the model output gives 3074. Since the question asks for the solution to 38 x 83, I need to verify which value is correct. The model output's final answer is 3074, which does not match the solution 3154. Therefore, the model output is incorrect.",
"The model output attempts to ... | [
"3074",
"3074",
"3074",
"3064",
"3074",
"B"
] | [
"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,
false,
false
] | [
"38",
"83"
] |
What is the solution to the long multiplication equation below?
38 x 83
Think step by step. | 3154 | [
"\\boxed{3074}",
"Wait, how? Let's break it down step by step:\n\n1) First, let's consider the multiplication of the two \"8's\". Imagine theivy walls supporting these giants:\n\n 8 8\n x3 3\n\n 64 24\n\n 72 48 (7 * 8 = 56, carry 5; 5 * 8 = 40, add the carry, making it 45)\n\n2) Moving to th... | [
"The solution provided is 3154, but the model output states 3074. Since the question asks for the solution to 38 x 83, I need to verify the correctness of the output. The model output's final answer is 3074, which does not match the solution 3154. Therefore, the output is incorrect.",
"The model output provides a... | [
"3074",
"3074",
"3074",
"3064",
"3074",
"B"
] | [
"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,
false,
false
] | [
"38",
"83"
] |
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