data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a park, there is a row of flags arranged in the sequence of 3 yellow flags, 2 red flags, and 4 pink flags. Xiaohong sees that the row ends with a pink flag. Given that the tot... | math | {
"ground_truth": "198",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let n be the smallest positive integer such that n is divisible by 30, n^2 is a perfect fourth power, and n^4 is a perfect square. Find the number of digits of n.",
"role": "... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways can we arrange 4 physics books and 6 history books on a shelf if all the physics books must stay together and all the history books must also stay together? The phy... | math | {
"ground_truth": "34560",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of the line symmetric to the line $x+2y-3=0$ with respect to the line $x=1$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "x-2y+1=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that vector $\\overrightarrow{e_{1}} \\neq \\overrightarrow{0}, \\lambda \\in R$, $\\overrightarrow{a} = \\overrightarrow{e_{1}} + \\lambda \\overrightarrow{e_{2}}$, $\\ove... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On an island, there are knights who always tell the truth and liars who always lie. The island's football team has 11 players. Player number 1 said: \"In our team, the number of ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, $6$, and $7$ children with no marbles left over. What is the least number of marbles that the set could ... | math | {
"ground_truth": "420",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose the cost $C$ of shipping a combination of a parcel post package weighing $P$ pounds and a flat-rate envelope together is calculated as follows: There is a fixed fee of $1... | math | {
"ground_truth": "\\text{A) } C = 5P + 27",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jane starts at dot $A$. She tosses a fair coin to determine which way to move. If she tosses a head, she moves up one dot, and if she tosses a tail, she moves right one dot. Afte... | math | {
"ground_truth": "\\frac{3}{8}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a standard deck of 52 cards, which includes 13 ranks and 4 suits, with each rank having one card per suit, what is the probability that the top card is either a King or a Quee... | math | {
"ground_truth": "\\frac{2}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cube with side length 10 is suspended above a plane. The vertex closest to the plane is labelled $A$ . The three vertices adjacent to vertex $A$ are at heights 10, 11, and 1... | math | {
"ground_truth": "330",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose the calculator's display shows 00050. What is the fewest number of times you must press the $\\frac{1}{x}$ key so that the display reads 00050 again?",
"role": "user"... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $f'(x)=2$, calculate $\\lim_{{\\Delta x}\\to 0}\\frac{f(x)-f(x+2\\Delta x)}{\\Delta x}$.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The angles in a triangle are in arithmetic progression, and the side lengths are 5, 7, and y. Find the sum of all possible values of y, which equals $d + \\sqrt{e} + \\sqrt{f}$ w... | math | {
"ground_truth": "47",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ a_1, a_2, \\ldots, a_{2n}$ be $ 2n$ real numbers satisfying the condition $ \\sum_{i \\equal{} 1}^{2n \\minus{} 1} (a_{i \\plus{} 1} \\minus{} a_i)^2 \\equal{} 1$ . F... | math | {
"ground_truth": "\\sqrt{2n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence consists of all positive multiples of 4 that contain at least one digit that is a 2. What is the $50^{\\mathrm{th}}$ term of the sequence?",
"role": "user"
}
] | math | {
"ground_truth": "260",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sohom constructs a square $BERK$ of side length $10$ . Darlnim adds points $T$ , $O$ , $W$ , and $N$ , which are the midpoints of $\\overline{BE}$ , $\\overline{ER}$ , ... | math | {
"ground_truth": "180",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are four brother-sister pairs from different families that need to take a trip in a van. The eight children will occupy the second and third rows, each of which has four se... | math | {
"ground_truth": "576",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ and $h(x)$ be polynomials such that $f(x) + h(x) = 3x^2 + 5x - 4$. Find $h(x)$ if $f(x) = x^4 - 2x^3 + x - 1$.",
"role": "user"
}
] | math | {
"ground_truth": "-x^4 + 2x^3 + 3x^2 + 4x - 3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The residents of an accommodation need to pay the rent for the accommodation. If each of them contributes $10 \\mathrm{Ft}$, the amount collected falls $88 \\mathrm{Ft}$ short of... | math | {
