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values | data_source stringclasses 1
value | source_prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict | messages listlengths 1 1 | ground_truth stringclasses 585
values | pass_count int64 9 31 | pass_rate stringclasses 23
values | num_samples int64 32 32 | generator_model stringclasses 1
value | generator_chat_template stringclasses 1
value | generator_temperature float64 1 1 | generator_top_p float64 1 1 | generator_max_tokens int64 8.19k 8.19k | source_split stringclasses 1
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Let $A$ be the set of positive integers that have no prime factors other than $2$, $3$, or $5$. The infinite sum \[ \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{12} + \frac{1}{15} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \c... | 19 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $A$ be the set of positive integers that have no prime factors other than $2$, $3$, or $5$. The infinite sum \\[ \... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eab8fc10-57fb-4d0c-9af5-3a331857ec74"
} | [
{
"content": "Let $A$ be the set of positive integers that have no prime factors other than $2$, $3$, or $5$. The infinite sum \\[ \\frac{1}{1} + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{12} + \\frac{1}{15} + \\frac{1}{16}... | 19 | 31 | 31/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the remainder when $2020!$ is divided by $2020^2$. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the remainder when $2020!$ is divided by $2020^2$.\n\nRemember to put your answer on its own line after \"Answer:... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b6c18ab0-f317-46b8-9d0a-7863266e63c7"
} | [
{
"content": "Find the remainder when $2020!$ is divided by $2020^2$.",
"role": "user"
}
] | 0 | 30 | 30/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the value of \((2^0-1+5^2-0)^{-1}\times5?\) Provide your answer in the form \(\frac{k}{m}\), where k and m are integers. Then, calculate the sum k + m. | 6 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of \\((2^0-1+5^2-0)^{-1}\\times5?\\) Provide your answer in the form \\(\\frac{k}{m}\\), where k and... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "229960d2-7b39-43d7-892c-45298fb042ff"
} | [
{
"content": "What is the value of \\((2^0-1+5^2-0)^{-1}\\times5?\\) Provide your answer in the form \\(\\frac{k}{m}\\), where k and m are integers. Then, calculate the sum k + m.",
"role": "user"
}
] | 6 | 30 | 30/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{1050}$ is defined? | 11 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the smallest integer $n$, greater than $1$, such that $n^{-1}\\pmod{1050}$ is defined?\n\nRemember to put your... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "798a0beb-583f-40c2-a7f3-ffd6799b64a5"
} | [
{
"content": "What is the smallest integer $n$, greater than $1$, such that $n^{-1}\\pmod{1050}$ is defined?",
"role": "user"
}
] | 11 | 29 | 29/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A three-quarter sector of a circle with a radius of \(4\) inches, together with its interior, can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches? Provide your answer in the form of \(a\pi \sqrt{b}\), whe... | 10 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA three-quarter sector of a circle with a radius of \\(4\\) inches, together with its interior, can be rolled up to fo... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3a2f10a0-cbb8-42ef-bb0b-6367d0c07908"
} | [
{
"content": "A three-quarter sector of a circle with a radius of \\(4\\) inches, together with its interior, can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches? Provide your answer in the form o... | 10 | 29 | 29/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the number of real values of $x$ satisfying the equation $2^{2x^2 - 7x + 5} = 1$. | 2 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of real values of $x$ satisfying the equation $2^{2x^2 - 7x + 5} = 1$.\n\nRemember to put your answer ... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e701fca2-dea1-4c9b-8583-58e5b0366155"
} | [
{
"content": "Find the number of real values of $x$ satisfying the equation $2^{2x^2 - 7x + 5} = 1$.",
"role": "user"
}
] | 2 | 29 | 29/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Diana and Apollo each roll a standard die obtaining a number at random from \(1\) to \(6\). What is the probability that Diana's number is larger than Apollo's number? Provide your answer as a fraction in simplest form \(\frac{k}{m}\), and then calculate the value of \(k + m\). | 17 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDiana and Apollo each roll a standard die obtaining a number at random from \\(1\\) to \\(6\\). What is the probabilit... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bd55ed9e-9840-415e-98a8-abc4462dde8d"
} | [
{
"content": "Diana and Apollo each roll a standard die obtaining a number at random from \\(1\\) to \\(6\\). What is the probability that Diana's number is larger than Apollo's number? Provide your answer as a fraction in simplest form \\(\\frac{k}{m}\\), and then calculate the value of \\(k + m\\).",
"rol... | 17 | 29 | 29/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the volume of a cube whose surface area is twice that of a cube with volume $1$? Provide your answer in the form of $a\sqrt{b}$ where $a$ and $b$ are integers, and give the value of $a + b$. | 4 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the volume of a cube whose surface area is twice that of a cube with volume $1$? Provide your answer in the fo... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d9531521-9e20-4690-bfb1-26fb05e0a357"
} | [
{
"content": "What is the volume of a cube whose surface area is twice that of a cube with volume $1$? Provide your answer in the form of $a\\sqrt{b}$ where $a$ and $b$ are integers, and give the value of $a + b$.",
"role": "user"
}
] | 4 | 29 | 29/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Determine the smallest $n$ such that $n \equiv (a - 1) \pmod{a}$ for all $a \in \{2,3,..., 10\}$. | 2519 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDetermine the smallest $n$ such that $n \\equiv (a - 1) \\pmod{a}$ for all $a \\in \\{2,3,..., 10\\}$.\n\nRemember to ... | MATH | {
"ground_truth": "2519",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "12134e2f-b3f8-4b0f-971a-b79e4c987098"
} | [
{
"content": "Determine the smallest $n$ such that $n \\equiv (a - 1) \\pmod{a}$ for all $a \\in \\{2,3,..., 10\\}$.",
"role": "user"
}
] | 2519 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $N$ be the set of natural numbers. Suppose $f: N \to N$ is a function satisfying the following conditions:
1. $f(mn) = f(m)f(n)$
2. $f(m) < f(n)$ if $m < n$
3. $f(2) = 2$
What is the sum of $\sum_{k=1}^{20}f(k)$? | 210 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $N$ be the set of natural numbers. Suppose $f: N \\to N$ is a function satisfying the following conditions: \n1. ... | MATH | {
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fa9477a6-cd0a-4950-a7bd-04fa75ef951c"
} | [
{
"content": "Let $N$ be the set of natural numbers. Suppose $f: N \\to N$ is a function satisfying the following conditions: \n1. $f(mn) = f(m)f(n)$ \n2. $f(m) < f(n)$ if $m < n$ \n3. $f(2) = 2$ \n\nWhat is the sum of $\\sum_{k=1}^{20}f(k)$?",
"role": "user"
}
] | 210 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The Flyfishing Club is choosing officers. There are $23$ members in the club: $14$ boys and $9$ girls. In how many ways can they choose a President and a Vice President if one of them must be a boy and the other must be a girl (either office can be held by the boy or the girl)? | 252 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe Flyfishing Club is choosing officers. There are $23$ members in the club: $14$ boys and $9$ girls. In how many way... | MATH | {
"ground_truth": "252",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a01e1dd8-7bc8-4d62-a257-2ec50ee2bcad"
} | [
{
"content": "The Flyfishing Club is choosing officers. There are $23$ members in the club: $14$ boys and $9$ girls. In how many ways can they choose a President and a Vice President if one of them must be a boy and the other must be a girl (either office can be held by the boy or the girl)?",
"role": "user... | 252 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Tsrutsuna starts in the bottom left cell of a $7 \times 7$ square table, while Tsuna is in the upper right cell. The center cell of the table contains cheese. Tsrutsuna wants to reach Tsuna and bring a piece of cheese with him. From a cell, Tsrutsuna can only move to the right or the top neighboring cell. Determine the... | 400 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTsrutsuna starts in the bottom left cell of a $7 \\times 7$ square table, while Tsuna is in the upper right cell. The ... | MATH | {
"ground_truth": "400",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c5ff01ff-1a85-48fd-8914-c9af0b08db66"
} | [
{
