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 that \\(\\sin 2 \\alpha = 2 \\sin 4^{\\circ}\\), find \\(\\tan (\\alpha + 2^{\\circ}) \\cot (\\alpha - 2^{\\circ})\\).",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $3x^2 - 9x = 0$ and $x \\neq 0$, what is the value of $x$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Determine the conditions for the expression $\\left(\\frac{n-3k-2}{k+2}\\right)\\frac{n!}{k!(n-k)!}$ to be an integer.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{The expression $\\left(\\frac{n-3k-2}{k+2}\\right)D^n_k$ is an integer for all $k$ and $n$ such that $1 \\le k < n$.}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the digit 9 is appended to the right of a given number and then the resulting number is added to double the given number, the sum will be 633. Find the original number.",
... | math | {
"ground_truth": "52",
"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": "10.6 Let the insphere of a pyramid $SABC$ touch the faces $SAB, SBC, SCA$ at $D, E, F$ respectively. Find all the possible values of the sum of the angles $SDA, SEB, SFC$... | math | {
"ground_truth": "360^\\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": "$N$ teams take part in a league. Every team plays every other team exactly once during the league, and receives 2 points for each win, 1 point for each draw, and 0 points for ea... | math | {
"ground_truth": "F_{N+1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The distance from point $A$ on the number line to the origin is $4$. Find the number that point $A$ represents.",
"role": "user"
}
] | math | {
"ground_truth": "4 \\text{ or } -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": "Among the natural numbers greater than 1999, calculate the maximum number of numbers that can be selected so that the sum of the last two digits of any two of them adds up to 0."... | math | {
"ground_truth": "20",
"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": "Among the following propositions: \n① If the domain of the function $f(x)$ is $\\mathbb{R}$, then $g(x) = f(x) + f(-x)$ is necessarily an even function; \n② If $f(x)$ is an odd... | math | {
"ground_truth": "\\text{①④}",
"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": "Solve for \\( y \\): \n\\[ \\log_3 \\frac{2y+6}{4y-1} + \\log_3 \\frac{4y-1}{y-3} = 3 \\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{87}{25}",
"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 natural numbers \\( k \\) and \\( n \\) such that \\( 1 < k \\leq n \\). What is the smallest \\( m \\) for which the following statement holds: for any placement of \\( m ... | math | {
"ground_truth": "n(k-1) + 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": "Set $u_0 = \\frac{1}{4}$, and for $k \\ge 0$ let $u_{k+1}$ be determined by the recurrence $u_{k+1} = 2u_k - 2u_k^2$.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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": "You are given 10 numbers - one one and nine zeros. You are allowed to select two numbers and replace each of them with their arithmetic mean.\n\nWhat is the smallest number that ... | math | {
"ground_truth": "\\frac{1}{512}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P$ be a point inside the equilateral triangle $ABC$ such that $6\\angle PBC = 3\\angle PAC = 2\\angle PCA$ . Find the measure of the angle $\\angle PBC$ .",
"r... | math | {
"ground_truth": "15^\\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": "Given a positive real number A that rounds to 20 and another positive real number B that rounds to 23, find the largest possible value of the largest integer not exceeding the va... | math | {
"ground_truth": "91",
"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": "Once in winter, 43 children were throwing snowballs. Each of them threw exactly one snowball at someone else. It is known that:\n\n- The first child threw a snowball at the one w... | 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": "Express $0.\\overline{2} + 0.\\overline{02} + 0.\\overline{0002}$ as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2426}{9999}",
"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 triplets $(x, y, z)$ , $x > y > z$ of positive integers such that $\\frac{1}{x}+\\frac{2}{y}+\\frac{3}{z}= 1$",
"role": "user"
}
] | math | {
"ground_truth": "(x, y, z) = \\{(36, 9, 4), (20, 10, 4), (15, 6, 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": "A new website registered $2000$ people. Each of them invited $1000$ other registered people to be their friends. Two people are considered to be friends if and only if they h... | math | {
"ground_truth": "1000",