"ground_truth": "10.54 \\ \\text{Ft}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An item's price is first increased by 10%, then by another 20%. If subsequently both these increments are reversed in the same order (i.e., first a 20% decrease, followed by a 10... | math | {
"ground_truth": "\\frac{10800}{9504}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $1 \\in \\{x, x^2\\}$, then $x = \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "x=-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of triangles with all sides being positive integers and the longest side being 11 is $\\boxed{36}$.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many different positive values of \\(x\\) will satisfy the condition: there are exactly \\(3\\) positive two-digit multiples of \\(x\\).",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is $\\frac{5}{6}$ divided by $1\\frac{3}{4}$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{10}{21}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: \\( 25 \\times 13 \\times 2 + 15 \\times 13 \\times 7 = \\)",
"role": "user"
}
] | math | {
"ground_truth": "2015",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five eight-sided dice (each sided from 1 to 8) are rolled. Calculate the probability that the sum of the numbers rolled is odd, provided that the product of the numbers is even."... | math | {
"ground_truth": "\\frac{15}{31}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Garfield and Odie are situated at $(0,0)$ and $(25,0)$ , respectively. Suddenly, Garfield and Odie dash in the direction of the point $(9, 12)$ at speeds of $7$ and $10$ ... | math | {
"ground_truth": "159",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In 2008, Investor Ian invested $200$ dollars for three years. During the first year his investment suffered a $10\\%$ loss, during the second year the remaining investment showed... | math | {
"ground_truth": "\\textbf{(B)}\\ 1.7\\% loss",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f(x)$ satisfies\n\\[b^2 f(a) = a^2 f(b)\\]\nfor all real numbers $a$ and $b.$ If $f(2) \\neq 0,$ find\n\\[\\frac{f(3) - f(4)}{f(2)}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{7}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A half-sector of a circle of radius 6 inches is rolled up to form the lateral surface area of a right circular cone by taping together along the two radii. Calculate the volume o... | math | {
"ground_truth": "9\\pi \\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A man on his way to dinner shortly after $7:00$ p.m. observes that the hands of his watch form an angle of $120^{\\circ}$. Returning before $8:00$ p.m., he notices that the hands... | math | {
"ground_truth": "43.64",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\[f(x) =\n\\begin{cases}\n3x^2 + 5&\\text{if } x\\le 4, \\\\\nbx - 2 &\\text{if } x>4.\n\\end{cases}\n\\]Find \\( b \\) if the graph of \\( y=f(x) \\) is continuous.",
"... | math | {
"ground_truth": "\\frac{55}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the initial odometer reading is $27472$ and the final odometer reading is the next palindrome after $27472$, calculate Lucas' average speed over the $4$-hour period.",... | math | {
"ground_truth": "252.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\\\(f(x)\\\\) and \\\\(g(x)\\\\) be odd and even functions defined on \\\\(\\mathbb{R}\\\\), respectively. When \\\\(x < 0\\\\), \\\\(f'(x)g(x) + f(x)g'(x) > 0\\\\), and \\\... | math | {
"ground_truth": "(-\\infty, -3) \\cup (0, 3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $g(m, n, p) = \\frac{m+p^2}{m-n}$, calculate $g(2, 3, -1)$.",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the arithmetic sequence $\\{a_n\\}$, it is known that $(a_3 + a_8 = 15)$, find the value of $(S_{10})$.",
"role": "user"
}
] | math | {
"ground_truth": "75",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence $a_1,a_2,\\dots,a_{13}$ is a geometric sequence with $a_1=a$ and common ratio $r$ , where $a$ and $r$ are positive integers. Given that $$ \\log_{2015}a_1+... | math | {
"ground_truth": "26^3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the line $5x + 8y + c = 0$, the sum of the $x$- and $y$-intercepts is $26$. Find $c$.",
"role": "user"
}
] | math | {
"ground_truth": "-80",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $p=2^{16}+1$ is a prime, find the maximum possible number of elements in a set $S$ of positive integers less than $p$ so no two distinct $a,b$ in $S$ satisfy $$ a^... | math | {
