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": "Given five distinct points are arranged on a plane so that the segments connecting them have lengths $a$, $a$, $a$, $b$, $c$, $c$, and two segments of length $a$ along with the s... | math | {
"ground_truth": "\\textbf{(C)}\\ \\sqrt{a^2 + b^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": "Expand and simplify the expression $(x + 3)(4x - 8) + x^2$.",
"role": "user"
}
] | math | {
"ground_truth": "5x^2 + 4x - 24",
"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": "Equilateral $\\triangle ABC$ is inscribed in a circle of radius $3$. Extend $\\overline{AB}$ through $B$ to point $D$ such that $AD = 15,$ and extend $\\overline{AC}$ through $C$... | math | {
"ground_truth": "6844",
"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 determinant:\n\\[\n\\begin{vmatrix} \n1 & k \\sin (a - b) & \\sin a \\\\ \nk \\sin(a - b) & 1 & k \\sin b \\\\ \n\\sin a & k \\sin b & 1 \n\\end{vmatrix}\n\\]\nwhere ... | math | {
"ground_truth": "1 - k^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": "Given the four-digit number 5005, calculate the total number of different numbers that can be formed by rearranging its four digits.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $f(x)$ is the inverse function of $y=e^x$, and $|f(a)|=|f(b)|$ with $a \\neq b$, then the range of values for $a+b$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "(2, +\\infty)",
"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": "(1) Given that $3^{m}=4$, $3^{m+4n}=324$, find the value of $2016^{n}$.\n(2) Simplify and then evaluate: $(a+2)(a-2)+a(1-a)$, where $a=5$.",
"role": "user"
}
] | 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": "In $\\triangle ABC$, the side lengths opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. If $c - a$ is equal to the height $h$ from vertex $A$ to side $BC$... | 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": "For each positive integer $n$ let $A_n$ be the $n \\times n$ matrix such that its $a_{ij}$ entry is equal to ${i+j-2 \\choose j-1}$ for all $1\\leq i,j \\leq n.$ Find... | math | {
"ground_truth": "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 sum of the solutions to\n\\[\n\\frac{1}{\\sin x} + \\frac{1}{\\cos x} = 4\n\\]\nin the interval $0 \\leq x \\leq 2\\pi$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find the maximum and minimum values of the function \\( y = x^5 - 5x^4 + 5x^3 + 3 \\) on the interval \\([-1, 2]\\).",
"role": "user"
}
] | math | {
"ground_truth": "-8 \\text{ (minimum)}, \\quad 4 \\text{ (maximum)}",
"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 $k<<n$ denote that $k<n$ and $k\\mid n$ . Let $f:\\{1,2,...,2013\\}\\rightarrow \\{1,2,...,M\\}$ be such that, if $n\\leq 2013$ and $k<<n$ , then $f(k)<<f(n)$ . Wh... | math | {
"ground_truth": "1024",
"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 Tycoon Tammy invested $100 dollars for two years, and during the first year her investment suffered a 15% loss, while during the second year the remaining investment showed... | math | {
"ground_truth": "2\\%",
"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": "The derivative of the function y=(x-2)^{2} at x=1 is equal to what value.",
"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": "Leo, who is 17 years old, flips a fair coin whose sides are labeled 5 and 15, and then he rolls a fair twelve-sided die numbered from 1 to 12. What is the probability that the su... | math | {
"ground_truth": "\\frac{1}{24}",
"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 $x, y, z$ be positive real numbers. Find the set of all possible values of \n\\[ g(x,y,z) = \\frac{x^2}{x^2 + y^2} + \\frac{y^2}{y^2 + z^2} + \\frac{z^2}{z^2 + x^2}. \\]",
... | math | {
"ground_truth": "\\left[\\frac{3}{2}, 2\\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": "Suppose $x$ and $y$ are nonzero real numbers simultaneously satisfying the equations $x + \\frac{2018}{y}= 1000$ and $ \\frac{9}{x}+ y = 1$ .\nFind the maximum possible val... | math | {
"ground_truth": "1991",
"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": "Investigate the function $f(x)=e^{x}-e^{-x}+\\sin x+1$, and let $a=\\frac{2023+2024}{2}=2023.5$. Determine the value of $f(-2023)+f(-2022)+\\ldots +f(2022)+f(2023)$.",