"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": "Four different stamps form a $2 \\times 2$ block. By tearing off 0 to 3 stamps from this block, you can obtain 13 different connected pieces of stamps. Determine the number of di... | math | {
"ground_truth": "\\frac{1}{4}(1+\\sqrt{2})^{n+3} + \\frac{1}{4}(1-\\sqrt{2})^{n+3} - 2n - \\frac{7}{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": "To investigate the understanding of the \"Belt and Road\" policy among students at a certain university, a stratified sampling method is used to draw a sample of 500 students, in... | math | {
"ground_truth": "7500",
"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 an acute triangle \\(ABC\\), inscribed in a circle, with \\(AB = AC\\), tangents at \\(B\\) and \\(C\\) meet at \\(D\\). Given that \\(\\angle ABC = \\angle ACB = 3 \\angle D\... | math | {
"ground_truth": "\\frac{5}{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": "In the arithmetic sequence $\\{a\\_n\\}$, $a\\_1=2$, $S\\_3=9$.\n\n(1) Find the general term formula $a\\_n$ of $\\{a\\_n\\}$;\n\n(2) Find the sum $S\\_n$ of the first $n$ terms ... | math | {
"ground_truth": "2^{n+2} - 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": "Given the function $f(x) = 1 + ae^{-x} + e^{-2x}$ and $g(x) = \\log_{\\frac{1}{2}} \\frac{x+1}{mx-1}$,\n\n1. Find the value of the real number $m$ if $g(x)$ is an odd function.\n... | math | {
"ground_truth": "-5 \\leq a \\leq 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A container is shaped like a square-based pyramid where the base has side length $23$ centimeters and the height is $120$ centimeters. The container is open at the base of th... | math | {
"ground_truth": "60",
"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 sets $A=\\{x|x^{2}-4x-5=0\\}$ and $B=\\{x|x^{2}-1=0\\}$, find $A\\cup B$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{-1,1,5\\}",
"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": "In triangle \\( \\triangle ABC \\), \\( AB = \\sqrt{2} \\), \\( AC = \\sqrt{3} \\), and \\( \\angle BAC = 30^\\circ \\). Let \\( P \\) be an arbitrary point in the plane containi... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2} - \\frac{5}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Quantitative determination of entropy - 5 points\n\nTotal: 10 points.",
"role": "user"
}
] | math | {
"ground_truth": "3 \\cdot 10^{26} \\, \\text{molecules}",
"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 product of all values of $t$ such that $t^2 - 64 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "-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": "A telecommunications company offers two billing methods, A and B, for mobile users to choose from. Method A charges a monthly rent of 8 yuan and a call fee of 0.2 yuan per minute... | math | {
"ground_truth": "x > 80",
"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 the consumer, a single discount of $n\\%$ is more advantageous than any of the following discounts:\n(1) Two successive $20\\%$ discounts\n(2) Three successive $13\\%$ discou... | math | {
"ground_truth": "\\textbf{(C)}\\ 38",
"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 function $f(x)=2\\tan (ωx+ϕ)(ω > 0,|ϕ| < \\dfrac {π}{2})$ with the smallest positive period of $\\dfrac {π}{2}$, and $f( \\dfrac {π}{2})=-2$, find the values of $ω=$ \\... | math | {
"ground_truth": "ϕ=- \\dfrac {π}{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": "Given a sequence $\\{a_n\\}$ satisfying $a_1=1$, $a_{n+1}= \\frac {2a_n}{a_n+2}$, and let $C_n= \\frac {2^n}{a_n}$, then the sum of the first $n$ terms of the sequence $\\{C_n\\}... | math | {
"ground_truth": "n\\cdot2^n",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ordered integer pairs $(x,y)$ $(0\\leq x,y < 31)$ satisfy the congruence $(x^2-18)^2\\equiv y^2 (\\mod 31)$?",
"role": "user"
}
] | math | {
"ground_truth": "60",
"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 vectors $\\overrightarrow {a}$ and $\\overrightarrow {b}$ that satisfy $|\\overrightarrow {a}| = |\\overrightarrow {b}| = 2$, and $\\overrightarrow {a} \\cdot \\overrightar... | math | {
"ground_truth": "\\theta = \\frac{1}{3}\\pi",
"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 $ S(n) $ be the sum of the squares of the positive integers less than and coprime to $ n $ . For example, $ S(5) = 1^2 + 2^2 + 3^2 + 4^2 $ , but $ S(4) = 1^2 + 3^2 $ . L... | math | {
"ground_truth": "7561",
"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 $|\\overrightarrow{a}|=|\\overrightarrow{b}|=|\\overrightarrow{c}|=\\lambda $, and satisfy $\\overrightarrow{a}\\cdot \\overrightarrow{b}=0$, $\\overrightarrow{a}\\cdot \\over... | math | {
