problem stringlengths 73 2.75k | solution stringlengths 335 3.59k | r1_distill_70b_response sequencelengths 3 3 | __original_row_idx int64 1 7.5k | r1_distill_70b_extracted_answer sequencelengths 3 3 | _majority_responses sequencelengths 1 3 | verified_r1_distill_70b_response stringlengths 590 77.4k | conversations listlengths 2 2 |
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At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students at Euclid Middle School are taking the co... | 1. **Identify the number of students in each class:**
- Mrs. Germain's class: 11 students
- Mr. Newton's class: 8 students
- Mrs. Young's class: 9 students
2. **Assumption of no overlap in students:**
Since the problem does not mention any students being in more than one class, we assume that all students ... | [
"<think>\nTo determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.\n\nFirst, there are 11 students in Mrs. Germain's class.\n\nNext, there are 8 students in Mr. Newton's class.\n\nFinally, there are 9 student... | 12 | [
"28",
"28",
"28"
] | [
"<think>\nTo determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.\n\nFirst, there are 11 students in Mrs. Germain's class.\n\nNext, there are 8 students in Mr. Newton's class.\n\nFinally, there are 9 student... | <think>
To determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.
First, there are 11 students in Mrs. Germain's class.
Next, there are 8 students in Mr. Newton's class.
Finally, there are 9 students in Mrs. Yo... | [
{
"from": "human",
"value": "At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students ... |
At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students at Euclid Middle School are taking the co... | 1. **Identify the number of students in each class:**
- Mrs. Germain's class: 11 students
- Mr. Newton's class: 8 students
- Mrs. Young's class: 9 students
2. **Assumption of no overlap in students:**
Since the problem does not mention any students being in more than one class, we assume that all students ... | [
"<think>\nTo determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.\n\nFirst, there are 11 students in Mrs. Germain's class.\n\nNext, there are 8 students in Mr. Newton's class.\n\nFinally, there are 9 student... | 12 | [
"28",
"28",
"28"
] | [
"<think>\nTo determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.\n\nFirst, there are 11 students in Mrs. Germain's class.\n\nNext, there are 8 students in Mr. Newton's class.\n\nFinally, there are 9 student... | <think>
First, note the number of students in each mathematics teacher's AMC 8 class:
- Mrs. Germain has 11 students.
- Mr. Newton has 8 students.
- Mrs. Young has 9 students.
Next, add these numbers together to find the total number of mathematics students taking the contest:
11 + 8 + 9 = 28.
Therefore, there are 28... | [
{
"from": "human",
"value": "At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students ... |
At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students at Euclid Middle School are taking the co... | 1. **Identify the number of students in each class:**
- Mrs. Germain's class: 11 students
- Mr. Newton's class: 8 students
- Mrs. Young's class: 9 students
2. **Assumption of no overlap in students:**
Since the problem does not mention any students being in more than one class, we assume that all students ... | [
"<think>\nTo determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.\n\nFirst, there are 11 students in Mrs. Germain's class.\n\nNext, there are 8 students in Mr. Newton's class.\n\nFinally, there are 9 student... | 12 | [
"28",
"28",
"28"
] | [
"<think>\nTo determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I will add the number of students from each teacher's class.\n\nFirst, there are 11 students in Mrs. Germain's class.\n\nNext, there are 8 students in Mr. Newton's class.\n\nFinally, there are 9 student... | <think>
To determine the total number of mathematics students at Euclid Middle School taking the AMC 8 contest, I'll add the number of students from each teacher's class.
There are 11 students in Mrs. Germain's class, 8 in Mr. Newton's class, and 9 in Mrs. Young's class.
Adding these together: 11 + 8 + 9 equals 28.
... | [
{
"from": "human",
"value": "At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in Mrs. Young's class taking the AMC $8$ this year. How many mathematics students ... |
The operation $\otimes$ is defined for all nonzero numbers by $a\otimes b =\frac{a^{2}}{b}$. Determine $[(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)]$.