"content": "Tsrutsuna starts in the bottom left cell of a $7 \\times 7$ square table, while Tsuna is in the upper right cell. The center cell of the table contains cheese. Tsrutsuna wants to reach Tsuna and bring a piece of cheese with him. From a cell, Tsrutsuna can only move to the right or the top neighbor... | 400 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Given that $\binom{23}{3}=1771$, $\binom{23}{4}=8855$, and $\binom{23}{5}=33649$, find $\binom{25}{5}$. | 53130 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven that $\\binom{23}{3}=1771$, $\\binom{23}{4}=8855$, and $\\binom{23}{5}=33649$, find $\\binom{25}{5}$.\n\nRemembe... | MATH | {
"ground_truth": "53130",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8c30e0ff-4671-4bd4-a659-835f15c8f272"
} | [
{
"content": "Given that $\\binom{23}{3}=1771$, $\\binom{23}{4}=8855$, and $\\binom{23}{5}=33649$, find $\\binom{25}{5}$.",
"role": "user"
}
] | 53130 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The polynomial equation \[x^3 + bx + c = 0,\]where $b$ and $c$ are rational numbers, has $5-\sqrt{2}$ as a root. It also has an integer root. What is it? | -10 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe polynomial equation \\[x^3 + bx + c = 0,\\]where $b$ and $c$ are rational numbers, has $5-\\sqrt{2}$ as a root. It... | MATH | {
"ground_truth": "-10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d92977cb-057d-4dfb-8dbf-8d98f7e31473"
} | [
{
"content": "The polynomial equation \\[x^3 + bx + c = 0,\\]where $b$ and $c$ are rational numbers, has $5-\\sqrt{2}$ as a root. It also has an integer root. What is it?",
"role": "user"
}
] | -10 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Solve the system \(\left\{\begin{array}{l}x^3-y^3=2b,\\x^2y-xy^2=b.\end{array}\right.\) Determine the value of \(b\) for which there exists a solution \(x, y\). | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSolve the system \\(\\left\\{\\begin{array}{l}x^3-y^3=2b,\\\\x^2y-xy^2=b.\\end{array}\\right.\\) Determine the value o... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "50114457-ada2-4f42-904e-6f6b1866ac11"
} | [
{
"content": "Solve the system \\(\\left\\{\\begin{array}{l}x^3-y^3=2b,\\\\x^2y-xy^2=b.\\end{array}\\right.\\) Determine the value of \\(b\\) for which there exists a solution \\(x, y\\).",
"role": "user"
}
] | 0 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Edward is trying to spell the word "CAT". He has an equal chance of spelling the word in any order of letters (e.g., TAC or TCA). What is the probability that he spells "CAT" incorrectly? Provide your answer as a simplified fraction in the form \(\frac{k}{m}\), and then calculate the value of k + m. | 11 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEdward is trying to spell the word \"CAT\". He has an equal chance of spelling the word in any order of letters (e.g.,... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c2191c86-e62b-465c-af4b-715a16835ba6"
} | [
{
"content": "Edward is trying to spell the word \"CAT\". He has an equal chance of spelling the word in any order of letters (e.g., TAC or TCA). What is the probability that he spells \"CAT\" incorrectly? Provide your answer as a simplified fraction in the form \\(\\frac{k}{m}\\), and then calculate the value ... | 11 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f(x) = x^{2}(1-x)^{2}$. What is the value of the sum
\begin{align*}
f\left(\frac{1}{2019}\right)-f\left(\frac{2}{2019}\right)+f\left(\frac{3}{2019}\right)-&f\left(\frac{4}{2019}\right)+\cdots\\
&\,+f\left(\frac{2017}{2019}\right) - f\left(\frac{2018}{2019}\right)?
\end{align*} | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f(x) = x^{2}(1-x)^{2}$. What is the value of the sum\n\\begin{align*}\nf\\left(\\frac{1}{2019}\\right)-f\\left(\\... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cda5c5e0-eaef-44be-ba3c-3e49d6381a2b"
} | [
{
"content": "Let $f(x) = x^{2}(1-x)^{2}$. What is the value of the sum\n\\begin{align*}\nf\\left(\\frac{1}{2019}\\right)-f\\left(\\frac{2}{2019}\\right)+f\\left(\\frac{3}{2019}\\right)-&f\\left(\\frac{4}{2019}\\right)+\\cdots\\\\\n &\\,+f\\left(\\frac{2017}{2019}\\right) - f\\left(\\frac{2018}{2019}\\right)?\n... | 0 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
In a geometric progression whose terms are positive, any term is equal to the sum of the next two following terms. What is the common ratio? Provide your answer in the form of \(\frac{\sqrt{k} - m}{n}\) and find the value of \(k + m + n\). | 8 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn a geometric progression whose terms are positive, any term is equal to the sum of the next two following terms. Wha... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "49a4436d-87d2-4ced-8063-bd3ae6bc8fb1"
} | [
{
"content": "In a geometric progression whose terms are positive, any term is equal to the sum of the next two following terms. What is the common ratio? Provide your answer in the form of \\(\\frac{\\sqrt{k} - m}{n}\\) and find the value of \\(k + m + n\\).",
"role": "user"
}
] | 8 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
How many different prime numbers are factors of $N$ if
\[ \log_2 (\log_3 (\log_5 (\log_7 N))) = 11? \] | 1 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many different prime numbers are factors of $N$ if \n\\[ \\log_2 (\\log_3 (\\log_5 (\\log_7 N))) = 11? \\]\n\nReme... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "affe547e-e5c7-413f-b10e-0a23f925e02b"
} | [
{
"content": "How many different prime numbers are factors of $N$ if \n\\[ \\log_2 (\\log_3 (\\log_5 (\\log_7 N))) = 11? \\]",
"role": "user"
}
] | 1 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A fair die is rolled six times. Find the probability of rolling at least a five at least five times. Express your answer as a fraction in simplest form. The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\). | 742 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA fair die is rolled six times. Find the probability of rolling at least a five at least five times. Express your answ... | MATH | {
"ground_truth": "742",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2a589873-615a-4f91-ba26-f394a2d2dcd0"
} | [
{
"content": "A fair die is rolled six times. Find the probability of rolling at least a five at least five times. Express your answer as a fraction in simplest form. The original answer is in \\(\\frac{k}{m}\\) format, please give the value of \\(k + m\\).",
"role": "user"
}
] | 742 | 28 | 28/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Suppose that $x, y, z$ are non-zero real numbers such that:
\[
\begin{cases}
x = 2 - \dfrac{y}{z} \\
y = 2 - \dfrac{z}{x} \\
z = 2 - \dfrac{x}{y}.
\end{cases}
\]
Find all possible values of $T = x + y + z$. | 3 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $x, y, z$ are non-zero real numbers such that:\n\\[\n\\begin{cases}\n x = 2 - \\dfrac{y}{z} \\\\\n y = ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "dd8e8517-8fd3-45ea-82fa-4eae7c7dc987"
} | [
{
"content": "Suppose that $x, y, z$ are non-zero real numbers such that:\n\\[\n\\begin{cases}\n x = 2 - \\dfrac{y}{z} \\\\\n y = 2 - \\dfrac{z}{x} \\\\\n z = 2 - \\dfrac{x}{y}.\n\\end{cases}\n\\]\nFind all possible values of $T = x + y + z$.",
"role": "user"
}
] | 3 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Determine all non-negative integers $k$ such that there exists a function $f : \mathbb{N} \to \mathbb{N}$ satisfying the equation:
\[
f^n(n) = n + k
\]
for all $n \in \mathbb{N}$. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDetermine all non-negative integers $k$ such that there exists a function $f : \\mathbb{N} \\to \\mathbb{N}$ satisfyin... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a5c6ec38-b653-4f04-be28-afbbd006b978"
} | [
{
"content": "Determine all non-negative integers $k$ such that there exists a function $f : \\mathbb{N} \\to \\mathbb{N}$ satisfying the equation:\n\\[\nf^n(n) = n + k\n\\]\nfor all $n \\in \\mathbb{N}$.",
"role": "user"
}
] | 0 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A pentagon has four interior angles each equal to $110^\circ$. Find the degree measure of the fifth interior angle. | 100 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA pentagon has four interior angles each equal to $110^\\circ$. Find the degree measure of the fifth interior angle.\n... | MATH | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a01882aa-8823-4607-a960-b6db3af42fe8"
} | [
{
"content": "A pentagon has four interior angles each equal to $110^\\circ$. Find the degree measure of the fifth interior angle.",
"role": "user"
}
] | 100 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f(x) = x^3 + ax + b$, where $a \neq b$. Suppose the tangent lines to the graph of $f$ at $x=a$ and $x=b$ are parallel. Find $f(1)$. | 1 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f(x) = x^3 + ax + b$, where $a \\neq b$. Suppose the tangent lines to the graph of $f$ at $x=a$ and $x=b$ are par... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "756522a1-9d81-4e4e-b192-5b3363ae6c08"
} | [
{
"content": "Let $f(x) = x^3 + ax + b$, where $a \\neq b$. Suppose the tangent lines to the graph of $f$ at $x=a$ and $x=b$ are parallel. Find $f(1)$.",
"role": "user"
}
] | 1 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0$. What is $a + b + c + d$?
