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": "Compute \\(\\binom{10}{5}\\).",
"role": "user"
}
] | math | {
"ground_truth": "252",
"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 an ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ $(a > b > 0)$ that passes through point $(0, 4)$, with an eccentricity of $\\frac{3}{5}$.\n\n$(1)$ Find the equati... | math | {
"ground_truth": "\\left( \\frac{3}{2} , -\\frac{6}{5} \\right)",
"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 points $A(2,0)$, $B(0,2)$, and $C(\\cos α,\\sin α)$ where $0 < α < π$,\n1. If $| \\overrightarrow{OA}+ \\overrightarrow{OC}|= \\sqrt {7}$, find the angle between $ \\overri... | math | {
"ground_truth": "\\cos α= \\dfrac {1- \\sqrt {7}}{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": "Let $A = (-2,1,3),$ $B = (2,3,4),$ and $C = (s,0,2),$ where $s$ is a real number. Find the smallest possible area of triangle $ABC.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{1}}{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": "Calculate:<br/>$(1)2\\cos 45^{\\circ}+(\\pi -\\sqrt{3})^{0}-\\sqrt{8}$;<br/>$(2)(\\frac{2}{{m-1}}+1)\\div \\frac{{2m+2}}{{{m^2}-2m+1}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{m-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": "Point $C$ is on the line segment $AB$ with endpoints $A(-3, -2)$ and $B(5, 10)$. Point $C$ is twice as far from point $A$ as it is from point $B$. What are the coordinates of poi... | math | {
"ground_truth": "\\left(\\frac{11}{3}, 8\\right)",
"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 coefficient of $x^2$ in the expansion of $(x+1)^5(x-2)$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "-15",
"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": "What is the least positive multiple of 35 that is greater than 500?",
"role": "user"
}
] | math | {
"ground_truth": "525",
"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 fan rotates 100 times in 1 minute on the \"slow\" setting. If the rate of rotation doubles on the \"medium\" setting and doubles again on the \"high\" setting, determine how ... | math | {
"ground_truth": "6000",
"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": "Compute: $6^2 - 4 \\cdot 5 + 4^2$.",
"role": "user"
}
] | math | {
"ground_truth": "32",
"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 $S_n$ is the sum of the first $n$ terms of the sequence $\\{a_n\\}$, and the sequence $\\{a_n\\}$ satisfies the condition\n$$ \\frac {1}{a_{1}} + \\frac {1}{2 \\cdot a... | math | {
"ground_truth": "\\frac {31}{32}",
"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 the smallest natural number $n$ for which there exist distinct nonzero naturals $a, b, c$ , such that $n=a+b+c$ and $(a + b)(b + c)(c + a)$ is a perfect cube.",
... | math | {
"ground_truth": "10",
"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 solution set of the inequalities ${x^{2}} > 1$ and $-{x^{2}}+2x+3 > 0$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{ x \\mid -1 < x < 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": "Find all positive values of \\( a \\) such that the equation \\( a^{2} x^{2}+a x+1-7 a^{2}=0 \\) has two integer roots.",
"role": "user"
}
] | math | {
"ground_truth": "1,\\ \\frac{1}{2},\\ \\frac{1}{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": "Let \\( P \\) be a polynomial of degree 2022 such that \\( P(1) = 1, P(2) = 2, \\ldots, P(2022) = 2022 \\) and \\( P(0) = 1 \\).\n\nDetermine \\( P(-1) \\).",
"role": "user"
... | math | {
"ground_truth": "2022",
"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": "If the function $f(x)$ satisfies $f(n^{2})=f(n)+2(n\\geqslant 2)$, and $f(2)=1$, then $f(256)=$\\_\\_\\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "f(256)=7",
"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": "Find all differentiable functions $f: (0,\\infty)\\mapsto (0,\\infty)$ for which there is a positive real number $a$ such that\r\n\\[ f'\\left(\\frac ax\\right)=\\frac x{f(x)... | math | {
"ground_truth": "f(x) = a^{1 - a/b} x^{a/b}",
"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 a function $f(x)$ for any $x, y \\in \\mathbb{R}$, satisfying the condition $f(x) + f(y) = 2 + f(x+y)$, and when $x > 0$, $f(x) > 2$, $f(3) = 5$. \n(1) Determine the monot... | math | {
"ground_truth": "-1 < a < 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": "Throwing a red and a blue die once each, the probability that the sum of the numbers is less than $7$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{12}",
"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": "Find all positive integers $m$ and $n$ such that $(2^{2^{n}}+1)(2^{2^{m}}+1) $ is divisible by $m\\cdot n $ .",
"role": "user"
}
] | math | {
"ground_truth": "(m, n) = (1, 1), (1, 5), (5, 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 maximum possible value of $k$ for which there exist distinct reals $x_1,x_2,\\ldots ,x_k $ greater than $1$ such that for all $1 \\leq i, j \\leq k$ , $$ x_i^{\\... | math | {