$\text{(A)}\ -\frac{2}{3}\qquad\text{(B)}\ -\frac{1}{4}\qquad\text{(C)}\ 0\qquad\text{(D)}\ \frac{1}{4}\qquad\text{(E)}\ \frac{2}{3}$ | 1. **Apply the operation $\otimes$ to the innermost parentheses first:**
\[
(1 \otimes 2) \otimes 3 = \left(\frac{1^2}{2}\right) \otimes 3 = \frac{1}{2} \otimes 3
\]
\[
1 \otimes (2 \otimes 3) = 1 \otimes \left(\frac{2^2}{3}\right) = 1 \otimes \frac{4}{3}
\]
2. **Calculate each part using the definit... | [
"<think>\nAlright, so I need to solve this problem where they define an operation called \"otimes,\" which is given by \\( a \\otimes b = \\frac{a^2}{b} \\). The question asks me to compute \\( [(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)] \\) and the options are given from A to E.\n\nOkay, let's break ... | 1 | [
"A",
"A",
"A"
] | [
"<think>\nAlright, so I need to solve this problem where they define an operation called \"otimes,\" which is given by \\( a \\otimes b = \\frac{a^2}{b} \\). The question asks me to compute \\( [(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)] \\) and the options are given from A to E.\n\nOkay, let's break ... | <think>
Alright, so I need to solve this problem where they define an operation called "otimes," which is given by \( a \otimes b = \frac{a^2}{b} \). The question asks me to compute \( [(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)] \) and the options are given from A to E.
Okay, let's break this down step by st... | [
{
"from": "human",
"value": "The operation $\\otimes$ is defined for all nonzero numbers by $a\\otimes b =\\frac{a^{2}}{b}$. Determine $[(1\\otimes 2)\\otimes 3]-[1\\otimes (2\\otimes 3)]$.\n$\\text{(A)}\\ -\\frac{2}{3}\\qquad\\text{(B)}\\ -\\frac{1}{4}\\qquad\\text{(C)}\\ 0\\qquad\\text{(D)}\\ \\frac{1}{4}... |
The operation $\otimes$ is defined for all nonzero numbers by $a\otimes b =\frac{a^{2}}{b}$. Determine $[(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)]$.
$\text{(A)}\ -\frac{2}{3}\qquad\text{(B)}\ -\frac{1}{4}\qquad\text{(C)}\ 0\qquad\text{(D)}\ \frac{1}{4}\qquad\text{(E)}\ \frac{2}{3}$ | 1. **Apply the operation $\otimes$ to the innermost parentheses first:**
\[
(1 \otimes 2) \otimes 3 = \left(\frac{1^2}{2}\right) \otimes 3 = \frac{1}{2} \otimes 3
\]
\[
1 \otimes (2 \otimes 3) = 1 \otimes \left(\frac{2^2}{3}\right) = 1 \otimes \frac{4}{3}
\]
2. **Calculate each part using the definit... | [
"<think>\nAlright, so I need to solve this problem where they define an operation called \"otimes,\" which is given by \\( a \\otimes b = \\frac{a^2}{b} \\). The question asks me to compute \\( [(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)] \\) and the options are given from A to E.\n\nOkay, let's break ... | 1 | [
"A",
"A",
"A"
] | [
"<think>\nAlright, so I need to solve this problem where they define an operation called \"otimes,\" which is given by \\( a \\otimes b = \\frac{a^2}{b} \\). The question asks me to compute \\( [(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)] \\) and the options are given from A to E.\n\nOkay, let's break ... | <think>
Alright, so I've got this problem here with a special operation defined as \( a \otimes b = \frac{a^2}{b} \). It asks me to find \( [(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)] \). Hmm, operation inside another operation, seems like I need to compute each part step by step.
First, I need to understand... | [
{
"from": "human",
"value": "The operation $\\otimes$ is defined for all nonzero numbers by $a\\otimes b =\\frac{a^{2}}{b}$. Determine $[(1\\otimes 2)\\otimes 3]-[1\\otimes (2\\otimes 3)]$.\n$\\text{(A)}\\ -\\frac{2}{3}\\qquad\\text{(B)}\\ -\\frac{1}{4}\\qquad\\text{(C)}\\ 0\\qquad\\text{(D)}\\ \\frac{1}{4}... |
The operation $\otimes$ is defined for all nonzero numbers by $a\otimes b =\frac{a^{2}}{b}$. Determine $[(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)]$.