$\textbf{(A)}\ 0 \ \textbf{(B)}\ 1 \ \textbf{(C)}\ 4 \ \textbf{(D)}\ 9 \ \textbf{(E)}\ 16$ | 9 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0$. What is $a... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f022021c-707d-4256-8cb6-aa871274e398"
} | [
{
"content": "The polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0$. What is $a + b + c + d$?\n\n$\\textbf{(A)}\\ 0 \\ \\textbf{(B)}\\ 1 \\ \\textbf{(C)}\\ 4 \\ \\textbf{(D)}\\ 9 \\ \\textbf{(E)}\\ 16$",
"role": "user"
}
] | 9 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Colin has $900$ Choco Pies. He realizes that for some integer values of $n \le 900$, if he eats $n$ pies a day, he will be able to eat the same number of pies every day until he runs out. How many possible values of $n$ are there? | 27 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nColin has $900$ Choco Pies. He realizes that for some integer values of $n \\le 900$, if he eats $n$ pies a day, he wi... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f3076125-6849-42a6-8c05-8e5cac9976e7"
} | [
{
"content": "Colin has $900$ Choco Pies. He realizes that for some integer values of $n \\le 900$, if he eats $n$ pies a day, he will be able to eat the same number of pies every day until he runs out. How many possible values of $n$ are there?",
"role": "user"
}
] | 27 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the sum of the real roots of the polynomial:
\[ \prod_{k=1}^{100} \left( x^2-11x+k \right) = \left( x^2-11x+1 \right)\left( x^2-11x+2 \right)\dots\left(x^2-11x+100\right). \] | 330 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the sum of the real roots of the polynomial:\n\\[ \\prod_{k=1}^{100} \\left( x^2-11x+k \\right) = \\left( x^2-11x... | MATH | {
"ground_truth": "330",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "86196489-a5ce-446c-b6e4-57d4dbc6b9c4"
} | [
{
"content": "Find the sum of the real roots of the polynomial:\n\\[ \\prod_{k=1}^{100} \\left( x^2-11x+k \\right) = \\left( x^2-11x+1 \\right)\\left( x^2-11x+2 \\right)\\dots\\left(x^2-11x+100\\right). \\]",
"role": "user"
}
] | 330 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let us consider a set of $6050$ points in the plane, where no three points are collinear. Determine the maximum number $k$ of non-overlapping triangles that can be formed such that no two triangles share a vertex. | 2016 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet us consider a set of $6050$ points in the plane, where no three points are collinear. Determine the maximum number... | MATH | {
"ground_truth": "2016",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d8c08d50-0be3-462a-89a4-bf7021979f79"
} | [
{
"content": "Let us consider a set of $6050$ points in the plane, where no three points are collinear. Determine the maximum number $k$ of non-overlapping triangles that can be formed such that no two triangles share a vertex.",
"role": "user"
}
] | 2016 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A positive integer $n$ is divisible by $3$ and $5$, but not by $2$. If $n > 20$, what is the smallest possible value of $n$? | 45 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA positive integer $n$ is divisible by $3$ and $5$, but not by $2$. If $n > 20$, what is the smallest possible value o... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5a2830e3-57fb-4c51-aec7-39bd040a04fa"
} | [
{
"content": "A positive integer $n$ is divisible by $3$ and $5$, but not by $2$. If $n > 20$, what is the smallest possible value of $n$?",
"role": "user"
}
] | 45 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Phil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number?The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n. | 643 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPhil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number?The answer is in t... | MATH | {
"ground_truth": "643",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ffc43dc4-de77-4077-9f2f-4715386bce61"
} | [
{
"content": "Phil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number?The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.",
"role": "user"
}
] | 643 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $ f(x) = x^3 + ax + b $, with $ a \ne b $, and suppose the tangent lines to the graph of $f$ at $x=a$ and $x=b$ are parallel. Find $f(1)$. | 1 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ f(x) = x^3 + ax + b $, with $ a \\ne b $, and suppose the tangent lines to the graph of $f$ at $x=a$ and $x=b$ a... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "54e0cec6-09d3-4b22-a870-034dab22a5d3"
} | [
{
"content": "Let $ f(x) = x^3 + ax + b $, with $ a \\ne b $, and suppose the tangent lines to the graph of $f$ at $x=a$ and $x=b$ are parallel. Find $f(1)$.",
"role": "user"
}
] | 1 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
How many positive two-digit integers are there in which each of the two digits is prime? | 16 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many positive two-digit integers are there in which each of the two digits is prime?\n\nRemember to put your answe... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35b704b5-7c1b-4bf7-8821-ab44c16d4cc0"
} | [
{
"content": "How many positive two-digit integers are there in which each of the two digits is prime?",
"role": "user"
}
] | 16 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find $x$, where $x$ is a square number which is divisible by four, and between 39 and 80. | 64 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind $x$, where $x$ is a square number which is divisible by four, and between 39 and 80.\n\nRemember to put your answ... | MATH | {
"ground_truth": "64",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5e818e8b-223b-49e2-ba35-9524458ce8ac"
} | [
{
"content": "Find $x$, where $x$ is a square number which is divisible by four, and between 39 and 80.",
"role": "user"
}
] | 64 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the smallest positive integer that is a multiple of both 30 and 40 but not a multiple of 16? | 120 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the smallest positive integer that is a multiple of both 30 and 40 but not a multiple of 16?\n\nRemember to pu... | MATH | {
"ground_truth": "120",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f93239e3-7261-4096-8ed3-d1117fc9de2d"
} | [
{
"content": "What is the smallest positive integer that is a multiple of both 30 and 40 but not a multiple of 16?",
"role": "user"
}
] | 120 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Evaluate the product \[ (a-10) \cdot (a-9) \cdot \dotsm \cdot (a-1) \cdot a, \] where $a=2$. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvaluate the product \\[ (a-10) \\cdot (a-9) \\cdot \\dotsm \\cdot (a-1) \\cdot a, \\] where $a=2$.\n\nRemember to put... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "99bd6cc6-ff78-434a-9014-55702a8dc8e6"
} | [
{
"content": "Evaluate the product \\[ (a-10) \\cdot (a-9) \\cdot \\dotsm \\cdot (a-1) \\cdot a, \\] where $a=2$.",
"role": "user"
}
] | 0 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
If I have four boxes arranged in a $2$ x $2$ grid, in how many distinct ways can I place the digits $1$, $2$, and $3$ in the boxes such that each box contains at most one digit? (I only have one of each digit, so one box will remain blank.) | 24 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf I have four boxes arranged in a $2$ x $2$ grid, in how many distinct ways can I place the digits $1$, $2$, and $3$ ... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "20dd9c9f-e0cd-4326-8d3d-8b54014b7368"
} | [
{
"content": "If I have four boxes arranged in a $2$ x $2$ grid, in how many distinct ways can I place the digits $1$, $2$, and $3$ in the boxes such that each box contains at most one digit? (I only have one of each digit, so one box will remain blank.)",
"role": "user"
}
] | 24 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
In triangle $ABC$, $BC = 8$. The length of median $AD$ is 5. Let $M$ be the largest possible value of $AB^2 + AC^2$, and let $m$ be the smallest possible value. Find $M - m$. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $BC = 8$. The length of median $AD$ is 5. Let $M$ be the largest possible value of $AB^2 + AC^2$,... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d90af8ec-96ec-4774-aaeb-5a0d6c6fed3f"
} | [
{