"role"... | math | {
"ground_truth": "4047",
"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": "Six fair coins are to be flipped. What is the probability that all six will be heads? Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{64}",
"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 number $2^{29}$ has a $9$ -digit decimal representation that contains all but one of the $10$ (decimal) digits. Determine which digit is missing",
"role": "user"
}... | 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": "For an integer \\( m \\geq 1 \\), we consider partitions of a \\( 2^m \\times 2^m \\) chessboard into rectangles consisting of cells of the chessboard, in which each of the \\( 2... | math | {
"ground_truth": "(m+1) \\cdot 2^{m+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": "Alice is thinking of a positive real number $x$ , and Bob is thinking of a positive real number $y$ . Given that $x^{\\sqrt{y}}=27$ and $(\\sqrt{x})^y=9$ , compute $xy$ .",... | math | {
"ground_truth": "16\\sqrt[4]{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": "On the number line, the numbers $12x$ and $-4x$ are represented. Illustrate zero and the number $x$ on this line.",
"role": "user"
}
] | math | {
"ground_truth": "0 \\text{ at fourth mark from left between } 12x \\text{ and }-4x \\text{; } x \\text{ at fourth mark from left between } 4x \\text{ and } 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": "The sum of the first five terms of an arithmetic sequence is $20$. If the sixth term is $8$, what is the seventh term?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{28}{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": "Given that Pat first divided a number by $8$ instead of multiplying it by $8$ and then subtracted $20$ instead of adding $20$, and the result was $12$, determine the value that w... | math | {
"ground_truth": "\\textbf{(D)}\\ \\text{between 1800 and 2200}",
"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 points $P$, $Q$, and $R$ are situated on the surface of a sphere with center $S$ and radius $25$. It is given that $PQ=17$, $QR=18$, $RP=19$, and that the distance from $S$ t... | math | {
"ground_truth": "50",
"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 $\\triangle ABC$, $\\angle ACB = 36^\\circ$ and the interior angle bisectors of $\\angle CAB$ and $\\angle ABC$ intersect at $P$. Find $\\angle APB$.",
"role": "user"
}
... | math | {
"ground_truth": "108^\\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": "Alexis notices Joshua working with Dr. Lisi and decides to join in on the fun. Dr. Lisi challenges her to compute the sum of all $2008$ terms in the sequence. Alexis thinks a... | math | {
"ground_truth": "18599100",
"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": "Compute \\[ \\left\\lfloor \\dfrac {2020^3}{2018 \\cdot 2019} - \\dfrac {2018^3}{2019 \\cdot 2020} \\right\\rfloor,\\]where $\\lfloor x \\rfloor$ denotes the greatest integer les... | 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": "Find all polynomials $p$ with integer coefficients such that the number $p(a) - p(b)$ is divisible by $a + b$ for all integers $a, b$ , provided that $a + b \\neq 0$ .",
... | math | {
"ground_truth": "p(x) = \\sum_{i=0}^{n} a_i x^{2i}",
"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 \\(\\mathbf{u}\\), \\(\\mathbf{v}\\), \\(\\mathbf{w}\\) be vectors in \\(\\mathbb{R}^3\\), and let \\(E\\) be the determinant of the matrix whose column vectors are \\(\\math... | math | {
"ground_truth": "E^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": "The sum of two nonnegative numbers is 10. What are the maximum and minimum values that the sum of their squares can take?",
"role": "user"
}
] | math | {
"ground_truth": "Максимальное значение = 100, Минимальное значение = 50",
"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 values of \\( a \\) for which the system \n\n\\[\n\\left\\{\n\\begin{array}{l}\nx^{2} + 4y^{2} = 1 \\\\\nx + 2y = a\n\\end{array}\n\\right.\n\\]\n\nhas a unique solution... | math | {
"ground_truth": "-1.41",
