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": "What is the probability that a randomly drawn positive factor of $72$ is less than $9$?\nA) $\\frac{1}{12}$\nB) $\\frac{1}{6}$\nC) $\\frac{1}{3}$\nD) $\\frac{1}{2}$\nE) $\\frac{2... | math | {
"ground_truth": "\\mathrm{(D)}\\ \\frac{1}{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 the sets\n$$\n\\begin{array}{l}\nA=\\left\\{x \\mid \\log _{2}(x-1)<1\\right\\}, \\\\\nB=\\{x \\mid | x-a |<2\\} .\n\\end{array}\n$$\nIf $A \\cap B \\neq \\varnothing$, det... | math | {
"ground_truth": "(-1, 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": "Problem 4.5. Hooligan Dima placed 38 wooden toothpicks into a rectangular structure of size $3 \\times 5$. Then he simultaneously ignited two adjacent corners of this rectangle, ... | math | {
"ground_truth": "65",
"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 complete graph of $y=g(x)$, consisting of four line segments, is shown in blue. The graph changes direction at the points $(-3, -4)$, $(-1, 0)$, $(2, -1)$, and $(3, 3)$. What... | 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": "A finite set of polygons on a plane is considered properly placed if, for any two polygons in the set, there exists a line passing through the origin that intersects both. \n\nFi... | math | {
"ground_truth": "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": "Find all completely multipiclative functions $f:\\mathbb{Z}\\rightarrow \\mathbb{Z}_{\\geqslant 0}$ such that for any $a,b\\in \\mathbb{Z}$ and $b\\neq 0$ , there exist inte... | math | {
"ground_truth": "f(x) = |x|^n s^{v_{p_0}(x)}",
"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 the equations using the specified methods:<br/>\n(1) $x^{2}-4x-2=0$ (using factoring method);<br/>\n(2) $2y^{2}-3y-1=0$ (using formula method);<br/>\n(3) $3x(x-1)=2-2x$ (us... | math | {
"ground_truth": "x_{1}=1, x_{2}=-\\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": "In the sequence $\\left\\{a_n\\right\\}$, each term $a_n$ represents the largest odd divisor of the positive integer $n$. For example, the divisors of 5 are $1$ and $5$, so $a_5 ... | math | {
"ground_truth": "\\frac{4^{2000} - 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": "A girl has the following six coins in her purse: $2$ pennies, $2$ nickels, $1$ dime, and $1$ half dollar. She takes out two coins, records the sum of their values, and then puts ... | math | {
"ground_truth": "8",
"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 angle between the hour hand and the minute hand of a clock at 5:30.",
"role": "user"
}
] | math | {
"ground_truth": "15^\\circ",
"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 expansion of ${\\left({x}^{ \\frac{2}{3}}+3{x}^{2}\\right)}^{n} $, the ratio of the sum of the coefficients of all terms to the sum of the binomial coefficients is $32$... | math | {
"ground_truth": "405{x}^{ \\frac{26}{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 that point R is the midpoint of the line segment PQ and S is the midpoint of the line segment QR, and P has coordinates (2, 1) and S has coordinates (14, 7), find the coord... | math | {
"ground_truth": "(18,9)",
"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": "Two standard dice are rolled. What is the expected number of 6's obtained? Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "Let $z_1$ and $z_2$ be the complex roots of $z^2 + az + b = 0,$ where $a$ and $b$ are complex numbers. In the complex plane, $0$, $z_1$, and $z_2$ form the vertices of an isoscel... | math | {
"ground_truth": "5 + i\\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 stock investment went up by 40% in 2006. Starting at this increased value, what percent would it have to go down in 2007 to return to its original price at the beginning of 200... | math | {
"ground_truth": "28.57\\%",
"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": "Al's age is 20 more than the sum of Bob's age and Carl's age, and the square of Al's age is 2000 more than the square of the sum of Bob's age and Carl's age. Calculate the sum of... | math | {
"ground_truth": "80",