"content": "In triangle $ABC$, $BC = 8$. The length of median $AD$ is 5. Let $M$ be the largest possible value of $AB^2 + AC^2$, and let $m$ be the smallest possible value. Find $M - m$.",
"role": "user"
}
] | 0 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $a_1, a_2, \ldots, a_n$ be real numbers, and let $b_1, b_2, \ldots, b_n$ be distinct positive integers. Suppose there is a polynomial $f(x)$ satisfying the identity $$(1-x)^n f(x)=1+\sum_{i=1}^n a_i x^{b_i}.$$ Find a simple expression (not involving any sums) for $f(1)$ in terms of $b_1, b_2, \ldots, b_n$ and $n$ (... | 7 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a_1, a_2, \\ldots, a_n$ be real numbers, and let $b_1, b_2, \\ldots, b_n$ be distinct positive integers. Suppose ... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "79947f8d-a77d-456b-9036-0de59f04c39b"
} | [
{
"content": "Let $a_1, a_2, \\ldots, a_n$ be real numbers, and let $b_1, b_2, \\ldots, b_n$ be distinct positive integers. Suppose there is a polynomial $f(x)$ satisfying the identity $$(1-x)^n f(x)=1+\\sum_{i=1}^n a_i x^{b_i}.$$ Find a simple expression (not involving any sums) for $f(1)$ in terms of $b_1, b_... | 7 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the maximum possible value of $5 - |6x - 80|$ over all integers $x$? | 3 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the maximum possible value of $5 - |6x - 80|$ over all integers $x$?\n\nRemember to put your answer on its own... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35199ee3-03bb-47c8-aae6-c750e896ce15"
} | [
{
"content": "What is the maximum possible value of $5 - |6x - 80|$ over all integers $x$?",
"role": "user"
}
] | 3 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The circumference of a circle is \(100\) inches. Find the length of the side of a square inscribed in this circle, expressed in inches. The original answer is in the form \(\frac{k\sqrt{m}}{n\pi}\). Please provide the value of \(k + m + n\). | 53 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe circumference of a circle is \\(100\\) inches. Find the length of the side of a square inscribed in this circle, e... | MATH | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ad741937-baa5-4925-9c65-3517c5bda60d"
} | [
{
"content": "The circumference of a circle is \\(100\\) inches. Find the length of the side of a square inscribed in this circle, expressed in inches. The original answer is in the form \\(\\frac{k\\sqrt{m}}{n\\pi}\\). Please provide the value of \\(k + m + n\\).",
"role": "user"
}
] | 53 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A$. Bethany adds the numbers in each column. The average of her $75$ sums is $B$. Find the value of \(\frac{A}{B}\). The answer should be in the form \(\frac{k}{m}\),... | 23 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAndy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each ro... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "74b8d78b-51dd-42c2-a69d-0fd1c33c89f7"
} | [
{
"content": "Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A$. Bethany adds the numbers in each column. The average of her $75$ sums is $B$. Find the value of \\(\\frac{A}{B}\\). The answer should be in ... | 23 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Represent the hypotenuse of a right triangle by $c$ and the area by $A$. What is the altitude on the hypotenuse? The original answer is in the form of $\frac{mA}{nc}$, where $m$ and $n$ are integers. Please give the value of $m + n$. | 3 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRepresent the hypotenuse of a right triangle by $c$ and the area by $A$. What is the altitude on the hypotenuse? The o... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8ee3c52a-848b-451d-8ca0-baa2d40f8f62"
} | [
{
"content": "Represent the hypotenuse of a right triangle by $c$ and the area by $A$. What is the altitude on the hypotenuse? The original answer is in the form of $\\frac{mA}{nc}$, where $m$ and $n$ are integers. Please give the value of $m + n$.",
"role": "user"
}
] | 3 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Five positive consecutive integers starting with $a$ have an average of $b$. What is the average of 5 consecutive integers that start with $b$? Provide your answer in the form of $a + k$, where $k$ is an integer. Please find the value of $k$. | 4 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFive positive consecutive integers starting with $a$ have an average of $b$. What is the average of 5 consecutive inte... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a8cbf5fb-da93-4b38-9438-d4e867c66173"
} | [
{
"content": "Five positive consecutive integers starting with $a$ have an average of $b$. What is the average of 5 consecutive integers that start with $b$? Provide your answer in the form of $a + k$, where $k$ is an integer. Please find the value of $k$.",
"role": "user"
}
] | 4 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn, the probability that a player knocks the bottle off the ledge is \(\tfrac{1}{2}\), independently of what has happened befo... | 5 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLarry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. ... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cc5a1be6-1d8d-4e0d-87c5-eb83be29cb53"
} | [
{
"content": "Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn, the probability that a player knocks the bottle off the ledge is \\(\\tfrac{1}{2}\\), independently ... | 5 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f(x) = x^{2}(1-x)^{2}$. Find the value of the sum
\[f \left(\frac{1}{2019} \right)-f \left(\frac{2}{2019} \right)+f \left(\frac{3}{2019} \right)-f \left(\frac{4}{2019} \right)+\cdots + f \left(\frac{2017}{2019} \right) - f \left(\frac{2018}{2019} \right).\] | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f(x) = x^{2}(1-x)^{2}$. Find the value of the sum\n\\[f \\left(\\frac{1}{2019} \\right)-f \\left(\\frac{2}{2019}... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2aecf51d-fc7e-445c-b07b-fe7c36b87ab8"
} | [
{
"content": "Let $f(x) = x^{2}(1-x)^{2}$. Find the value of the sum\n\\[f \\left(\\frac{1}{2019} \\right)-f \\left(\\frac{2}{2019} \\right)+f \\left(\\frac{3}{2019} \\right)-f \\left(\\frac{4}{2019} \\right)+\\cdots + f \\left(\\frac{2017}{2019} \\right) - f \\left(\\frac{2018}{2019} \\right).\\]",
"role"... | 0 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
If the area of \(\triangle ABC\) is \(64\) square units and the geometric mean (mean proportional) between sides \(AB\) and \(AC\) is \(12\) inches, find the value of \(\sin A\). The answer should be in the format \(\frac{k}{m}\), where \(\frac{k}{m}\) is a simplified fraction. Please provide the value of \(k + m\). | 17 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf the area of \\(\\triangle ABC\\) is \\(64\\) square units and the geometric mean (mean proportional) between sides ... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "262ba3dc-45dd-4a58-a9ff-6122057180b6"
} | [
{
"content": "If the area of \\(\\triangle ABC\\) is \\(64\\) square units and the geometric mean (mean proportional) between sides \\(AB\\) and \\(AC\\) is \\(12\\) inches, find the value of \\(\\sin A\\). The answer should be in the format \\(\\frac{k}{m}\\), where \\(\\frac{k}{m}\\) is a simplified fraction.... | 17 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The average (arithmetic mean) age of a group consisting of doctors and lawyers is 40. If the doctors average 35 years old and the lawyers average 50 years old, what is the ratio of the number of doctors to the number of lawyers? Express your answer as a simplified ratio in the form $m: n$, and then calculate the value ... | 3 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe average (arithmetic mean) age of a group consisting of doctors and lawyers is 40. If the doctors average 35 years ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0095a9a5-9b61-4d2b-b15d-512ef72029cb"
} | [
{
"content": "The average (arithmetic mean) age of a group consisting of doctors and lawyers is 40. If the doctors average 35 years old and the lawyers average 50 years old, what is the ratio of the number of doctors to the number of lawyers? Express your answer as a simplified ratio in the form $m: n$, and the... | 3 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The point $(-3, 2)$ is rotated $90^\circ$ clockwise around the origin to point $B$. Point $B$ is then reflected over the line $y = x$ to point $C$. What are the coordinates of $C$? Provide your answer as an ordered pair $(k, m)$, and then find the sum of k and m. | 5 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe point $(-3, 2)$ is rotated $90^\\circ$ clockwise around the origin to point $B$. Point $B$ is then reflected over ... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e41f27da-64fd-4a02-b139-771d13ca4a24"