"ground_truth": "4",
"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 a new game show $\\text{\\emph{Wheel of Fortune Plus}}$, the wheel is divided into six equal sections with the values: Bankrupt, $\\$2000$, $\\$500$, $\\$6000$, $\\$700$, and ... | math | {
"ground_truth": "\\frac{1}{36}",
"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": "For which values of \\( B \\) and \\( C \\) are the line \\(\\frac{x-3}{1} = \\frac{y-2}{B} = \\frac{z+2}{C}\\) and the plane \\(3x - 2y + 5z = 0\\) perpendicular?",
"role": ... | math | {
"ground_truth": "B = -\\frac{2}{3}, \\quad C = \\frac{5}{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": "A special deck of cards contains $49$ cards, each labeled with a number from $1$ to $7$ and colored with one of seven colors. Each number-color combination appears on exactly one... | math | {
"ground_truth": "13",
"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": "Find the fraction equivalent to the repeating decimal $0.\\overline{215}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{215}{999}",
"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 \\(k\\) is a constant such that \\(x^2 - 60x + k\\) is equal to the square of a binomial, then what is \\(k\\)?",
"role": "user"
}
] | math | {
"ground_truth": "900",
"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 natural numbers from 1 to 2023 are written in a row in some order. It turns out that any three numbers, arranged with one number in between, give different remainders when di... | math | {
"ground_truth": "\\text{Any number giving a remainder of 1 when divided 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": "Find the smallest positive period of the function \\( f(x) = 3 \\sin 2x + 2^{|\\sin^2 2x|} + 5|\\sin 2x| \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{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 $f(x)$ be a function such that $f(0) = 2$ and\n\\[ f(xy) = f\\left(\\frac{x^2 + y^2}{2}\\right) + 3(x - y)^2 \\]\nfor all real numbers $x$ and $y.$ Find $f(x)$.",
"role":... | math | {
"ground_truth": "f(x) = 2 - 3x^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": "Let $r$ be the number of red balls, $b$ be the number of blue balls, and $g$ be the number of green balls in the bag. Given that $\\frac{1}{3}$ of the balls are red, $\\frac{2}{7... | 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": "Formulate a differential equation for which \\( y_{1}(x)=e^{x} \\) and \\( y_{2}(x)=e^{-x} \\) form a fundamental system of solutions.",
"role": "user"
}
] | math | {
"ground_truth": "y'' - y = 0",
"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 vectors $\\overrightarrow{m} = \\left(\\sqrt{3}\\sin\\frac{x}{4}, 1\\right)$, $\\overrightarrow{n} = \\left(\\cos\\frac{x}{4}, \\cos^2\\frac{x}{4}\\right)$, let $f(x) = \\o... | math | {
"ground_truth": "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": "Two different numbers are randomly selected from the set $\\{ -2, -1, 0, 3, 4, 5\\}$ and multiplied together. Calculate the probability that the product is $0$.",
"role": "us... | math | {
"ground_truth": "\\frac{1}{3}",
"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": "Derivative the function $y=(2x+1)^2$ at $x=1$.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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": "Use the bisection method to find an approximate zero of the function $f(x) = \\log x + x - 3$, given that approximate solutions (accurate to 0.1) are $\\log 2.5 \\approx 0.398$, ... | math | {
"ground_truth": "2.6",
"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": "Let \\(\\omega\\) be a primitive third root of unity. Find the value of \\((1-\\omega)(1-\\omega^{2})(1-\\omega^{4})(1-\\omega^{8})\\).",
"role": "user"
}
] | 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": "In a round-robin football tournament, there are $n$ teams participating. Among them, 2 teams played 3 matches each and then withdrew from the competition. These two teams did not... | math | {
"ground_truth": "10",
"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 diagram below, semicircles are constructed on diameters $\\overline{AB}$, $\\overline{AC}$, and $\\overline{CB}$, such that they are mutually tangent. If $\\overline{CD} \... | math | {
"ground_truth": "\\frac{11}{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": "Find the volume of a regular triangular pyramid with height \\(h\\) and radius \\(r\\) of the inscribed sphere.",
"role": "user"
}
] | math | {
"ground_truth": "V_{ABCD} = \\frac{(2 + h \\sqrt{3})^2 h^2 \\sqrt{3}}{12 (h^2 - 2rh)}",
"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 triangle \\( \\triangle ABC \\), for \\( \\angle A \\) to be the largest angle, it must be that \\( m < x < n \\). The side lengths of the triangle are given by \\( AB = x+5... | math | {
"ground_truth": "6",
"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 rectangle where the diagonal equals $p + q$, and the length is twice the breadth, find the area of the rectangle.\nA) $\\frac{(p+q)^2}{5}$\nB) $\\frac{2(p+q)^2}{3}$\nC) $... | math | {
