data_source
stringclasses 5
values | prompt
listlengths 1
1
| ability
stringclasses 2
values | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
TestDataset.amc
|
[
{
"content": "Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy? \nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "50.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 322,
"question": "Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy? \nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "When $n$ standard six-sided dice are rolled, the product of the numbers rolled can be any of $936$ possible values. What is $n$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "11.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 323,
"question": "When $n$ standard six-sided dice are rolled, the product of the numbers rolled can be any of $936$ possible values. What is $n$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "Suppose that $a$, $b$, $c$ and $d$ are positive integers satisfying all of the following relations.\n\\[abcd=2^6\\cdot 3^9\\cdot 5^7\\]\n\\[\\text{lcm}(a,b)=2^3\\cdot 3^2\\cdot 5^3\\]\n\\[\\text{lcm}(a,c)=2^3\\cdot 3^3\\cdot 5^3\\]\n\\[\\text{lcm}(a,d)=2^3\\cdot 3^3\\cdot 5^3\\]\n\\[\\text{lcm}(b,c)=2^1\\cdot 3^3\\cdot 5^2\\]\n\\[\\text{lcm}(b,d)=2^2\\cdot 3^3\\cdot 5^2\\]\n\\[\\text{lcm}(c,d)=2^2\\cdot 3^3\\cdot 5^2\\]\nWhat is $\\text{gcd}(a,b,c,d)$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 324,
"question": "Suppose that $a$, $b$, $c$ and $d$ are positive integers satisfying all of the following relations.\n\\[abcd=2^6\\cdot 3^9\\cdot 5^7\\]\n\\[\\text{lcm}(a,b)=2^3\\cdot 3^2\\cdot 5^3\\]\n\\[\\text{lcm}(a,c)=2^3\\cdot 3^3\\cdot 5^3\\]\n\\[\\text{lcm}(a,d)=2^3\\cdot 3^3\\cdot 5^3\\]\n\\[\\text{lcm}(b,c)=2^1\\cdot 3^3\\cdot 5^2\\]\n\\[\\text{lcm}(b,d)=2^2\\cdot 3^3\\cdot 5^2\\]\n\\[\\text{lcm}(c,d)=2^2\\cdot 3^3\\cdot 5^2\\]\nWhat is $\\text{gcd}(a,b,c,d)$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "A $3-4-5$ right triangle is inscribed in circle $A$, and a $5-12-13$ right triangle is inscribed in circle $B$. Find the ratio of the area of circle $A$ to the area of circle $B$. The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "194.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 325,
"question": "A $3-4-5$ right triangle is inscribed in circle $A$, and a $5-12-13$ right triangle is inscribed in circle $B$. Find the ratio of the area of circle $A$ to the area of circle $B$. The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "Jackson's paintbrush makes a narrow strip with a width of $6.5$ millimeters. Jackson has enough paint to make a strip $25$ meters long. How many square centimeters of paper could Jackson cover with paint?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1625.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 326,
"question": "Jackson's paintbrush makes a narrow strip with a width of $6.5$ millimeters. Jackson has enough paint to make a strip $25$ meters long. How many square centimeters of paper could Jackson cover with paint?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "You are playing a game. A $2 \\times 1$ rectangle covers two adjacent squares (oriented either horizontally or vertically) of a $3 \\times 3$ grid of squares, but you are not told which two squares are covered. Your goal is to find at least one square that is covered by the rectangle. A \"turn\" consists of you guessing a square, after which you are told whether that square is covered by the hidden rectangle. What is the minimum number of turns you need to ensure that at least one of your guessed squares is covered by the rectangle?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 327,
"question": "You are playing a game. A $2 \\times 1$ rectangle covers two adjacent squares (oriented either horizontally or vertically) of a $3 \\times 3$ grid of squares, but you are not told which two squares are covered. Your goal is to find at least one square that is covered by the rectangle. A \"turn\" consists of you guessing a square, after which you are told whether that square is covered by the hidden rectangle. What is the minimum number of turns you need to ensure that at least one of your guessed squares is covered by the rectangle?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "When the roots of the polynomial \n\\[P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \\cdot \\cdot \\cdot (x-10)^{10}\\]\nare removed from the number line, what remains is the union of $11$ disjoint open intervals. On how many of these intervals is $P(x)$ positive?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 328,
"question": "When the roots of the polynomial \n\\[P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \\cdot \\cdot \\cdot (x-10)^{10}\\]\nare removed from the number line, what remains is the union of $11$ disjoint open intervals. On how many of these intervals is $P(x)$ positive?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "901.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 329,
"question": "For how many integers $n$ does the expression\\[\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}\\]represent a real number, where log denotes the base $10$ logarithm?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "How many nonempty subsets $B$ of ${0, 1, 2, 3, \\cdots, 12}$ have the property that the number of elements in $B$ is equal to the least element of $B$? For example, $B = {4, 6, 8, 11}$ satisfies the condition.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "144.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 330,
"question": "How many nonempty subsets $B$ of ${0, 1, 2, 3, \\cdots, 12}$ have the property that the number of elements in $B$ is equal to the least element of $B$? For example, $B = {4, 6, 8, 11}$ satisfies the condition.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
TestDataset.amc
|
[
{
"content": "What is the area of the region in the coordinate plane defined by\n$| | x | - 1 | + | | y | - 1 | \\le 1$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "8.0",
"style": "rule"
}
|
{
"accuracy": 0,
"index": 331,
"question": "What is the area of the region in the coordinate plane defined by\n$| | x | - 1 | + | | y | - 1 | \\le 1$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"split": "test"
}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.