"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": "For the graph of a certain quadratic $y = ax^2 + bx + c$, the vertex of the parabola is $(5,10)$ and one of the $x$-intercepts is $(0,0)$. What is the $x$-coordinate of the other... | 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": "Given a single-elimination tennis tournament with 128 players, where the strongest 20 players automatically advance to the next round, determine the total number of matches playe... | math | {
"ground_truth": "181",
"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 possible areas are there in a convex hexagon with all of its angles being equal and its sides having lengths $1, 2, 3, 4, 5$ and $6,$ in any order?",
"role": "us... | math | {
"ground_truth": "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": "A shape consists of one square and an isosceles right triangle placed inside another square. The areas of the two squares are 64 and 256 respectively. What is the area of the iso... | math | {
"ground_truth": "B) 32",
"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 three non-zero real numbers: $x(y-z)$, $y(z-x)$, and $z(y-x)$ form a geometric sequence. The common ratio $q$ equals \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "q = \\frac{1\\pm \\sqrt{5}}{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 $m\\in R$, determine the condition for the lines $l_{1}$: $mx+2y-1=0$ and $l_{2}$: $3x+\\left(m+1\\right)y+1=0$ to be perpendicular.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{2}{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": "Let \\( N = 30^{2015} \\). Find the number of ordered 4-tuples of integers \\((A, B, C, D) \\in \\{1, 2, \\ldots, N\\}^{4}\\) (not necessarily distinct) such that for every integ... | math | {
"ground_truth": "24",
"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 sphere with center $O$ has radius $8$. A triangle with sides of length $13$, $13$, and $10$ is situated in space so that each of its sides is tangent to the sphere. Calculate t... | math | {
"ground_truth": "\\frac{2\\sqrt{119}}{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": "Find the product of the values of $x$ that satisfy the equation $|3x - 2| + 5 = 23$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-320}{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 function $f\\left(x\\right)=|2x-1|+|2x-k|$.<br/>$(1)$ If $f\\left(x\\right)\\geqslant 1$ holds for all $x\\in R$, find the range of real number $k$;<br/>$(2)$ When $k=4... | 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": "A machine processes a positive integer \\( N \\) according to the following modified rule:\n\n- If \\( N \\) is odd, the output \\( O = 2N + 2 \\).\n- If \\( N \\) is even, the o... | math | {
"ground_truth": "B) 66",
"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 $x+y+z=6$, $xy+yz+zx=11$, and $xyz=6$, then $\\frac{x}{yz}+\\frac{y}{zx}+\\frac{z}{xy}=\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{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 \\( f(x) \\) and \\( g(x) \\) be a function defined on \\( \\mathbb{R} \\), where \\( f(x) \\) is an odd function and \\( g(x) \\) is an even function. Given that \\( f(x) + ... | math | {
"ground_truth": "\\left[-\\frac{17}{6}, +\\infty \\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": "The \"High School Twelve\" soccer conference has 12 teams. Each season, each team plays every other conference team three times, and each team also plays 5 games against non-conf... | math | {
"ground_truth": "B) 258",
"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": "Find the value of $a+b$ given that $(a,b)$ is a solution to the system \\begin{align*}3a+7b&=1977,5a+b&=2007.\\end{align*} $\\begin{array}{c@{\\hspace{14em}}c@{\\hspace{14em}... | math | {
"ground_truth": "498",
"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 garden is shaped like a right triangle combined with a rectangle. The right triangle's hypotenuse runs along one side of the rectangle. The rectangle's dimensions are 4 units a... | math | {
"ground_truth": "C) 28 \\text{ units}",
"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 positive real numbers \\( a, b, \\) and \\( c \\) that satisfy \\( 9a + 4b = abc \\), find the minimum value of \\( a + b + c \\).",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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 the graph of the function $f(x) = x$ is symmetric to the graph of the function $g(x)$ with respect to the line $y = x$, and let $h(x) = g(1 - |x|)$, then concerning th... | math | {