"ground_truth": "\\frac{2(p+q)^2}{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": "If two distinct members of the set $\\{ 6, 14, 18, 35, 42, 49, 54 \\}$ are randomly selected and multiplied, what is the probability that the product is a multiple of 126? Expres... | math | {
"ground_truth": "\\frac{5}{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": "What is the greatest common divisor of $5039$ and $3427$?",
"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": "In a deck consisting of three red cards labeled A, B, C and three green cards labeled A, B, C, calculate the probability of drawing a winning pair.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{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 $A = (2,4)$ be a point on the parabola $y = 2x^2$. The normal to the parabola at point $A$ is drawn, intersecting the parabola again at point $B$ and the x-axis at point $C$.... | math | {
"ground_truth": "(34, 0)",
"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": "Let $ABCD$ be a square of side length $13$ . Let $E$ and $F$ be points on rays $AB$ and $AD$ respectively, so that the area of square $ABCD$ equals the area of trian... | math | {
"ground_truth": "\\sqrt{13}",
"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 the total of 5 coins is divided among 5 people, A, B, C, D, and E, such that the amounts received by A and B are equal to the amounts received by C, D, and E, and the amoun... | math | {
"ground_truth": "\\frac{2}{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": "Let $R$ be a square, one diagonal of which has endpoints $(0,1)$ and $(1,0)$. A point $w=(x,y)$ is chosen uniformly at random such that $0 \\le x \\le 100$ and $0 \\le y \\le 100... | math | {
"ground_truth": "\\textbf{(B) }\\frac{10000}{10201}",
"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 triangle $ABC$, it is known that $AB=3$, $AC=4$, and $\\angle BAC=60^\\circ$. The extension of the angle bisector $AA_1$ intersects the circumcircle of triangle $ABC$ at point... | math | {
"ground_truth": "S_{\\triangle A_{1}A_{2}C} = \\frac{13 \\sqrt{3}}{21}",
"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": "There are 52 students participating in a park event. Among them, 12 students visited the botanical exhibit, 26 students visited the animal exhibit, and 23 students visited the te... | math | {
"ground_truth": "1",
"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": "Determine the median length of the names of 25 individuals recorded in a survey.",
"role": "user"
}
] | math | {
"ground_truth": "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": "a) We call *admissible sequence* a sequence of 4 even digits in which no digits appears more than two times. Find the number of admissible sequences.\r\n\r\nb) For each integer ... | math | {
"ground_truth": "\\{2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540\\}",
"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 domain of the function \\( f(x) = \\frac{\\sin 2x \\cos x}{1 - \\sin x} \\) is \\(\\qquad\\), and the range is \\(\\qquad\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\{ x \\mid x \\neq 2k\\pi + \\frac{\\pi}{2}, k \\in \\mathbb{Z} \\}, \\left[-\\frac{1}{2}, 4\\right)",
"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": "Consider a point $P$ with coordinates $(x, y, z)$ in a 3D space. Let $r$ be the distance from the origin to this point, and define $s = \\frac{y}{r}$ and $c = \\frac{x}{r}$. Comp... | math | {
"ground_truth": "D) between -1 and +1, both included",
"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 ratio of $a$ to $b$ is $5:4$, of $c$ to $d$ is $4:3$, and of $d$ to $b$ is $1:9$. Find the ratio of $a$ to $c$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{135}{16}",
"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 trapezium \\( PQRS \\), \\( \\angle RSP = 2 \\times \\angle SPQ \\) and \\( \\angle SPQ = 2 \\times \\angle PQR \\). Also \\( \\angle QRS = k \\times \\angle PQR \\). What is ... | math | {
"ground_truth": "5",
"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 different set of checkerboards is being considered for covering with dominoes, each domino encompassing two squares. Determine which one of the following boards cannot be entir... | math | {
"ground_truth": "B) 5x5 and C) 3x7",
"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 Alice has 24 apples, find the number of ways she can share them with Becky and Chris so that each of the three people has at least two apples.",
"role": "user"
}... | math | {
"ground_truth": "190",
"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": "Let the function $f(x)$ defined on $\\mathbb{R}$ satisfy $f'(x) - f(x) = xe^x$, and $f(0) = \\frac{1}{2}$. Find the maximum value of $\\frac{f'(x)}{f(x)}$.",
"role": "user"
... | 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": "Two cyclists start from two points that are $50$ miles apart. If they travel towards each other, they meet in $2$ hours. However, if one cyclist starts from a point $10$ miles be... | math | {