"ground_truth": "\\sqrt[4]{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": "A circle with center $A$ and radius four feet is tangent at $C$ to a circle with center $B$, as shown. If point $B$ is on the small circle, what is the area of the shaded region?... | math | {
"ground_truth": "48\\pi",
"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 are four different passwords, $A$, $B$, $C$, and $D$, used by an intelligence station. Each week, one of the passwords is used, and each week it is randomly chosen with equ... | math | {
"ground_truth": "\\frac{61}{243}",
"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 $f(n) = n^4 - 400n^2 + 900$. Determine the sum of all values of $f(n)$ that are prime numbers.",
"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": "Given $a_n = \\frac{2n}{3n+2}$.\n\n(1) Find $a_3$ and $a_{n-1}$.\n\n(2) Determine whether $\\frac{8}{13}$ is a term of the sequence $\\left\\{a_n\\right\\}$. If so, identify its ... | 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": "The area of a circular garden with radius 6 feet is N percent larger than the area of a similar garden with radius 4 feet. Calculate the integer closest to the percent N.",
"... | math | {
"ground_truth": "125",
"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": "I have 13 distinguishable socks in my drawer: 5 white, 4 brown, 2 blue, and 2 black. In how many ways can I choose a pair of socks, provided that I get two socks of the same colo... | 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": "Determine the range of the function $f(x) = \\sin(x + 18^\\circ) - \\cos(x + 48^\\circ)$.",
"role": "user"
}
] | math | {
"ground_truth": "[-\\sqrt{3}, \\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": "In triangle $ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given that $2c - a = 2b\\cos A$.\n\n1. Find the measure of a... | math | {
"ground_truth": "c = 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 coat, a hat, and a pair of shoes originally sold for $100$ dollars, $50$ dollars, and $75$ dollars, respectively. During a sale, Alex bought the $100$ dollar coat at a $30\\%$ ... | math | {
"ground_truth": "30.556\\%",
"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 fair die is rolled seven times, find the probability of rolling a number less than four at least six times.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{15}{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": "For positive numbers $x$ and $y$, define the operation $\\heartsuit(x, y)$ as\n\\[\n\\heartsuit(x, y) = x - \\sqrt{\\frac{1}{y}}\n\\]\nCalculate $\\heartsuit(3, \\heartsuit(3, 3)... | math | {
"ground_truth": "\\frac{27-\\sqrt{3(9+\\sqrt{3})}}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The image below consists of a large triangle divided into $13$ smaller triangles. Let $N$ be the number of ways to color each smaller triangle one of red, green, and blue suc... | math | {
"ground_truth": "35",
"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 *Revolution* $(x) = x^3 +Ux^2 +Sx + A$ , where $U$ , $S$ , and $A$ are all integers and $U +S + A +1 = 1773$ . Given that *Revolution* has exactly two distinct nonzero i... | math | {
"ground_truth": "392",
"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": "Consider the set $S$ of $100$ numbers: $1; \\frac{1}{2}; \\frac{1}{3}; ... ; \\frac{1}{100}$ .\r\nAny two numbers, $a$ and $b$ , are eliminated in $S$ , and the number ... | math | {
"ground_truth": "100",
"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": "Determine when the equation \\(4x - 7 + a = (b - 1)x + 2\\) has a unique solution for \\(x\\).\nA) \\(a \\neq 9\\)\nB) \\(b \\neq 5\\)\nC) \\(a \\neq 7\\)\nD) \\(b \\neq 4\\)\nE)... | math | {
"ground_truth": "B) \\(b \\neq 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": "Find the value of real parameter $ a$ such that $ 2$ is the smallest integer solution of \\[ \\frac{x\\plus{}\\log_2 (2^x\\minus{}3a)}{1\\plus{}\\log_2 a} >2.\\]",
"role"... | math | {
"ground_truth": "a \\in \\left( \\frac{1}{2}, 1 \\right)",
"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": "An ellipse has its foci at $(1, 1)$ and $(1, 5)$. Given that it passes through the point $(-4, 3)$, its equation can be written in the form \\[\\frac{(x-h)^2}{a^2} + \\frac{(y-k)... | 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": "If $4x^3 - 12x^2 + kx - 16$ is divisible by $x - 4$, then determine the corresponding divisor among the given options.",
"role": "user"
}
] | math | {
"ground_truth": "4x^2 + 4",
"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 nine horizontal and nine vertical lines on an $8\\times8$ checkerboard form $r$ rectangles, of which $s$ are squares. The number $s/r$ can be written in the form $m... | math | {