"ground_truth": "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": "Given that the angle between vectors $\\overset{\\to }{a}$ and $\\overset{\\to }{b}$ is $60^{\\circ}$, and $|\\overset{\\to }{a}|=2$, $|\\overset{\\to }{a}-2\\overset{\\to }{b}|=... | 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": "Let \\( f(x) \\) be a function defined for all real numbers \\( x \\neq 0 \\) such that for any non-zero real numbers \\( x_1 \\) and \\( x_2 \\), the equation \\( f(x_1 x_2) = f... | math | {
"ground_truth": "\\left[\\frac{1-\\sqrt{17}}{4}, 0\\right) \\cup \\left(0, \\frac{1}{2}\\right) \\cup \\left(\\frac{1}{2}, \\frac{1+\\sqrt{17}}{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": "Given that the angle between the plane vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $\\dfrac {π}{3}$, and $|\\overrightarrow{b}|=1$, $|\\overrightarrow{a}+2\\overri... | 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": "If \\[f(x) =\n\\begin{cases}\nx^2-4 &\\quad \\text{if } x \\ge -2, \\\\\nx + 4 &\\quad \\text{otherwise},\n\\end{cases}\n\\]then for how many values of $x$ is $f(f(x)) = 6$?",
... | 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": "Let $\\mathbf{R}^{+}$ be the set of all positive real numbers. Find all functions \\( f: \\mathbf{R}^{+} \\rightarrow \\mathbf{R}^{+} \\) such that \\( f(x) + f(y) = f(x y f(x+y)... | math | {
"ground_truth": "f(x) = \\frac{1}{x}",
"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 friction coefficient between the motorcycle tires and the walls is $\\mu$, determine how the minimum $\\mu$ needed to prevent the motorcycle from slipping downwards var... | math | {
"ground_truth": "\\mu \\propto s^{-2}",
"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 three $\\Delta$'s balance twelve $\\bullet$'s and one $\\Delta$ balances two $\\diamondsuit$'s and three $\\bullet$'s, determine how many $\\bullet$'s will balance four $\\... | math | {
"ground_truth": "\\frac{8}{3}b",
"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 $p,$ $q,$ $r$ be complex numbers such that\n\\[p + q + r = 2, \\quad pq + qr + rp = 3, \\quad pqr = 2.\\]\nFind the values of $p,$ $q,$ and $r$, separated by commas, in any o... | math | {
"ground_truth": "1, \\frac{1 + i\\sqrt{7}}{2}, \\frac{1 - i\\sqrt{7}}{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 $S$ be the set of the $1700$ smallest positive multiples of $5$, and let $T$ be the set of the $1700$ smallest positive multiples of $9$. Determine the number of elements tha... | math | {
"ground_truth": "188",
"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 radius of a sphere is \\( r = 10 \\text{ cm} \\). Determine the volume of the spherical segment whose surface area is in the ratio 10:7 compared to the area of its base.",
... | math | {
"ground_truth": "288 \\pi \\, \\text{cm}^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) = log$_2$x, where x belongs to the interval [$\\frac{1}{2}$, 2], a point x$_0$ is randomly chosen from the interval [$\\frac{1}{2}$, 2]. The probability t... | 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": "Given that 528 can be written as the sum of an increasing sequence of two or more consecutive positive integers, determine the number of ways this can be achieved.",
"role": ... | math | {
"ground_truth": "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": "Four pumps of equal capacity, working together, filled the first tanker and one-third of a second tanker (of different volume) in 11 hours. If three pumps filled the first tanker... | math | {
"ground_truth": "8 \\text{ hours}",
"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 chord, which is the perpendicular bisector of a radius of length 10 in a circle, intersects the radius at its midpoint. Calculate the length of the chord.",
"role": "user"
... | math | {
"ground_truth": "10\\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": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence with $a_2=3$ and $a_6=7$, find the value of $a_{11}$.",
"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": "Given that Gerry the Giraffe ate 220 bananas over the period from June 1 to June 8, each day eating 8 more bananas than the previous day, except on June 4 when he did not eat any... | math | {