} | [
{
"content": "The point $(-3, 2)$ is rotated $90^\\circ$ clockwise around the origin to point $B$. Point $B$ is then reflected over the line $y = x$ to point $C$. What are the coordinates of $C$? Provide your answer as an ordered pair $(k, m)$, and then find the sum of k and m.",
"role": "user"
}
] | 5 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
An ice ballerina rotates at a constant angular velocity at one particular point, meaning she does not translationally move. Her arms are fully extended as she rotates, and her moment of inertia is \(I\). Now, she pulls her arms in, and her moment of inertia becomes \(\frac{7}{10}I\). What is the ratio of the new kineti... | 17 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn ice ballerina rotates at a constant angular velocity at one particular point, meaning she does not translationally ... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3ac0f421-5045-472b-89e7-70ceea9cf4f2"
} | [
{
"content": "An ice ballerina rotates at a constant angular velocity at one particular point, meaning she does not translationally move. Her arms are fully extended as she rotates, and her moment of inertia is \\(I\\). Now, she pulls her arms in, and her moment of inertia becomes \\(\\frac{7}{10}I\\). What is ... | 17 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Calculate the product \(8 \times 0.25 \times 2 \times 0.125\). Provide your answer in the form of \(\frac{k}{m}\), where the fraction is in its simplest form. Find the value of \(k + m\). | 3 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCalculate the product \\(8 \\times 0.25 \\times 2 \\times 0.125\\). Provide your answer in the form of \\(\\frac{k}{m}... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "73af046a-81c5-429a-829c-38625150641f"
} | [
{
"content": "Calculate the product \\(8 \\times 0.25 \\times 2 \\times 0.125\\). Provide your answer in the form of \\(\\frac{k}{m}\\), where the fraction is in its simplest form. Find the value of \\(k + m\\).",
"role": "user"
}
] | 3 | 27 | 27/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A box of strawberries, containing $12$ strawberries total, costs $2$. A box of blueberries, containing $48$ blueberries total, costs $3$. Suppose that for $12$, Sareen can either buy $m$ strawberries total or $n$ blueberries total. Find $n - m$. | 120 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA box of strawberries, containing $12$ strawberries total, costs $2$. A box of blueberries, containing $48$ blueberrie... | MATH | {
"ground_truth": "120",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4304abf3-78e6-4ed1-82f3-fdd2225ae4ae"
} | [
{
"content": "A box of strawberries, containing $12$ strawberries total, costs $2$. A box of blueberries, containing $48$ blueberries total, costs $3$. Suppose that for $12$, Sareen can either buy $m$ strawberries total or $n$ blueberries total. Find $n - m$.",
"role": "user"
}
] | 120 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the second smallest positive integer $n$ such that when $n$ is divided by $5$, the remainder is $3$, and when $n$ is divided by $7$, the remainder is $4$. | 53 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the second smallest positive integer $n$ such that when $n$ is divided by $5$, the remainder is $3$, and when $n$... | MATH | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "28ae91c9-727a-4fb0-a759-7686f46994de"
} | [
{
"content": "Find the second smallest positive integer $n$ such that when $n$ is divided by $5$, the remainder is $3$, and when $n$ is divided by $7$, the remainder is $4$.",
"role": "user"
}
] | 53 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f(x) = \sin(\sin(x))$. Evaluate:
\[
\lim_{h \to 0} \frac{f(x+h) - f(h)}{x}
\] at $x = \pi$. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f(x) = \\sin(\\sin(x))$. Evaluate:\n\\[\n\\lim_{h \\to 0} \\frac{f(x+h) - f(h)}{x}\n\\] at $x = \\pi$.\n\nRemembe... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d0b05edf-c496-4b37-8fd2-0e2cf984ad6f"
} | [
{
"content": "Let $f(x) = \\sin(\\sin(x))$. Evaluate:\n\\[\n\\lim_{h \\to 0} \\frac{f(x+h) - f(h)}{x}\n\\] at $x = \\pi$.",
"role": "user"
}
] | 0 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find $x$ such that:
\[
\frac{\frac{5}{x-50} + \frac{7}{x+25}}{\frac{2}{x-50} - \frac{3}{x+25}} = 17.
\] | 125 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind $x$ such that:\n\\[\n\\frac{\\frac{5}{x-50} + \\frac{7}{x+25}}{\\frac{2}{x-50} - \\frac{3}{x+25}} = 17.\n\\]\n\nR... | MATH | {
"ground_truth": "125",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "09d8f5f5-add8-4eb4-941f-c232b7d17c7a"
} | [
{
"content": "Find $x$ such that:\n\\[\n\\frac{\\frac{5}{x-50} + \\frac{7}{x+25}}{\\frac{2}{x-50} - \\frac{3}{x+25}} = 17.\n\\]",
"role": "user"
}
] | 125 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the minimum value of $m$ such that any $m$-element subset of the set of integers \( \{1, 2, \ldots, 2016\} \) contains at least two distinct numbers \( a \) and \( b \) which satisfy \(|a - b| \le 3\). | 505 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the minimum value of $m$ such that any $m$-element subset of the set of integers \\( \\{1, 2, \\ldots, 2016\\} \\... | MATH | {
"ground_truth": "505",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f1bfecde-fa11-47a9-9e5c-fefa18e5c5d6"
} | [
{
"content": "Find the minimum value of $m$ such that any $m$-element subset of the set of integers \\( \\{1, 2, \\ldots, 2016\\} \\) contains at least two distinct numbers \\( a \\) and \\( b \\) which satisfy \\(|a - b| \\le 3\\).",
"role": "user"
}
] | 505 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Ten points are marked on a circle . How many distinct convex polygons of three or more sides can be drawn using some (or all) of the ten points as vertices ? | 968 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTen points are marked on a circle . How many distinct convex polygons of three or more sides can be drawn using some (... | MATH | {
"ground_truth": "968",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6f407d11-7dd5-4570-bf9e-57f78e55206b"
} | [
{
"content": "Ten points are marked on a circle . How many distinct convex polygons of three or more sides can be drawn using some (or all) of the ten points as vertices ?",
"role": "user"
}
] | 968 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The lengths of the sides of a triangle with positive area are $\log_{10} 12$, $\log_{10} 75$, and $\log_{10} n$, where $n$ is a positive integer. Find the number of possible values for $n$. | 893 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe lengths of the sides of a triangle with positive area are $\\log_{10} 12$, $\\log_{10} 75$, and $\\log_{10} n$, wh... | MATH | {
"ground_truth": "893",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "678ff6ac-a8bf-405a-b99e-ad18d2a58371"
} | [
{
"content": "The lengths of the sides of a triangle with positive area are $\\log_{10} 12$, $\\log_{10} 75$, and $\\log_{10} n$, where $n$ is a positive integer. Find the number of possible values for $n$.",
"role": "user"
}
] | 893 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The sum of an infinite geometric series is $27$ times the series that results if the first three terms of the original series are removed. What is the value of the series' common ratio?The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n. | 4 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe sum of an infinite geometric series is $27$ times the series that results if the first three terms of the original... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "87f17ef5-228a-40c5-8473-2375a80215b0"
} | [
{
"content": "The sum of an infinite geometric series is $27$ times the series that results if the first three terms of the original series are removed. What is the value of the series' common ratio?The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.",
"role": "use... | 4 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The values of a function $f(x)$ are given in the table below.