"ground_truth": "43691",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular prism has dimensions 2 units by 3 units by 4 units. Find the sum of the number of edges, vertices (corners), and faces.",
"role": "user"
}
] | math | {
"ground_truth": "26",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The probability it will rain on Friday is 70%, on Saturday is 50%, and on Sunday is 30%. Assuming the probability of rain on a given day is independent of the weather on any othe... | math | {
"ground_truth": "10.5\\%",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum \n\\[ \\sum_{k=0}^{\\infty} \\frac{2^{k}}{5^{2^{k}}+1}\\]\ncan be written in the form $\\frac{p}{q}$ where $p$ and $q$ are relatively prime positive integers. Find ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two grade seven students were allowed to enter a chess tournament otherwise composed of grade eight students. Each contestant played once with each other contestant and received ... | math | {
"ground_truth": "n = 7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, angle $A$ measures $45^\\circ$ and altitude $CD$ from $C$ to hypotenuse $AB$ measures $2$ centimeters. What is the number of square centimeters in the area of ... | math | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From 6 different given colors, choose several colors to color the 6 faces of a cube. Each face must be colored with a different color, and adjacent faces must have different colo... | math | {
"ground_truth": "230",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the units digit of the number $4539^{201}$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest positive integer \\( n \\) such that \\( \\sqrt{n} - \\sqrt{n-1} < 0.05 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "101",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of the square of the expression\n\n$$\n1+\\frac{x}{2}-\\frac{x^{2}}{8}+\\frac{x^{3}}{16}-\\frac{5 x^{4}}{128}\n$$\n\nto 6 decimal places for $x= \\pm 0.1, \\p... | math | {
"ground_truth": "0.990000",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sides of rectangle $ABCD$ have lengths 10 and 11. An equilateral triangle is drawn so that no point of the triangle lies outside $ABCD.$ The maximum possible area of su... | math | {
"ground_truth": "554",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $f(x)$ is a quadratic function, and it satisfies $f(0) = 1$, $f(x+1) - f(x) = 2x$, find the expression for $f(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 - x + 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A $9\\times 7$ rectangle is tiled with tiles of the two types: L-shaped tiles composed by three unit squares (can be rotated repeatedly with $90^\\circ$ ) and square tiles com... | math | {
"ground_truth": "\\{2, 5, 8, 11, 14, 17, 20\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve:\n\n$$\nx^{3} + y^{3} = 3(z^{3} + t^{3})\n$$\n\nwhere \\( x, y, z, \\) and \\( t \\) are integers.",
"role": "user"
}
] | math | {
"ground_truth": "x \\text{ and } y \\text{ are divisible by 3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\cos x(\\sin x+\\sqrt{3}\\cos x)-\\frac{\\sqrt{3}}{2}$, where $x\\in \\mathbb{R}$. Let $\\alpha > 0$, if the function $g(x)=f(x+\\alpha)$ is an odd func... | math | {
"ground_truth": "\\alpha= \\frac{k\\pi}{2}- \\frac{\\pi}{6}(k\\in\\mathbb{N}^{*})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Anne-Marie has a deck of $16$ cards, each with a distinct positive factor of $2002$ written on it. She shuffles the deck and begins to draw cards from the deck without replac... | math | {
"ground_truth": "4.0625",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the set of $x$-values satisfying the inequality $|\\frac{6 - 2x + 5}{4}| < 3$. Simplify your answer.\n**A** $x > -\\frac{1}{2}$ \n**B** $x < \\frac{23}{2}$ \n**C** $ -\\fr... | math | {
"ground_truth": "\\textbf{(C)}\\ -\\frac{1}{2} < x < \\frac{23}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each segment with endpoints at the vertices of a regular 100-gon is painted red if there is an even number of vertices between its endpoints, and blue otherwise (in particular, a... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that in a collection of red, blue, green, and yellow marbles, there are $30\\%$ more red marbles than blue marbles, and there are $50\\%$ more green marbles than red marble... | math | {
"ground_truth": "4.47r",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a rhombus $EFGH$ with a perimeter of $64$ meters and the length of diagonal $\\overline{EH}$ of $30$ meters, calculate the area of the rhombus $EFGH$.",
"role": "user"
... | math | {