"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 chest of gold coins is divided among 10 pirates where the kth pirate takes k/10 of the remaining coins. Determine the smallest number of coins initially in the chest such that ... | math | {
"ground_truth": "362880",
"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 domain of the function $f(x)= \\sqrt {1-3^{x}}+ \\dfrac {1}{x^{2}}$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty,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": "Consider the graphs of \n\\[(1)\\quad y = x^2 - 2x + 5\\] \nand \n\\[(2)\\quad y = x^2 + 3x + 5\\]\non the same set of axes. Determine their relative positions and the points whe... | math | {
"ground_truth": "D) Graph (1) is to the right of Graph (2); they intersect at (0, 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": "Given the set $A=\\{-1, 0\\}$, and the set $B=\\{0, 1, x+2\\}$, and $A \\subseteq B$, then the value of the real number $x$ is.",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of 8 balls is randomly and independently painted either black or white with equal probability. What is the probability that every ball is different in color from more than h... | math | {
"ground_truth": "\\textbf{(A)} \\frac{35}{256}",
"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 range of the function\n\\[ f(x) = \\frac{3x + 4}{x + 2}. \\]",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 3) \\cup (3, \\infty)",
"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 line $l$ with an inclination angle of $60^{\\circ}$ passes through the focus $F$ of the parabola $y^2=4x$ and intersects the portion of the parabola on the $x$-axis at point $A... | math | {
"ground_truth": "\\sqrt{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": "Ellen wants to color some of the cells of a $4 \\times 4$ grid. She wants to do this so that each colored cell shares at least one side with an uncolored cell and each uncolored ... | math | {
"ground_truth": "A: 12",
"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": "Numbers $1, 2, 3, \\ldots, 16$ are written in a $4 \\times 4$ array, one number in each square, such that if two numbers are consecutive, then they occupy squares that share an e... | math | {
"ground_truth": "10",
"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 hyperbola $mx^{2}-ny^{2}=1\\,(m > 0,n > 0)$ with an eccentricity of $2$, find the eccentricity of the ellipse $mx^{2}+ny^{2}=1$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{6}}{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 $x$, $y$, and $z$ be real numbers such that\n\\[\\cos x + \\cos y + \\cos z = 1\\] and \\[\\sin x + \\sin y + \\sin z = 0.\\] Find the sum of all possible values of $\\cos 2x... | math | {
"ground_truth": "-1",
"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": "How many three-digit whole numbers do not contain the digits 1, 3, or 5?",
"role": "user"
}
] | math | {
"ground_truth": "606",
"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 square with side length $3$, points $E$ and $F$ are midpoints of opposite sides, and line segment $AG$ is perpendicular to $BF$. The square is dissected into four pieces, wh... | 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": "Among the following four propositions about conic sections: \n(1) The two real roots of the equation $2x^2-5x+2=0$ can be used as the eccentricities of an ellipse and a hyperbol... | math | {
"ground_truth": "(1), (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": "Sequences $a_n$ and $b_n$ are defined for all positive integers $n$ such that $a_1 = 5,$ $b_1 = 7,$ $$ a_{n+1} = \\frac{\\sqrt{(a_n+b_n-1)^2+(a_n-b_n+1)^2}}{2}, $$ a... | math | {
"ground_truth": "24",
"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": "Petya is three times older than Anya, and Anya is 8 years younger than Petya. Determine how old each of them is. Justify your answer.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Petya is 12 years old, and Anya is 4 years old.}",
"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": "Ten women sit in $10$ seats in a line. All of the $10$ get up and then reseat themselves using all $10$ seats, with each woman allowed to sit in her original seat or a seat withi... | math | {