\begin{tabular}{|c||c|c|c|c|c|} \hline $x$ & 1 & 2 & 3 & 4 & 5 \\ \hline $f(x)$ & 3 & 1 & 5 & 4 & 2 \\ \hline
\end{tabular}If $f^{-1}$ exists, then what is $f^{-1}(f^{-1}(f^{-1}(1)))$? | 3 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe values of a function $f(x)$ are given in the table below.\n\n\\begin{tabular}{|c||c|c|c|c|c|} \\hline $x$ & 1 & 2 ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2496c250-ec75-4bfc-8721-4538cd83ccf1"
} | [
{
"content": "The values of a function $f(x)$ are given in the table below.\n\n\\begin{tabular}{|c||c|c|c|c|c|} \\hline $x$ & 1 & 2 & 3 & 4 & 5 \\\\ \\hline $f(x)$ & 3 & 1 & 5 & 4 & 2 \\\\ \\hline\n\\end{tabular}If $f^{-1}$ exists, then what is $f^{-1}(f^{-1}(f^{-1}(1)))$?",
"role": "user"
}
] | 3 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Kimberly borrows $1000$ dollars from Lucy, who charged interest of $5\%$ per month (which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed? | 15 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nKimberly borrows $1000$ dollars from Lucy, who charged interest of $5\\%$ per month (which compounds monthly). What is... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8bc2f8d2-d75c-4a67-9ca0-aa6cfcc1178a"
} | [
{
"content": "Kimberly borrows $1000$ dollars from Lucy, who charged interest of $5\\%$ per month (which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed?",
"role": "user"
}
] | 15 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as shown. [asy]
draw((0,0)--(9,0)--(9,9)--(0,9)--(0,0));
fill((1,1)--(2,1)--(2,2)--(1,2)--cycle,gray(.8));
fill((4,1)--(5,1)--(5,2)--(4,2)--cycle,gray(.8));
fill((7,1)--(8,1)--(8,2)--(7,2)--cy... | 17 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squ... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1cadc253-40ec-42cf-8cd2-0047d433f5c4"
} | [
{
"content": "A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as shown. [asy]\n\ndraw((0,0)--(9,0)--(9,9)--(0,9)--(0,0));\n\nfill((1,1)--(2,1)--(2,2)--(1,2)--cycle,gray(.8));\n\nfill((4,1)--(5,1)--(5,2)--(4,2)--cycle,gray(.8));\n\nfill(... | 17 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
How many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since $\sqrt[3]{20}<10.$ | 999 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since $\\sqrt[3... | MATH | {
"ground_truth": "999",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "37d40f0c-0b6e-4a28-badd-373bd90228ab"
} | [
{
"content": "How many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since $\\sqrt[3]{20}<10.$",
"role": "user"
}
] | 999 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the smallest positive integer with exactly 14 positive divisors? | 192 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the smallest positive integer with exactly 14 positive divisors?\n\nRemember to put your answer on its own lin... | MATH | {
"ground_truth": "192",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e05b7557-0c84-4452-8e54-434c4918b852"
} | [
{
"content": "What is the smallest positive integer with exactly 14 positive divisors?",
"role": "user"
}
] | 192 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
If $n = 2^{10} \cdot 3^{14} \cdot 5^{8}$, how many of the natural-number factors of $n$ are multiples of 150? | 980 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf $n = 2^{10} \\cdot 3^{14} \\cdot 5^{8}$, how many of the natural-number factors of $n$ are multiples of 150?\n\nRem... | MATH | {
"ground_truth": "980",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ea654e39-bddb-48ff-adc9-1e7b12fc0708"
} | [
{
"content": "If $n = 2^{10} \\cdot 3^{14} \\cdot 5^{8}$, how many of the natural-number factors of $n$ are multiples of 150?",
"role": "user"
}
] | 980 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Given that $a$ is a multiple of $456$, find the greatest common divisor of $3a^3+a^2+4a+57$ and $a$. | 57 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven that $a$ is a multiple of $456$, find the greatest common divisor of $3a^3+a^2+4a+57$ and $a$.\n\nRemember to pu... | MATH | {
"ground_truth": "57",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "69e3de4f-5944-4dca-9e1a-3416c39d24c1"
} | [
{
"content": "Given that $a$ is a multiple of $456$, find the greatest common divisor of $3a^3+a^2+4a+57$ and $a$.",
"role": "user"
}
] | 57 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
To calculate $31^2$, Emily mentally figures the value $30^2$ and adds 61. Emily subtracts a number from $30^2$ to calculate $29^2$. What number does she subtract? | 59 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTo calculate $31^2$, Emily mentally figures the value $30^2$ and adds 61. Emily subtracts a number from $30^2$ to calc... | MATH | {
"ground_truth": "59",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0cad4bab-11b4-4aab-9df2-71404cfa2235"
} | [
{
"content": "To calculate $31^2$, Emily mentally figures the value $30^2$ and adds 61. Emily subtracts a number from $30^2$ to calculate $29^2$. What number does she subtract?",
"role": "user"
}
] | 59 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What percent of $x$ is equal to $40\%$ of $50\%$ of $x$? | 20 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat percent of $x$ is equal to $40\\%$ of $50\\%$ of $x$?\n\nRemember to put your answer on its own line after \"Answ... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "14555d20-5110-4467-ad4b-d96d73b9c3b7"
} | [
{
"content": "What percent of $x$ is equal to $40\\%$ of $50\\%$ of $x$?",
"role": "user"
}
] | 20 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $O$ and $H$ be the circumcenter and orthocenter of triangle $ABC$, respectively. Let $a$, $b$, and $c$ denote the side lengths, and let $R$ denote the circumradius. Find $OH^2$ if $R = 7$ and $a^2 + b^2 + c^2 = 29$. | 412 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $O$ and $H$ be the circumcenter and orthocenter of triangle $ABC$, respectively. Let $a$, $b$, and $c$ denote the... | MATH | {
"ground_truth": "412",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b9b37c9a-b1d6-48c5-9168-6cb89dabfcd1"
} | [
{
"content": "Let $O$ and $H$ be the circumcenter and orthocenter of triangle $ABC$, respectively. Let $a$, $b$, and $c$ denote the side lengths, and let $R$ denote the circumradius. Find $OH^2$ if $R = 7$ and $a^2 + b^2 + c^2 = 29$.",
"role": "user"
}
] | 412 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the product of all real numbers that are doubled when added to their reciprocals? | -1 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the product of all real numbers that are doubled when added to their reciprocals?\n\nRemember to put your answ... | MATH | {
"ground_truth": "-1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "39e792e8-0715-4fb7-955a-43bbcfe98298"
} | [
{
"content": "What is the product of all real numbers that are doubled when added to their reciprocals?",
"role": "user"
}
] | -1 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Points $A$, $B$, $C$, and $T$ are in space such that each of $\overline{TA}$, $\overline{TB}$, and $\overline{TC}$ is perpendicular to the other two. If $TA = TB = 10$ and $TC = 9$, then what is the volume of pyramid $TABC$? | 150 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPoints $A$, $B$, $C$, and $T$ are in space such that each of $\\overline{TA}$, $\\overline{TB}$, and $\\overline{TC}$ ... | MATH | {
"ground_truth": "150",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6d3c991f-1d51-408a-9c00-6c5358377ae3"
} | [
{
"content": "Points $A$, $B$, $C$, and $T$ are in space such that each of $\\overline{TA}$, $\\overline{TB}$, and $\\overline{TC}$ is perpendicular to the other two. If $TA = TB = 10$ and $TC = 9$, then what is the volume of pyramid $TABC$?",
"role": "user"
}
] | 150 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Jack rewrites the quadratic $9x^2 - 30x - 42$ in the form of $(ax + b)^2 + c,$ where $a,$ $b,$ and $c$ are all integers. What is $ab$? | -15 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJack rewrites the quadratic $9x^2 - 30x - 42$ in the form of $(ax + b)^2 + c,$ where $a,$ $b,$ and $c$ are all integer... | MATH | {
"ground_truth": "-15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "858cea0b-a66f-4eb5-963b-ebc6e96bd194"
} | [
{
"content": "Jack rewrites the quadratic $9x^2 - 30x - 42$ in the form of $(ax + b)^2 + c,$ where $a,$ $b,$ and $c$ are all integers. What is $ab$?",
"role": "user"
}
] | -15 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Given the equation $a + b = 30$, where $a$ and $b$ are positive integers, how many distinct ordered-pair solutions $(a, b)$ exist? | 29 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven the equation $a + b = 30$, where $a$ and $b$ are positive integers, how many distinct ordered-pair solutions $(a... | MATH | {
"ground_truth": "29",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "447c5d17-c6fe-4539-b7ea-334c44d31c42"
} | [
{
"content": "Given the equation $a + b = 30$, where $a$ and $b$ are positive integers, how many distinct ordered-pair solutions $(a, b)$ exist?",
"role": "user"
}
] | 29 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The median of the set of numbers $\{$12, 38, 45, $x$, 14$\}$ is five less than the mean. If $x$ is a negative integer, what is the value of $x$? | -14 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe median of the set of numbers $\\{$12, 38, 45, $x$, 14$\\}$ is five less than the mean. If $x$ is a negative intege... | MATH | {
"ground_truth": "-14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a2d7437b-2311-48a0-9690-75fcbeaf877d"
} | [
{
"content": "The median of the set of numbers $\\{$12, 38, 45, $x$, 14$\\}$ is five less than the mean. If $x$ is a negative integer, what is the value of $x$?",
"role": "user"
}
] | -14 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the value of $k$ so that the line $3x + 5y + k = 0$ is tangent to the parabola $y^2 = 24x.$ | 50 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the value of $k$ so that the line $3x + 5y + k = 0$ is tangent to the parabola $y^2 = 24x.$\n\nRemember to put yo... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d579c856-5e62-466f-9bcf-a0fc3612b72c"
} | [
{
"content": "Find the value of $k$ so that the line $3x + 5y + k = 0$ is tangent to the parabola $y^2 = 24x.$",
"role": "user"
}
] | 50 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What percent of the positive integers less than or equal to $100$ have no remainders when divided by $5?$ | 20 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat percent of the positive integers less than or equal to $100$ have no remainders when divided by $5?$\n\nRemember ... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "22063de2-a7a2-4214-895f-e015e0b78f87"
} | [
{
"content": "What percent of the positive integers less than or equal to $100$ have no remainders when divided by $5?$",
"role": "user"
}
] | 20 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find all positive integer pairs $(x, y)$ such that $x^{2}-y^{119}=1$. Please provide the sum of all possible $x$ and $y$ values from the solutions.If the equation has no solution, then the answer is 0. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind all positive integer pairs $(x, y)$ such that $x^{2}-y^{119}=1$. Please provide the sum of all possible $x$ and $... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2a43ebf5-9271-4cdd-825a-bf046f043e25"
} | [
{
"content": "Find all positive integer pairs $(x, y)$ such that $x^{2}-y^{119}=1$. Please provide the sum of all possible $x$ and $y$ values from the solutions.If the equation has no solution, then the answer is 0.",
"role": "user"
}
] | 0 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the largest integer that divides each of the numbers in the sequence \(1^5 - 1, 2^5 - 2, 3^5 - 3, \cdots, n^5 - n, \cdots\). | 30 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the largest integer that divides each of the numbers in the sequence \\(1^5 - 1, 2^5 - 2, 3^5 - 3, \\cdots, n^5 -... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "171b8c97-de1f-4950-8453-47b8fe9e1543"
} | [
{
"content": "Find the largest integer that divides each of the numbers in the sequence \\(1^5 - 1, 2^5 - 2, 3^5 - 3, \\cdots, n^5 - n, \\cdots\\).",
"role": "user"
}
] | 30 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly? Pro... | 7 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "609d2cd9-fe0a-4c58-a293-a620d5db179a"
} | [
{
"content": "A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match al... | 7 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
$ABCD$ is a square and $M$ and $N$ are the midpoints of $BC$ and $CD$ respectively. Find the value of $\sin \theta$. The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).