"ground_truth": "\\frac{17}{13}",
"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": "Inside a square, point $P$ has distances $a, b, c$ from vertices $A, B, C$ respectively. What is the area of the square? What is it in the case when $a = b = c$?",
"role": "u... | math | {
"ground_truth": "2a^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": "Each face of a tetrahedron has three possible choices for the edges of a stripe, made at random and independently for each face. Calculate the probability that there is a continu... | math | {
"ground_truth": "\\frac{2}{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": "If the function $f(x) = -x^2 + 2ax + 1$ is monotonically decreasing on the interval $[1, 2]$, then the range of values for $a$ is.",
"role": "user"
}
] | math | {
"ground_truth": "a \\leq 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 degree of the polynomial $x^{2}-2x+3$ is ______.",
"role": "user"
}
] | 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": "Given that circles $A$ and $B$ each have a radius of 1 and are tangent to each other, and circle $C$ has a radius of 2 and is tangent to the midpoint $M$ of $\\overline{AB}$, cal... | math | {
"ground_truth": "2\\pi",
"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 midpoints of the non-parallel sides of a trapezoid and the midpoints of the diagonals lie on a line parallel to the base. The distance between the midpoints of the non-parall... | math | {
"ground_truth": "\\frac{1}{2}(DC + AB) \\quad \\text{and} \\quad \\frac{1}{2}(AB - DC)",
"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 natural number $k$ is said $n$ -squared if by colouring the squares of a $2n \\times k$ chessboard, in any manner, with $n$ different colours, we can find $4$ separate... | math | {
"ground_truth": "2n^2 - 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": "Let $\\overline{AD},$ $\\overline{BE},$ $\\overline{CF}$ be the altitudes of acute triangle $XYZ.$ If \n\\[5 \\overrightarrow{AD} + 3 \\overrightarrow{BE} + 8 \\overrightarrow{CF... | math | {
"ground_truth": "90^\\circ",
"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": "When \\(2x^2\\) is added to the quadratic polynomial \\(f(x)\\), its maximum value increases by 10. When \\(5x^2\\) is subtracted from it, its maximum value decreases by \\(\\fra... | math | {
"ground_truth": "\\frac{45}{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 a CNC machine starts its daily operations at $9:00 \\text{ AM}$ and completes one-fourth of the day's planned tasks by $12:30 \\text{ PM}$, calculate the time at which... | math | {
"ground_truth": "11:00 \\text{ PM}",
"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 for any positive real numbers $x$ and $y$, $({2y-\\frac{x}{e}})(\\ln x-\\ln y)-\\frac{y}{m}≤0$, then the range of real number $m$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "(0,1]",
"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": "$$10 \\times \\frac {1}{8} - 6.4 \\div 8 + 1.2 \\times 0.125$$．",
"role": "user"
}
] | math | {
"ground_truth": "0.6",
"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": "If the line $ax+2y+2=0$ is perpendicular to the line $3x-y-2=0$, determine the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{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": "A box contains 3 red marbles, 3 green marbles, and 3 yellow marbles. Cheryl picks 3 marbles at random; then Claudia picks 3 of the remaining marbles at random; and then Carol pic... | math | {
"ground_truth": "\\frac{1}{28}",
"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 minimum number of trials that must be conducted so that the event \\( A \\) is expected to occur at least once with a probability not less than \\(\\alpha \\) (\\(0 <... | math | {
"ground_truth": "n_0 = \\left\\lbrack \\frac{\\log_{10} (1 - \\alpha)}{\\log_{10} (1 - p) }\\right\\rbrakk + 1",
"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": "Define the function $g(x) = 3x + 4$. For what value of $x$ is $g(x)$ equal to $g^{-1}(x)$?",
"role": "user"
}
] | math | {
"ground_truth": "-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": "In the expansion of $\\left(x-\\frac{1}{x}-1\\right)^4$, the constant term is ______.",
"role": "user"
}
] | math | {
"ground_truth": "-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": "Two identical cubes are to be painted, and each face can independently be painted red, black, or white. Calculate the probability that after they are painted, and allowed any rot... | math | {
"ground_truth": "\\frac{32}{9841}",
"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": "Determine the fifth number in a row of Pascal's Triangle that has 21 numbers.",
"role": "user"
}
] | math | {
"ground_truth": "4845",
"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": "Define the sequence $a_1,a_2,a_3,\\ldots$ by $a_n=\\sum_{k=1}^n\\sin(k)$ , where $k$ represents radian measure. Find the index of the $100$ th term for which $a_n<0$ .",