"ground_truth": "B) 480",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the sequence $\\{a_n\\}$, we have $a_1=0$ and $\\frac{1}{1-a_{n+1}}=\\frac{2-a_n}{1-a_n}$. Let $b_n=\\frac{1-\\sqrt{a_{n+1}}}{\\sqrt{n}}$ and $S_n$ be the sum of the first $n$... | math | {
"ground_truth": "\\frac{9}{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": "Let \\( A_{1}, \\ldots, A_{2022} \\) be the vertices of a regular 2022-gon in the plane. Alice and Bob play a game. Alice secretly chooses a line and colors all points in the pla... | math | {
"ground_truth": "22",
"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": "Peter Pan and Crocodile are each getting hired for a job. Peter wants to get paid 6.4 dollars daily, but Crocodile demands to be paid 10 cents on day 1, 20 cents on day 2, 40 cen... | 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 minimum score Liam would need on his next test so that his average increases by at least $5$ points after six test scores.",
"role": "user"
}
] | math | {
"ground_truth": "115",
"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 greatest positive real number $M$ such that for all positive real sequence $(a_n)$ and for all real number $m < M$ , it is possible to find some index $n \\ge 1$ ... | math | {
"ground_truth": "M = 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": "The sequence ${a_{n}}$ $n\\in \\mathbb{N}$ is given in a recursive way with $a_{1}=1$ , $a_{n}=\\prod_{i=1}^{n-1} a_{i}+1$ , for all $n\\geq 2$ .\nDetermine the least numbe... | math | {
"ground_truth": "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": "There are $n$ positive integers on the board. We can add only positive integers $c=\\frac{a+b}{a-b}$ , where $a$ and $b$ are numbers already writted on the board. $a)$ F... | math | {
"ground_truth": "\\{1, 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": "The area of the smallest square that will contain a circle of radius 4.",
"role": "user"
}
] | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the right triangle $ABC$ with shorter side $AC$ the hypotenuse $AB$ has length $12$ . Denote $T$ its centroid and $D$ the feet of altitude from the vertex $C$ . D... | math | {
"ground_truth": "\\frac{\\pi}{8}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the average of $x_1$, $x_2$, $x_3$ is 2, then the average of $2x_1+4$, $2x_2+4$, $2x_3+4$ is .",
"role": "user"
}
] | math | {
"ground_truth": "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": "After the appearance of purple sand flowerpots in the Ming and Qing dynasties, their development momentum was soaring, gradually becoming the collection target of collectors. Wit... | math | {
"ground_truth": "39",
"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 an arithmetic sequence $\\{a_n\\}$ with a common difference of $\\pi$; let $S=\\{\\sin{a}_{n}|n\\in {N}^{*}\\}$. If $S=\\{a,b\\}$, then $a+b=$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\frac{3}{8}$ of the knights are silver and the rest are golden, and $\\frac{1}{4}$ of all knights possess shields, with the fraction of silver knights who have shiel... | math | {
"ground_truth": "\\frac{3}{7}",
"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 derivative of the function $f(x)$ is $f'(x)$, and it satisfies $f(x) = 2xf'(e) + \\ln x$, determine the value of $f'(e)$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{e}",
"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 a sequential pattern of diagrams, each main triangle is divided into smaller triangles where a complex pattern fills more of these at each step. By the seventh diagram, the ve... | math | {
"ground_truth": "\\frac{13}{5040}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the average of the series $z$, $3z$, $5z$, $9z$, and $17z$.",
"role": "user"
}
] | math | {
"ground_truth": "7z",
"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 slope of a line is $-3$ and its $x$-intercept is $(4,0)$. What is the $y$-intercept point of the line? Express your answer as an ordered pair.",
"role": "user"
}
] | math | {
"ground_truth": "(0,12)",