```asy
\draw((0,0)--(2,0)--(2,2)--(0,2)--cycle);
\draw((0,0)--(2,1));
\draw((0,0)--(1,2));
\label("A", (0,0), SW);
\... | 8 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$ABCD$ is a square and $M$ and $N$ are the midpoints of $BC$ and $CD$ respectively. Find the value of $\\sin \\theta$.... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8e82cae6-3cf6-40bb-b133-517c9a4e3743"
} | [
{
"content": "$ABCD$ is a square and $M$ and $N$ are the midpoints of $BC$ and $CD$ respectively. Find the value of $\\sin \\theta$. The original answer is in \\(\\frac{k}{m}\\) format, please give the value of \\(k + m\\).\n\n```asy\n\\draw((0,0)--(2,0)--(2,2)--(0,2)--cycle);\n\\draw((0,0)--(2,1));\n\\draw((0,... | 8 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The number of positive integers $k$ for which the equation $kx - 12 = 3k$ has an integer solution for $x$ is ___. | 6 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe number of positive integers $k$ for which the equation $kx - 12 = 3k$ has an integer solution for $x$ is ___.\n\nR... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c23088fe-0dbc-496a-b713-11dec4a4cb78"
} | [
{
"content": "The number of positive integers $k$ for which the equation $kx - 12 = 3k$ has an integer solution for $x$ is ___.",
"role": "user"
}
] | 6 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
In how many ways can $47$ be written as the sum of two primes? | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn how many ways can $47$ be written as the sum of two primes?\n\nRemember to put your answer on its own line after \"... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "42ce5d24-a317-43d7-9184-15aa2e9f3a94"
} | [
{
"content": "In how many ways can $47$ be written as the sum of two primes?",
"role": "user"
}
] | 0 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
In a far-off land, three fish can be traded for two loaves of bread, and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth? Provide your answer in the form \(\frac{k}{m}\), where \(k\) and \(m\) are integers, and give the value of \(k + m\). | 11 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn a far-off land, three fish can be traded for two loaves of bread, and a loaf of bread can be traded for four bags o... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2ade82d5-e655-48f2-a603-4ece8494e536"
} | [
{
"content": "In a far-off land, three fish can be traded for two loaves of bread, and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth? Provide your answer in the form \\(\\frac{k}{m}\\), where \\(k\\) and \\(m\\) are integers, and give the value of \\(k + m\\).",
... | 11 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Compute the sum of all the roots of
\((2x+3)(x-4)+(2x+3)(x-6)=0\).
Express your answer as a fraction in simplest form \(\frac{k}{m}\), and provide the value of \(k + m\). | 9 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute the sum of all the roots of \n\\((2x+3)(x-4)+(2x+3)(x-6)=0\\). \nExpress your answer as a fraction in simple... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35f0edbd-c5c1-4afd-afd2-918812c1ae4a"
} | [
{
"content": "Compute the sum of all the roots of \n\\((2x+3)(x-4)+(2x+3)(x-6)=0\\). \nExpress your answer as a fraction in simplest form \\(\\frac{k}{m}\\), and provide the value of \\(k + m\\).",
"role": "user"
}
] | 9 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the value of \(x\) if \(|x-1|=|x-2|\)? Provide your answer in the form of \(\frac{k}{m}\), where \(k\) and \(m\) are integers. Calculate the value of \(k + m\). | 5 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the value of \\(x\\) if \\(|x-1|=|x-2|\\)? Provide your answer in the form of \\(\\frac{k}{m}\\), where \\(k\\... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "675b66ee-7762-4ef7-a480-954033781bdf"
} | [
{
"content": "What is the value of \\(x\\) if \\(|x-1|=|x-2|\\)? Provide your answer in the form of \\(\\frac{k}{m}\\), where \\(k\\) and \\(m\\) are integers. Calculate the value of \\(k + m\\).",
"role": "user"
}
] | 5 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let \(a\) and \(b\) be the roots of the equation \(x^2-mx+2=0\). Suppose that \(a+\frac{1}{b}\) and \(b+\frac{1}{a}\) are the roots of the equation \(x^2-px+q=0\). The original answer for the value of \(q\) is in the form \(\frac{k}{m}\). Please find the value of \(k + m\). | 11 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet \\(a\\) and \\(b\\) be the roots of the equation \\(x^2-mx+2=0\\). Suppose that \\(a+\\frac{1}{b}\\) and \\(b+\\fr... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "66d7c687-a852-4247-88cf-6543fe33a921"
} | [
{
"content": "Let \\(a\\) and \\(b\\) be the roots of the equation \\(x^2-mx+2=0\\). Suppose that \\(a+\\frac{1}{b}\\) and \\(b+\\frac{1}{a}\\) are the roots of the equation \\(x^2-px+q=0\\). The original answer for the value of \\(q\\) is in the form \\(\\frac{k}{m}\\). Please find the value of \\(k + m\\).",
... | 11 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression? Provide your answer as an integer. | 59 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progress... | MATH | {
"ground_truth": "59",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8e4f862d-1fa1-44ae-b299-75ed049204a9"
} | [
{
"content": "How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression? Provide your answer as an integer.",
"role": "user"
}
] | 59 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
The polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0.$ Find the value of $a + b + c + d$. | 9 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0.$ Find the v... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "464f29a4-8faf-40f1-ae19-ebe3c61ddba6"
} | [
{
"content": "The polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0.$ Find the value of $a + b + c + d$.",
"role": "user"
}
] | 9 | 26 | 26/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Determine all integers $m$ for which all solutions of the equation $3x^3 - 3x^2 + m = 0$ are rational. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDetermine all integers $m$ for which all solutions of the equation $3x^3 - 3x^2 + m = 0$ are rational.\n\nRemember to ... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3da20697-ce17-4435-a17b-1e71485c8c5b"
} | [
{
"content": "Determine all integers $m$ for which all solutions of the equation $3x^3 - 3x^2 + m = 0$ are rational.",
"role": "user"
}
] | 0 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f(n)$ be a function defined on the set of all positive integers and having its values in the same set. Suppose that $f(f(n) + f(m)) = m + n$ for all positive integers $n, m$. Find the possible value for $f(1988)$. | 1988 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f(n)$ be a function defined on the set of all positive integers and having its values in the same set. Suppose th... | MATH | {
"ground_truth": "1988",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "97bbab6a-1822-4f43-843c-33821c99d895"
} | [
{
"content": "Let $f(n)$ be a function defined on the set of all positive integers and having its values in the same set. Suppose that $f(f(n) + f(m)) = m + n$ for all positive integers $n, m$. Find the possible value for $f(1988)$.",
"role": "user"
}
] | 1988 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
$AB$ is the diameter of circle $O$. A random point $P$ is selected on $O$ such that $AP = 4$ and $BP = 3$. Points $C$ and $D$ are drawn on circle $O$ such that $OC$ bisects $AP$ and $OD$ bisects $BP$. What is the degree measure of $\angle COD$? | 90 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$AB$ is the diameter of circle $O$. A random point $P$ is selected on $O$ such that $AP = 4$ and $BP = 3$. Points $C$ ... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "66cc7cb4-174d-4291-87ae-582038c0fa38"
} | [
{
"content": "$AB$ is the diameter of circle $O$. A random point $P$ is selected on $O$ such that $AP = 4$ and $BP = 3$. Points $C$ and $D$ are drawn on circle $O$ such that $OC$ bisects $AP$ and $OD$ bisects $BP$. What is the degree measure of $\\angle COD$?",
"role": "user"
}
] | 90 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the second smallest positive integer $n$ such that:
1. When $n$ is divided by $5$, the remainder is $3$.
2. When $n$ is divided by $7$, the remainder is $4$. | 53 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the second smallest positive integer $n$ such that:\n1. When $n$ is divided by $5$, the remainder is $3$.\n2. Whe... | MATH | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d17cc2bb-2686-4725-b542-ed505b87ec6c"
} | [
{
"content": "Find the second smallest positive integer $n$ such that:\n1. When $n$ is divided by $5$, the remainder is $3$.\n2. When $n$ is divided by $7$, the remainder is $4$.",
"role": "user"
}
] | 53 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Find the last two digits of $2023 + 202^3 + 20^{23}$. | 31 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the last two digits of $2023 + 202^3 + 20^{23}$.\n\nRemember to put your answer on its own line after \"Answer:\"... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "85a2e3a2-2d82-42a7-b922-621c73522f3f"
} | [
{
"content": "Find the last two digits of $2023 + 202^3 + 20^{23}$.",
"role": "user"
}
] | 31 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Suppose that $a, b, c$ are complex numbers satisfying the system of equations:
\[a^2 = b - c,\]
\[b^2 = c - a,\]
\[c^2 = a - b.\]
Compute all possible values of $a + b + c$. | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $a, b, c$ are complex numbers satisfying the system of equations: \n\\[a^2 = b - c,\\] \n\\[b^2 = c - a... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "56579010-692c-4e75-9aea-1346fe36f5e8"
} | [
{
"content": "Suppose that $a, b, c$ are complex numbers satisfying the system of equations: \n\\[a^2 = b - c,\\] \n\\[b^2 = c - a,\\] \n\\[c^2 = a - b.\\] \nCompute all possible values of $a + b + c$.",
"role": "user"
}
] | 0 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f : \mathbb{N} \to \mathbb{N}$ be a function such that $f(f(1995)) = 95$, $f(xy) = f(x)f(y)$, and $f(x) \le x$ for all $x, y$. Find all possible values of $f(1995)$. | 95 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f : \\mathbb{N} \\to \\mathbb{N}$ be a function such that $f(f(1995)) = 95$, $f(xy) = f(x)f(y)$, and $f(x) \\le x... | MATH | {
"ground_truth": "95",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "16a93ef7-6826-4aae-b219-a5c2d18dea98"
} | [
{
"content": "Let $f : \\mathbb{N} \\to \\mathbb{N}$ be a function such that $f(f(1995)) = 95$, $f(xy) = f(x)f(y)$, and $f(x) \\le x$ for all $x, y$. Find all possible values of $f(1995)$.",
"role": "user"
}
] | 95 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Let $f(x) = x^3 - 3x + b$ and $g(x) = x^2 + bx - 3$, where $b$ is a real number. What is the sum of all possible values of $b$ for which the equations $f(x) = 0$ and $g(x) = 0$ have a common root? | 0 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $f(x) = x^3 - 3x + b$ and $g(x) = x^2 + bx - 3$, where $b$ is a real number. What is the sum of all possible value... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fc4008c7-0667-4252-89e6-5b712103fd39"
} | [
{
"content": "Let $f(x) = x^3 - 3x + b$ and $g(x) = x^2 + bx - 3$, where $b$ is a real number. What is the sum of all possible values of $b$ for which the equations $f(x) = 0$ and $g(x) = 0$ have a common root?",
"role": "user"
}
] | 0 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Compute the smallest positive integer $N$ for which $N \cdot 2^{2024}$ is a multiple of $2024$. | 253 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute the smallest positive integer $N$ for which $N \\cdot 2^{2024}$ is a multiple of $2024$.\n\nRemember to put yo... | MATH | {
"ground_truth": "253",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "051e2a7a-f841-4872-853e-0fa29de0f1ea"
} | [
{
"content": "Compute the smallest positive integer $N$ for which $N \\cdot 2^{2024}$ is a multiple of $2024$.",
"role": "user"
}
] | 253 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
Calculate the single-digit result obtained from the repeated sum of the digits of the number $2^{2004}$. Follow these steps:
1. Calculate the sum $S$ of all digits of $2^{2004}$.
2. Calculate the sum of the digits of $S$ to obtain $R$.
3. Continue calculating the sum of the digits until a single-digit number is reached... | 1 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCalculate the single-digit result obtained from the repeated sum of the digits of the number $2^{2004}$. Follow these ... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c1227a8a-2f8b-4483-b5db-794c47fcec60"
} | [
{
"content": "Calculate the single-digit result obtained from the repeated sum of the digits of the number $2^{2004}$. Follow these steps:\n1. Calculate the sum $S$ of all digits of $2^{2004}$.\n2. Calculate the sum of the digits of $S$ to obtain $R$.\n3. Continue calculating the sum of the digits until a singl... | 1 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is $1$ and whose common difference is $k$. For example, $S_3$ is the sequence $1,4,7,10,\ldots.$ For how many values of $k$ does $S_k$ contain the term $2005$?
| 12 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is $1... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "33b07191-12e8-47bf-8017-668f4dc9b275"
} | [
{
"content": "For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is $1$ and whose common difference is $k$. For example, $S_3$ is the sequence $1,4,7,10,\\ldots.$ For how many values of $k$ does $S_k$ contain the term $2005$?",
"role": "user"
... | 12 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
A square pyramid has a base edge of 32 inches and an altitude of 1 foot. A square pyramid whose altitude is one-fourth of the original altitude is cut away at the apex of the original pyramid. The volume of the remaining frustum is what fractional part of the volume of the original pyramid?The answer is in the form ra... | 127 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA square pyramid has a base edge of 32 inches and an altitude of 1 foot. A square pyramid whose altitude is one-fourth... | MATH | {
"ground_truth": "127",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "47172d47-def7-4864-8cb5-6f5af562090c"
} | [
{
"content": "A square pyramid has a base edge of 32 inches and an altitude of 1 foot. A square pyramid whose altitude is one-fourth of the original altitude is cut away at the apex of the original pyramid. The volume of the remaining frustum is what fractional part of the volume of the original pyramid?The ans... | 127 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
What is the probability that at least two of the faces match when you roll three fair six-sided dice? Express your answer as a common fraction.The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n. | 13 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the probability that at least two of the faces match when you roll three fair six-sided dice? Express your ans... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f8f7aab6-4f70-404e-ad91-6223ff52b641"
} | [
{
"content": "What is the probability that at least two of the faces match when you roll three fair six-sided dice? Express your answer as a common fraction.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.",
"role": "user"
}
] | 13 | 25 | 25/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | math_dapo_quartile0 |
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