"ground_truth": "30\\sqrt{31}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that triangle $ABC$ has an area of $96$, and $D$ is the midpoint of $AB$, $E$ is the midpoint of $DB$, and $F$ is the midpoint of $BC$, determine the area of $\\triangle AE... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Personal income from manuscript remuneration is taxed based on the remainder after stipulated expenses are deducted from the income earned on each occasion. For income not exceed... | math | {
"ground_truth": "2800",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "You are given that \\[17! = 355687ab8096000\\] for some digits $a$ and $b$ . Find the two-digit number $\\overline{ab}$ that is missing above.",
"role": "user"
}
] | math | {
"ground_truth": "75",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any positive integer $x$ , let $S(x)$ be the sum of the digits of $x$ , and let $T(x)$ be $|S(x+2)-S(x)|.$ For example, $T(199)=|S(201)-S(199)|=|3-19|=16.$ How ma... | math | {
"ground_truth": "222",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose 7 cans of soda can be purchased from a vending machine for 10 quarters. If there is a 10% discount for purchases made of more than $5, calculate the number of cans of sod... | math | {
"ground_truth": "A) 61 cans",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When you simplify $\\sqrt[3]{40a^6b^3c^{14}}$, what is the sum of the exponents of the variables that are outside the radical?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( g(x) = 2x^3 - 3x + 1 \\), what is the value of \\( g(g(2)) \\)?",
"role": "user"
}
] | math | {
"ground_truth": "2630",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the total square feet of walls Carl needs to paint given that each of the 4 bedrooms has walls with a length of 15 feet, a width of 11 feet, and a height of 9 feet, wit... | math | {
"ground_truth": "1552",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a small town with a total population of $600$, the population is divided into four parts, and one part represents males, one part represents females, and the other two parts r... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the graph of the power function $y=f(x)$ passes through the point $(2, \\sqrt{2})$, then $f(9) =$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a larger grid where each block is 1 unit by 1 unit, suppose we wish to walk from point $A$ to point $B$ but must pass through point $C$. The grid dimensions have increased to ... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a right rectangular prism $B$ with edge lengths $1,$ $3,$ and $4$, and the set $S(r)$ of points within a distance $r$ of some point in $B$, express the volume of $S(r)$ as ... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given Tom paid $180, Dorothy paid $200, Sammy paid $240, and Alice paid $280, and they agreed to split the costs evenly, calculate the amount that Tom gave to Sammy minus the amo... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the lengths of the arcs of curves given by the equations in the rectangular coordinate system.\n\n$$\ny=\\frac{e^{x}+e^{-x}}{2}+3, \\ 0 \\leq x \\leq 2\n$$",
"role"... | math | {
"ground_truth": "\\frac{1}{2} (e^2 - e^{-2})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola $C_1: x^2 = 2py$ whose focus is on the parabola $C_2: y = x^2 + 1$, and point $P$ is a moving point on parabola $C_1$.\n\n$(1)$ Find the equation of parabola $... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points $(2, -3)$ and $(8, 9)$ are opposite vertices of a parallelogram. One side of this parallelogram is parallel to the x-axis. Find the coordinates of the other pair of opposi... | math | {
"ground_truth": "(5, 9)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$ passes through the point $P(1, \\frac{\\sqrt{3}}{2})$, and its eccentricity $e = \\frac{\\sqrt{3}}{2}... | math | {
"ground_truth": "1 \\text{ point}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the sum \\(+1+3+9+27+81+243+729\\), it is allowed to cross out any terms and change the signs of some of the remaining numbers from \"+\" to \"-\". Masha wants to obtain an ex... | math | {
"ground_truth": "1093",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate \\[\\dfrac{4}{\\,\\,\\frac{8}{13}\\,\\,}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using the renovation law, what is the minimum number of buildings that can remain in the city if the city has dimensions:\n\na) $20 \\times 20$ cells;\n\nb) $50 \\times 90$ cells... | math | {