"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": "Given $\\sin \\left(\\alpha+ \\frac{\\pi}{5}\\right)= \\frac{ \\sqrt{3}}{3}$, find the value of $\\cos \\left(2\\alpha+ \\frac{2\\pi}{5}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "There are 100 points on a circle, dividing the circle into 100 equal arcs. Some of these points are randomly colored red. To ensure that at least 4 red points form the vertices o... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ represent the smallest integer that satisfies the following conditions:\n- $\\frac{n}{2}$ is a perfect square.\n- $\\frac{n}{3}$ is a perfect cube.\n- $\\frac{n}{5}$ is a... | math | {
"ground_truth": "19005",
"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, B, and C are guessing a two-digit number.\nA says: Its number of factors is even, and it is greater than 50.\nB says: It is an odd number, and it is greater than 60.\nC says: ... | math | {
"ground_truth": "64",
"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 $\\mathcal{R}$ denote the circular region in the $xy-$ plane bounded by the circle $x^2+y^2=36$ . The lines $x=4$ and $y=3$ divide $\\mathcal{R}$ into four regions ... | math | {
"ground_truth": "0",
"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 no student has better performance than another, and there are no two students with the same score in both Chinese and Mathematics, determine the maximum number of students in ... | 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 $f(x) = 4x^4 + 12x^3 - 9x^2 + x + 3$ and $d(x) = x^3 + 3x - 2$. If $f(x) = q(x)d(x) + r(x)$ for some polynomials $q(x)$ and $r(x)$ where $\\deg r < \\deg d$, calculate $q(1) ... | math | {
"ground_truth": "1",
"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": "Caden, Zoe, Noah, and Sophia shared a pizza. Caden ate 20 percent of the pizza. Zoe ate 50 percent more of the pizza than Caden ate. Noah ate 50 percent more of the pizza than Zo... | math | {
"ground_truth": "5\\%",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Hexagon $ABCDEF$ is inscribed in a circle. If $\\measuredangle ACE = 35^{\\circ}$ and $\\measuredangle CEA = 55^{\\circ}$ , then compute the sum of the degree measures of ... | math | {
"ground_truth": "270^\\circ",
"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 in the arithmetic sequence $\\{a_n\\}$, $a_3+a_4+a_5=12$, calculate the value of $a_1+a_2+\\ldots+a_7$.",
"role": "user"
}
] | math | {
"ground_truth": "28",
"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": "Suppose \\(a, b,\\) and \\(c\\) are nonnegative real numbers such that the sum of their squares is 52 and the sum of their pairwise products is 28. What is the maximum possible v... | math | {
"ground_truth": "6\\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": "Convert the quadratic function $y=x^{2}-4x+5$ into the form $y=a\\left(x-h\\right)^{2}+k$.",
"role": "user"
}
] | math | {
"ground_truth": "y=(x-2)^{2}+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": "In quadrilateral \\(ABCD\\), points \\(X, Y, Z\\) are the midpoints of segments \\(AB, AD, BC\\), respectively. It is known that \\(XY\\) is perpendicular to \\(AB\\), \\(YZ\\) i... | math | {
"ground_truth": "90^\\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": "Technological innovation is the driving force of development. A research company has launched an innovative product to the market. The cost price of the product is $40$ yuan per ... | math | {
"ground_truth": "46 \\leqslant y \\leqslant 54",
"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": "Suppose the same operation $\\nabla$ is defined as before: $$a \\nabla b = \\dfrac{a + b}{1 + ab}.$$ However, now let's consider two sequential operations where we use $\\nabla$ ... | math | {
"ground_truth": "\\dfrac{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": "Given that $x_{1}$ and $x_{2}$ are two real roots of the one-variable quadratic equation $x^{2}-6x+k=0$, and (choose one of the conditions $A$ or $B$ to answer the following ques... | math | {
"ground_truth": "-11",
"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": "suppose that polynomial $p(x)=x^{2010}\\pm x^{2009}\\pm...\\pm x\\pm 1$ does not have a real root. what is the maximum number of coefficients to be $-1$ ?(14 points)",
"ro... | math | {