"ground_truth": "56.67",
"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": "Consider an isosceles triangle $\\triangle ABC$ where $AB = AC = 3$ and $BC = 4$. Let $D$ be the midpoint of $\\overline{AB}$, and $E$ be a point on $\\overline{AC}$ such that $A... | math | {
"ground_truth": "1.2",
"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": "There are two blackboards \\( A \\) and \\( B \\), each with several different integers written on them, where each integer is not less than 2 and not greater than 20. If each ti... | math | {
"ground_truth": "65",
"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 the polar coordinate system, given that the circle $\\rho=2\\cos\\theta$ is tangent to the line $5\\rho\\cos\\theta+12\\rho\\sin\\theta+a=0$, find the value of the real number... | math | {
"ground_truth": "-18",
"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": "Consider the set $M=\\{1,2,...,n\\},n\\in\\mathbb N$ . Find the smallest positive integer $k$ with the following property: In every $k$ -element subset $S$ of $M$ there e... | math | {
"ground_truth": "k = \\left\\lceil \\frac{n}{2} \\right\\rceil + 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 $y$ be a positive integer such that $7y \\equiv 1 \\pmod{31}$. What is the remainder when $15 + 3y$ is divided by $31$?",
"role": "user"
}
] | math | {
"ground_truth": "11",
"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": "There is a pack of 27 distinct cards, and each card has three values on it. The first value is a shape from $\\{\\Delta,\\square,\\odot\\}$ ; the second value is a letter from ... | math | {
"ground_truth": "2358",
"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 \\( \\{x_{n}\\} \\) is defined as follows:\n\\[ \nx_{1} = \\frac{2}{3}, \\quad x_{n+1} = \\frac{x_{n}}{2(2n+1)x_{n} + 1} \\quad (n \\in \\mathbb{Z}_{+}). \n\\]\n\nFi... | math | {
"ground_truth": "\\frac{4028}{4029}",
"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 $S$ be the set of all the odd positive integers that are not multiples of $5$ and that are less than $30m$ , $m$ being an arbitrary positive integer. What is the small... | math | {
"ground_truth": "k = 8m + 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": "A $40$ feet high screen is put on a vertical wall $10$ feet above your eye-level. How far should you stand to maximize the angle subtended by the screen (from top to bottom) ... | math | {
"ground_truth": "10\\sqrt{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": "Mia's dad places 4 toys into the box every 45 seconds, but immediately after, Mia removes 3 toys, resulting in a net gain of 1 toy every 45 seconds. Determine the time, in minute... | math | {
"ground_truth": "36.75",
"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": "Alice has an equilateral triangle \\(ABC\\) with an area of 1. Point \\(D\\) is on \\(BC\\) such that \\(BD = DC\\), point \\(E\\) is on \\(CA\\) such that \\(CE = 2EA\\), and po... | math | {
"ground_truth": "\\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": "Given the following four propositions: \n① Two lines parallel to the same plane are parallel; \n② Two lines perpendicular to the same plane are parallel; \n③ If a line is para... | math | {
"ground_truth": "\\text{②④}",
"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": "We have two positive integers both less than $1000$ . The arithmetic mean and the geometric mean of these numbers are consecutive odd integers. Find the maximum possible value o... | math | {
"ground_truth": "62",
"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 that \\(\\triangle ABC\\) is an isosceles triangle, \\(AB = AC = \\sqrt{2}\\), and \\(D_1, D_2, \\ldots, D_Q\\) are \\(Q\\) points on \\(BC\\). Let \\(m_i = AD_i^2 + BD_i \... | math | {
"ground_truth": "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": "The base of a quadrilateral prism \\( A B C D A_1 B_1 C_1 D_1 \\) is a rhombus \\( A B C D \\) with \\( CD = 3 \\) and \\( \\angle A B D = 30^\\circ \\). A sphere passes through ... | math | {
"ground_truth": "81",