"ground_truth": "282",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A set $ X$ of positive integers is called *nice* if for each pair $ a$ , $ b\\in X$ exactly one of the numbers $ a \\plus{} b$ and $ |a \\minus{} b|$ belongs to $ X$ (... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ordered triples of positive integers \\((a, b, c)\\) are there for which \\(a^{4} b^{2} c = 54000\\)?",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "5 oxen and 2 sheep cost 10 taels, and 2 oxen and 8 sheep cost 8 taels. How much do an ox and a sheep each cost separately?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{вол стоит } \\frac{16}{9} \\text{ таэль, баран стоит } \\frac{5}{9} \\text{ таэль}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "During the first year, DEF's stock price starts at $ \\$120 $ and increases by $ 50\\% $. During the second year, its stock price decreases by $ 30\\% $ from its price at the end... | math | {
"ground_truth": "\\$151.2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the hyperbola \\[\\frac{(x-5)^2}{7^2} - \\frac{(y-10)^2}{3^2} = 1.\\] This hyperbola has two foci, which have different $x-$coordinates. Find the coordinates of the focu... | math | {
"ground_truth": "(5 + \\sqrt{58}, 10)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ such that there exists an infinite set $A$ of positive integers with the following property: For all pairwise distinct numbers $a_1, a_2, \\ld... | math | {
"ground_truth": "n = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the remainder when \\[9 \\times 99 \\times 999 \\times \\cdots \\times \\underbrace{99\\cdots9}_{\\text{999 9's}}\\] is divided by $ 1000$ .",
"role": "user"
}
] | math | {
"ground_truth": "109",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $d_k$ be the greatest odd divisor of $k$ for $k = 1, 2, 3, \\ldots$ . Find $d_1 + d_2 + d_3 + \\ldots + d_{1024}$ .",
"role": "user"
}
] | math | {
"ground_truth": "349526",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The shortest distance from a point on the curve $y=\\ln(2x-1)$ to the line $2x-y+3=0$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagram shows a shaded semicircle of diameter 4, from which a smaller semicircle has been removed. The two semicircles touch at exactly three points. What fraction of the lar... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n \\ge 3$ be a positive integer. Suppose that $\\Gamma$ is a unit circle passing through a point $A$ . A regular $3$ -gon, regular $4$ -gon, \\dots, regular $n$ -gon... | math | {
"ground_truth": "63",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When $x^{2}$ was added to the quadratic polynomial $f(x)$, its minimum value increased by 1. When $x^{2}$ was subtracted from it, its minimum value decreased by 3. How will the m... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a$ and $b$ are the roots of the equation $x^2-2cx-5d = 0$, and $c$ and $d$ are the roots of the equation $x^2-2ax-5b=0$, where $a,b,c,d$ are distinct real numbers, find $a... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The parabola \\( y = ax^2 + bx + c \\) has vertex \\((p, -p)\\) and passes through the point \\( (0, p) \\), where \\( p \\neq 0 \\). Determine the value of \\( b \\).",
"rol... | math | {
"ground_truth": "-\\frac{4}{p}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of $b$ such that the graphs of $y=bx^2 + 5x + 2$ and $y=-2x-2$ intersect at only one point.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{49}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the function $f(x) = x^2 + 3\\sqrt{x} + x$. Evaluate $3f(3) + f(9)$.",
"role": "user"
}
] | math | {
"ground_truth": "135 + 9\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A driver travels for 3 hours at 50 miles per hour, during which her car gets 30 miles per gallon of gasoline. She is paid $0.75 per mile, and her only expense is gasoline at $2.5... | math | {
"ground_truth": "33.33",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jimmy runs a successful pizza shop. In the middle of a busy day, he realizes that he is running low on ingredients. Each pizza must have 1 lb of dough, $\\frac14$ lb of chees... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Adam is playing Minesweeper on a $9\\times9$ grid of squares, where exactly $\\frac13$ (or 27) of the squares are mines (generated uniformly at random over all such boards). ... | math | {
"ground_truth": "\\frac{88}{379}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 ho... | math | {
"ground_truth": "204",
"style": "rule"
} | {
"id": "aime24-60",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle inscribed in circle $\\omega$. Let the tangents to $\\omega$ at $B$ and $C$ intersect at point $D$, and let $\\overline{AD}$ intersect $\\omega$ at $P$. I... | math | {
"ground_truth": "113",
"style": "rule"
} | {
"id": "aime24-61",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
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