data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "A 3x3x3 cube is made of $27$ normal dice. Each die's opposite sides sum to $7$. What is the smallest possible sum of all of the values visible on the $6$ faces of the large cube?\n$\\t... | math | {
"ground_truth": "(D)\\90",
"style": "rule"
} | {
"answer": "(D)\\90",
"difficulty": "1/8",
"index": 52300,
"problem": "A 3x3x3 cube is made of $27$ normal dice. Each die's opposite sides sum to $7$. What is the smallest possible sum of all of the values visible on the $6$ faces of the large cube?\n$\\text{(A)}\\ 60 \\qquad \\text{(B)}\\ 72 \\qquad \\text{(C... |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "$4 \\cdot 212$ The river water is flowing, and at point $Q$ it flows into a still lake. A swimmer travels downstream from $P$ to $Q$, and then across the lake to $R$, taking a total of... | math | {
"ground_truth": "\\dfrac{15}{2}",
"style": "rule"
} | {
"answer": "\\dfrac{15}{2}",
"difficulty": "0/8",
"index": 52301,
"problem": "$4 \\cdot 212$ The river water is flowing, and at point $Q$ it flows into a still lake. A swimmer travels downstream from $P$ to $Q$, and then across the lake to $R$, taking a total of 3 hours. If he travels from $R$ to $Q$ and then ... |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $\\alpha$ is inversely proportional to $\\beta$. If $\\alpha = 4$ when $\\beta = 9$, find $\\alpha$ when $\\beta = -72$. Let's think step by step and output the final ans... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"answer": "-\\frac{1}{2}",
"difficulty": "4/8",
"index": 52302,
"problem": "Suppose that $\\alpha$ is inversely proportional to $\\beta$. If $\\alpha = 4$ when $\\beta = 9$, find $\\alpha$ when $\\beta = -72$."
} |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Given Abby finished the softball season with a total of 45 hits, among which were 2 home runs, 3 triples, and 7 doubles, calculate the percentage of her hits that were singles. Let's t... | math | {
"ground_truth": "73.33\\%",
"style": "rule"
} | {
"answer": "73.33\\%",
"difficulty": "7/8",
"index": 52303,
"problem": "Given Abby finished the softball season with a total of 45 hits, among which were 2 home runs, 3 triples, and 7 doubles, calculate the percentage of her hits that were singles."
} |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "4.9. The circumference of each of two equal circles of radius $R$ passes through the center of the other. Find the area of the common part of these circles. Let's think step by step an... | math | {
"ground_truth": "\\left( \\dfrac{2\\pi}{3} - \\dfrac{\\sqrt{3}}{2} \\right) R^2",
"style": "rule"
} | {
"answer": "\\left( \\dfrac{2\\pi}{3} - \\dfrac{\\sqrt{3}}{2} \\right) R^2",
"difficulty": "4/8",
"index": 52304,
"problem": "4.9. The circumference of each of two equal circles of radius $R$ passes through the center of the other. Find the area of the common part of these circles."
} |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "In the sequence \\(\\left\\{x_{n}\\right\\}\\), \\(x_{1} > 3\\), and \\(x_{n}=\\frac{3 x_{n-1}^{2}-x_{n-1}}{4\\left(x_{n-1}-1\\right)} \\ \\text{for} \\ n=2,3, \\cdots\\). Prove that \... | math | {
"ground_truth": "3 < x_{n+1} < x_n \\text{ for all } n \\geq 1",
"style": "rule"
} | {
"answer": "3 < x_{n+1} < x_n \\text{ for all } n \\geq 1",
"difficulty": "0/8",
"index": 52305,
"problem": "In the sequence \\(\\left\\{x_{n}\\right\\}\\), \\(x_{1} > 3\\), and \\(x_{n}=\\frac{3 x_{n-1}^{2}-x_{n-1}}{4\\left(x_{n-1}-1\\right)} \\ \\text{for} \\ n=2,3, \\cdots\\). Prove that \\(3 < x_{n+1} < x_... |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ be a real number such that\n\\[x^2 + 4 \\left( \\frac{x}{x - 2} \\right)^2 = 45.\\]Find all possible values of $y = \\frac{(x - 2)^2 (x + 3)}{2x - 3}.$ Enter all possible valu... | math | {
"ground_truth": "2,16",
"style": "rule"
} | {
"answer": "2,16",
"difficulty": "0/8",
"index": 52306,
"problem": "Let $x$ be a real number such that\n\\[x^2 + 4 \\left( \\frac{x}{x - 2} \\right)^2 = 45.\\]Find all possible values of $y = \\frac{(x - 2)^2 (x + 3)}{2x - 3}.$ Enter all possible values, separated by commas."
} |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Chun, Tian, Zhen, Mei, and Li each take some candies from a box in sequence. After taking the candies, they say the following statements:\n- Chun: \"Everyone took a different number of... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"difficulty": "2/8",
"index": 52307,
"problem": "Chun, Tian, Zhen, Mei, and Li each take some candies from a box in sequence. After taking the candies, they say the following statements:\n- Chun: \"Everyone took a different number of candies.\"\n- Tian: \"I took half of the remaining candies.\... |
POLARIS-Project/Polaris-Dataset-53K | [
{
"content": "Please reason step by step and put the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Jerry is mowing a rectangular lawn which is $77$ feet north to south by $83$ feet east to west. His lawn mower cuts a path $18$ inches wide. Jerry mows the grass by cutting a path from... | math | {
"ground_truth": "102",
"style": "rule"
} | {
"answer": "102",
"difficulty": "0/8",
"index": 52308,
"problem": "Jerry is mowing a rectangular lawn which is $77$ feet north to south by $83$ feet east to west. His lawn mower cuts a path $18$ inches wide. Jerry mows the grass by cutting a path from west to east across the north side of the lawn and then mak... |
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