"ground_truth": "1005",
"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 rectangular box with dimensions A, B, and C, and surface areas of its faces given as 40, 40, 90, 90, 100, and 100 square units, determine the sum A + B + C.",
"role":... | math | {
"ground_truth": "\\frac{83}{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": "Let $a$ and $b$ be the roots of the equation $x^2 - mx + \\frac{3}{2} = 0$. Suppose $a + \\frac{1}{b}$ and $b + \\frac{1}{a}$ are the roots of the equation $x^2 - px + q = 0$. De... | math | {
"ground_truth": "\\frac{19}{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": "If $16^{x+1} = 256$, then find the value of $x$.\nA) 0\nB) 1\nC) 2\nD) 3\nE) 4",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(B)}\\ 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a class of 40 students, 10 students received an A in history and 18 received an A in math, including 6 that received an A in both courses. How many students did not receive an... | math | {
"ground_truth": "18",
"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": "Starting with a $5 \\times 5$ grid, choose a $4 \\times 4$ square in it. Then, choose a $3 \\times 3$ square in the $4 \\times 4$ square, and a $2 \\times 2$ square in ... | math | {
"ground_truth": "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": "Given the parabola $ y \\equal{} x^2 \\plus{} a^2$ and the line $ y \\equal{} x \\plus{} a$, find the number of values of $ a$ for which the line passes through the vertex of t... | math | {
"ground_truth": "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": "How many more digits does the base-4 representation of \\(1024_{10}\\) have than the base-5 representation of \\(1024_{10}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "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": "What is the maximal dimension of a linear subspace $ V$ of the vector space of real $ n \\times n$ matrices such that for all $ A$ in $ B$ in $ V$ , we have $ \\text{tr... | math | {
"ground_truth": "\\frac{n(n-1)}{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": "The complex number $z$ satisfies $(1+2i)z=5$, then $z=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "1-2i",
"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": "For how many positive integer values of \\( N \\) is the expression \\( \\frac{48}{N+3} \\) an integer?\nA) 5\nB) 6\nC) 7\nD) 8\nE) 9",
"role": "user"
}
] | math | {
"ground_truth": "\\text{(C)}\\ 7",
"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": "Amanda is four years younger than Carlos. Carlos is five years older than Beth. Denise is two years older than Beth. Amanda is 16 years old. How old is Denise?",
"role": "use... | math | {
"ground_truth": "17",
"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 Leevi, Max, Nolan, and Ollie have a total amount of money, and Ollie initially has no money, calculate the fraction of the group's total money Ollie has after Max gives Oll... | math | {
"ground_truth": "\\frac{3}{11}",
"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 positive integer sequences \\( \\{a_n\\} : a_n = 3n + 2 \\) and \\( \\{b_n\\} : b_n = 5n + 3 \\) (where \\( n \\in \\mathbb{N} \\)) intersect within the set \\( M = \\{1, 2, ... | math | {
"ground_truth": "135",
"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 integers $a \\ne 0, b$ and $c$ such that $x = 2 +\\sqrt3$ would be a solution of the quadratic equation $ax^2 + bx + c = 0$ .",
"role": "user"
}
] | math | {
"ground_truth": "(a, b, c) = (x, -4x, x) \\text{ where } x \\text{ is a nonzero integer}",
"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 $a, b, c$ be positive real numbers such that $abc = 3$. Compute the minimum value of\n\\[a^2 + 8ab + 24b^2 + 16bc + 6c^2.\\]",
"role": "user"
}
] | math | {
"ground_truth": "54",
"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": "Central High School is competing against Northern High School in a backgammon match. Each school has three players, and the contest rules require that each player play two games ... | math | {
"ground_truth": "900",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
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