... | math | {
"ground_truth": "628",
"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 equation of the tangent line to the curve $y=x^{3}-2x$ at the point $(1,-1)$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "x-y-2=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": "Find the sum of all possible sums $a + b$ where $a$ and $b$ are nonnegative integers such that $4^a + 2^b + 5$ is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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": "Three brothers returned from fishing. Their mother asked each of them how many fish they caught together. Vasya said, \"More than ten,\" Petya said, \"More than eighteen,\" and K... | math | {
"ground_truth": "16, 17, 18",
"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": "Petya and Vasya competed in a 60-meter race. When Petya finished, Vasya was 9 meters behind him. In the second race, Petya started exactly 9 meters behind Vasya. Who finished fir... | math | {
"ground_truth": "1.35 \\text{ meters}",
"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": "Find the smallest positive integer $n$ with the property that in the set $\\{70, 71, 72,... 70 + n\\}$ you can choose two different numbers whose product is the square of an ... | math | {
"ground_truth": "28",
"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 bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the t... | math | {
"ground_truth": "1195",
"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": "What is the value of $x$ for which $(10-x)^2 = 2x^2 + 4x$?",
"role": "user"
}
] | math | {
"ground_truth": "3.62 \\text{ and } -27.62",
"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": "In an urn, there are 10 balls that are identical in size and weight, consisting of 4 red balls and 6 blue balls. One ball is drawn from the urn. What is the probability that the ... | math | {
"ground_truth": "0.6",
"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": "Point $ A$ lies at $ (0, 4)$ and point $ B$ lies at $ (3, 8)$ . Find the $ x$ -coordinate of the point $ X$ on the $ x$ -axis maximizing $ \\angle AXB$ .",
"role... | math | {
"ground_truth": "5\\sqrt{2} - 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": "Use 7 matchsticks to form a triangle by connecting them end to end. The number of different triangles that can be formed is .",
"role": "user"
}
] | 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": "The sum of all eight numbers \\( a_{1}, a_{2}, \\ldots, a_{8} \\) is \\(\\frac{4}{3}\\), and the sum of any seven of them is positive. Find all possible values of the smallest of... | math | {
"ground_truth": "-8<a_{1} \\leq \\frac{1}{6}",
"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": "On a sheet of paper, several non-zero numbers are written, each of which is equal to the half-sum of the others. How many numbers are written?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Evaluate $\\log_8 64 + \\log_9 81$.",
"role": "user"
}
] | math | {
"ground_truth": "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 standard $8$-sided dice is rolled twice, and the sum of the numbers rolled is used as the diameter of a circle. Find the probability that the numerical value of the area of the... | math | {
"ground_truth": "\\frac{3}{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": "Emma has a choice between four snacks (apple, orange, banana, cookie) to eat at three different snack times a day, chosen at random with equal likelihood. What is the probability... | math | {
"ground_truth": "\\frac{15}{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": "You walk for 30 minutes at a rate of 3 mph, then run for 20 minutes at a rate of 8 mph, followed by another walking session of 10 minutes at a rate of 2 mph. Calculate the total ... | math | {
"ground_truth": "4.5",
"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": "Compute the number of ordered quadruples $(a,b,c,d)$ of distinct positive integers such that $\\displaystyle \\binom{\\binom{a}{b}}{\\binom{c}{d}}=21$ .\n\n*Proposed by Luke R... | math | {
"ground_truth": "13",
"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": "Manzi has $n$ stamps and an album with $10$ pages. He distributes the $n$ stamps in the album such that each page has a distinct number of stamps. He finds that, no matter ... | math | {
"ground_truth": "135",
"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 different positive, five-digit integers can be formed using the digits 1, 1, 1, 8, and 8?",
"role": "user"
}
] | math | {
"ground_truth": "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": "In quadrilateral $ABCD$, let the bisectors of the exterior angles at $A$ and $C$ meet at a point $E$. If all angle measurements are in degrees, what is $\\angle AEC$?\n**A)** $\\... | math | {
"ground_truth": "\\frac{360^\\circ - (B + D)}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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