$\text{(A)}\ -\frac{2}{3}\qquad\text{(B)}\ -\frac{1}{4}\qquad\text{(C)}\ 0\qquad\text{(D)}\ \frac{1}{4}\qquad\text{(E)}\ \frac{2}{3}$ | 1. **Apply the operation $\otimes$ to the innermost parentheses first:**
\[
(1 \otimes 2) \otimes 3 = \left(\frac{1^2}{2}\right) \otimes 3 = \frac{1}{2} \otimes 3
\]
\[
1 \otimes (2 \otimes 3) = 1 \otimes \left(\frac{2^2}{3}\right) = 1 \otimes \frac{4}{3}
\]
2. **Calculate each part using the definit... | [
"<think>\nAlright, so I need to solve this problem where they define an operation called \"otimes,\" which is given by \\( a \\otimes b = \\frac{a^2}{b} \\). The question asks me to compute \\( [(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)] \\) and the options are given from A to E.\n\nOkay, let's break ... | 1 | [
"A",
"A",
"A"
] | [
"<think>\nAlright, so I need to solve this problem where they define an operation called \"otimes,\" which is given by \\( a \\otimes b = \\frac{a^2}{b} \\). The question asks me to compute \\( [(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)] \\) and the options are given from A to E.\n\nOkay, let's break ... | <think>
Okay, so I have this problem here about an operation called "otimes," which is defined for all nonzero numbers as \( a \otimes b = \frac{a^2}{b} \). The question is asking me to find the value of \( [(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)] \). The answer choices are A through E: -2/3, -1/4, 0, 1/4,... | [
{
"from": "human",
"value": "The operation $\\otimes$ is defined for all nonzero numbers by $a\\otimes b =\\frac{a^{2}}{b}$. Determine $[(1\\otimes 2)\\otimes 3]-[1\\otimes (2\\otimes 3)]$.\n$\\text{(A)}\\ -\\frac{2}{3}\\qquad\\text{(B)}\\ -\\frac{1}{4}\\qquad\\text{(C)}\\ 0\\qquad\\text{(D)}\\ \\frac{1}{4}... |
"If $991+993+995+997+999=5000-N$, then $N=$\n$\\text{(A)}\\ 5 \\qquad \\text{(B)}\\ 10 \\qquad \\tex(...TRUNCATED) | "1. **Identify the problem and express each term in a form that reveals a pattern:**\n \\[\n 991(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I(...TRUNCATED) | 15 | [
"E",
"E",
"E"
] | ["<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I(...TRUNCATED) | "<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I (...TRUNCATED) | [{"from":"human","value":"If $991+993+995+997+999=5000-N$, then $N=$\n$\\text{(A)}\\ 5 \\qquad \\tex(...TRUNCATED) |
"If $991+993+995+997+999=5000-N$, then $N=$\n$\\text{(A)}\\ 5 \\qquad \\text{(B)}\\ 10 \\qquad \\tex(...TRUNCATED) | "1. **Identify the problem and express each term in a form that reveals a pattern:**\n \\[\n 991(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I(...TRUNCATED) | 15 | [
"E",
"E",
"E"
] | ["<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I(...TRUNCATED) | "<think>\nAlright, let me try to solve this problem. It says that 991 + 993 + 995 + 997 + 999 equals(...TRUNCATED) | [{"from":"human","value":"If $991+993+995+997+999=5000-N$, then $N=$\n$\\text{(A)}\\ 5 \\qquad \\tex(...TRUNCATED) |
"If $991+993+995+997+999=5000-N$, then $N=$\n$\\text{(A)}\\ 5 \\qquad \\text{(B)}\\ 10 \\qquad \\tex(...TRUNCATED) | "1. **Identify the problem and express each term in a form that reveals a pattern:**\n \\[\n 991(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I(...TRUNCATED) | 15 | [
"E",
"E",
"E"
] | ["<think>\nOkay, so I have this problem here: 991 + 993 + 995 + 997 + 999 equals 5000 minus N, and I(...TRUNCATED) | "<think>\nAlright, so I came across this math problem, and at first glance, it seems straightforward(...TRUNCATED) | [{"from":"human","value":"If $991+993+995+997+999=5000-N$, then $N=$\n$\\text{(A)}\\ 5 \\qquad \\tex(...TRUNCATED) |
"The total in-store price for an appliance is $\\textdollar 99.99$. A television commercial advertis(...TRUNCATED) | "1. **Calculate the total cost of buying the appliance from the television advertiser:**\n The adv(...TRUNCATED) | ["<think>\nOkay, so I need to figure out how much money is saved by buying the appliance through the(...TRUNCATED) | 18 | [
"B",
"B",
"B"
] | ["<think>\nOkay, so I need to figure out how much money is saved by buying the appliance through the(...TRUNCATED) | "<think>\nOkay, so I need to figure out how much money is saved by buying the appliance through the (...TRUNCATED) | [{"from":"human","value":"The total in-store price for an appliance is $\\textdollar 99.99$. A telev(...TRUNCATED) |
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