"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 circle having $(0,0)$ and $(8,6)$ as the endpoints of a diameter intersects the $x$-axis at a second point. Find the $x$-coordinate of this point.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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": "Determine the nonnegative difference between the roots for the equation $x^2 + 44x + 352 = -16$.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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": "\\(\\frac{81^{\\frac{1}{\\log _{5} 9}}+3^{\\frac{3}{\\log _{\\sqrt{6}} 3}}}{409} \\cdot\\left((\\sqrt{7})^{\\frac{2}{\\log _{25} 7}}-125^{\\log _{25} 6}\\right)\\)",
"role": ... | 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": "The sides of rectangle $EFGH$ have lengths $8$ and $15$. An equilateral triangle is drawn so that no point of the triangle lies outside $EFGH$. Find the maximum possible area of ... | math | {
"ground_truth": "64 \\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": "The following statements: ① The synthetic method is a cause-and-effect method; ② The analytic method is an indirect proof method; ③ The analytic method is a result-to-cause metho... | math | {
"ground_truth": "①③",
"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 solution set of the inequality $mx^{2}-mx+2 \\gt 0$ is $R$, then the range of real number $m$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "[0,8)",
"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": "Simplify the expression $(5 - 4x) - (2 + 7x - y)$.",
"role": "user"
}
] | math | {
"ground_truth": "3 - 11x + y",
"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 remainder when $x^5 + 4$ is divided by $(x - 3)^2.$",
"role": "user"
}
] | math | {
"ground_truth": "331x - 746",
"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 $a$ , $b$ , $c$ be positive real numbers for which \\[\n \\frac{5}{a} = b+c, \\quad\n \\frac{10}{b} = c+a, \\quad \\text{and} \\quad\n \\frac{13}{c} = a+b. \\] If $a+... | math | {
"ground_truth": "55",
"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": "At noon on a certain day, Minneapolis is $N$ degrees warmer than St. Louis. At $4{:}00$, the temperature in Minneapolis has fallen by $7$ degrees, while the temperature in St. Lo... | math | {
"ground_truth": "128",
"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 $f(x) = e^{mx} + x^{4} - mx$. \n$(1)$ Find the monotonic intervals of $f(x)$. \n$(2)$ If for any $x_{1}$, $x_{2} \\in [-2,2]$, $|f(x_{1}) - f(x_{2})| \\leq e^{4} + 11$, fin... | math | {
"ground_truth": "[-2,2]",
"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": "There is an average of 1 birth every 6 hours and an average of 1 death every 30 hours in the nation of North Southland.",
"role": "user"
}
] | math | {
"ground_truth": "1200",
"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 $q$ be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of $4$ consecutive heads before encountering a run of $3$ consecutive... | math | {
"ground_truth": "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": "Let $ABC$ be an equilateral triangle. $A $ point $P$ is chosen at random within this triangle. What is the probability that the sum of the distances from point $P$ to the... | math | {
"ground_truth": "\\frac{1}{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": "Evaluate\n\\[\n\\begin{vmatrix} 0 & 3\\sin x & -2\\cos x \\\\ -\\sin x & 0 & \\cos y \\\\ 2\\cos x & -\\sin y & 0 \\end{vmatrix}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "2\\sin x \\cos x (3\\cos y + \\sin y)",
"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 Carl uses 26 fence posts, with one post at each of the four corners and the remaining posts evenly distributed, and the number of posts on the longer side is twice as ... | math | {
"ground_truth": "900",
"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": "One root of the equation $7x^2 - 3x = 10$ is -2. What is the other root?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{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": "(1) Find the possible number of roots for the equation $|x + 1| + |x + 2| + |x + 3| = a$ , where $x \\in R$ and $a$ is parameter.\r\n\r\n(2) Let $\\{ a_1, a_2, \\ldots, a_n... | math | {
"ground_truth": "n \\leq 26",
"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 $\\sqrt{a-5}+\\sqrt{5-a}=b+3$<br/>$(1)$ Find the value of $a$;<br/>$(2)$ Find the square root of $a^{2}-b^{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\pm 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": "A circle passes through vertex \\( B \\) of the triangle \\( ABC \\), intersects its sides \\( AB \\) and \\( BC \\) at points \\( K \\) and \\( L \\), respectively, and touches ... | math | {
"ground_truth": "75^\\circ",
"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": "Two unit squares are selected at random without replacement from an $n \\times n$ grid of unit squares. Find the least positive integer $n$ such that the probability that the two... | math | {
"ground_truth": "90",
"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": "Consider a nonzero integer number $n$ and the function $f:\\mathbb{N}\\to \\mathbb{N}$ by \n\\[ f(x) = \\begin{cases}\n\t\t\\frac{x}{2} & \\text{if } x \\text{ is even} \n\t\... | math | {
"ground_truth": "A = \\{1, 2, \\dots, 2^n\\}",
"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": "If $x = (\\log_9 3)^{(\\log_3 9)}$, then $\\log_5x$ equals?\nA) $-\\log_5 2$\nB) $-\\frac{1}{2} \\log_5 2$\nC) $-2 \\log_5 2$\nD) $2 \\log_5 2$\nE) $0$",
"role": "user"
}
] | math | {
"ground_truth": "-2 \\log_5 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 a complex number \\( z = x + yi \\) where \\( x, y \\) are real parts forming the point \\( (x, y) \\) on the ellipse \\( \\frac{x^2}{9} + \\frac{y^2}{16} = 1 \\). If \\( \... | math | {
"ground_truth": "\\pm \\frac{3 \\sqrt{15}}{4} + \\mathrm{i}",
"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 \\( n > 2016 \\) such that \\( 1^{n} + 2^{n} + 3^{n} + 4^{n} \\) is not divisible by 10.",
"role": "user"
}
] | math | {
"ground_truth": "2020",
"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 geometric sequence $\\{a_n\\}$ with $a_1 = 1$ and common ratio $q = 2$, calculate the sum of the squares of the first four terms of the sequence.",
"role": "user"
... | math | {
"ground_truth": "85",
"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 $N$ be the number of ways of distributing $52$ identical balls into $4$ distinguishable boxes such that no box is empty and the difference between the number of balls i... | math | {
"ground_truth": "a + b = 69 + 12 = 81",
"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": "Triangle $XYZ$ is inside square $KLMN$ shown below so that its vertices each lie on three different sides of the square. It is known that: $\\bullet$ The area of square $KL... | math | {
"ground_truth": "\\frac{11}{50}",
"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 $L$ be the measure of the area bounded by the $x$-axis, the line $x=10$, and the curve defined by\n\\[ f={(x,y) \\quad | \\quad y=x \\text{ when } 0 \\le x \\le 5, y=3x-10 \\... | math | {
"ground_truth": "75",
"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 interval where the root of the function $f(x)= \\sqrt {x}-x+1$ is located.",
"role": "user"
}
] | math | {
"ground_truth": "(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": "Find all positive integers $k$ for which there exist positive integers $x, y$ , such that $\\frac{x^ky}{x^2+y^2}$ is a prime.",
"role": "user"
}
] | math | {
"ground_truth": "k \\in \\{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": "For each positive integer $n$ and non-negative integer $k$ , define $W(n,k)$ recursively by \n\\[\nW(n,k) = \n\\begin{cases}\n\tn^n & k = 0 \n\tW(W(n,k-1), k-1) & k > 0.\n\\... | math | {
"ground_truth": "375",
"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": "Seyed has 998 white coins, a red coin, and an unusual coin with one red side and one white side. He can not see the color of the coins instead he has a scanner which checks if al... | math | {
"ground_truth": "f(1000) \\leq 17",
"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 bag contains 4 red marbles and 6 white marbles. Two marbles are drawn successively without replacement. What is the probability that the first marble drawn is white and the sec... | math | {
"ground_truth": "\\frac{4}{15}",
"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": "Compute the range of \\(y = |x+5| - |x-3|\\).",
"role": "user"
}
] | math | {
"ground_truth": "[-2, 12]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
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