"ground_truth": "125",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest integer $n$ such that $n$ is divisible by every integer less than $\\sqrt[3]{n}$ ?",
"role": "user"
}
] | math | {
"ground_truth": "420",
"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": "Determine the set of $x$-values for which $|\\frac{7-x}{4}| < 3$.",
"role": "user"
}
] | math | {
"ground_truth": "2 < x < 19",
"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 subsets of {1,2,3,4,5,6,7,8,9,10,11,12} have the property that no two of its elements differ by more than 5? For example, count the sets {3}, {2,5,7}, and {5,6,7,8,9} but... | math | {
"ground_truth": "256",
"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 \\[g(x) =\n\\begin{cases}\n7x+10 &\\text{if }x<3, \\\\\n3x-18&\\text{if }x\\ge3.\n\\end{cases}\n\\]If $g(x)=5$, find the sum of all possible values of $x$.",
"role": "use... | math | {
"ground_truth": "\\frac{18}{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": "Assume triangle $\\triangle ABC$ has one angle $A$ that is $15^\\circ$ smaller than another angle $B$. An altitude from angle $C$ bisects $C$ into two angles $C_1$ and $C_2$, wit... | 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": "Calculate the difference between the sums of two arithmetic sequences: sequence A consisting of numbers from 2001 to 2093 and sequence B consisting of numbers from 101 to 193.\nA... | math | {
"ground_truth": "C) 176700",
"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 $m$ and $n$ are positive integers such that $\\gcd(m,n) = 10$, then what is the smallest possible value of $\\gcd(8m,12n)$?",
"role": "user"
}
] | math | {
"ground_truth": "40",
"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 perpendicular to the line $y=-\\frac{b}{a}x$ passing through the right focus $F$ of the hyperbola $\\frac{x^2}{a^2}-\\frac{y^2}{b^2}=1$ ($a > 0, b > 0$) intersects the hyp... | math | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When $x = -5$, the value of the algebraic expression $ax^4 + bx^2 + c$ is 3. Then, when $x = 5$, find the value of $ax^4 + bx^2 + c$.",
"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": "A real number $\\alpha$ is given. Find all functions $f : R^+ \\to R^+$ satisfying $\\alpha x^2f\\left(\\frac{1}{x}\\right) +f(x) =\\frac{x}{x+1}$ for all $x > 0$ .",
... | math | {
"ground_truth": "f(x) = \\frac{x - \\alpha x^2}{(x+1)(1 - \\alpha^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": "Blue and yellow lights are hung on a string 8 inches apart in the order blue, blue, blue, yellow, yellow, and this pattern of 3 blue lights followed by 2 yellow lights continues.... | math | {
"ground_truth": "14.67",
"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": "Joseph divides a circle into 15 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measu... | math | {
"ground_truth": "**B) 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": "Seven points are placed on a circle. If five of the chords joining pairs of these seven points are selected at random, what is the probability that these five chords form a conve... | math | {
"ground_truth": "\\frac{1}{969}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine every prime numbers $p$ and $q , p \\le q$ for which $pq | (5^p - 2^ p )(7^q -2 ^q )$",
"role": "user"
}
] | math | {
"ground_truth": "(p, q) = (3, 5), (3, 3), (5, 37), (5, 83)",
"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 tourist is learning an incorrect way to sort a permutation $(p_1, \\dots, p_n)$ of the integers $(1, \\dots, n)$ . We define a *fix* on two adjacent elements $p_i$ and $p... | math | {
"ground_truth": "1009! \\cdot 1010!",
"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 $x=-2016$. What is the value of $\\bigg|$ $||x|-x|-|x|$ $\\bigg|$ $-x$?",
"role": "user"
}
] | math | {
"ground_truth": "4032",
"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 how many distinct rational numbers k exist such that |k| < 300 and the equation 3x^2 + kx + 18 = 0 has at least one integer solution for x, and k is a multiple of 3.",
... | math | {
"ground_truth": "108",
"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 a $12 \\times 12 \\times 12$ wooden cube formed by gluing together $12^3$ smaller unit cubes. What is the maximum number of unit cubes that can be seen from a single poi... | math | {
"ground_truth": "C) 400",
"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 function $f(x) = \\begin{cases} 1+ \\frac{1}{x} & (x>1) \\\\ x^{2}+1 & (-1\\leq x\\leq 1) \\\\ 2x+3 & (x<-1)\\end{cases}$.\n1. Find the value of $f\\{f[f(-2)]\\}$;\n2. ... | math | {
"ground_truth": "a=2 \\text{ or } a=\\pm \\frac{\\sqrt{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": "How many pairs of positive integer solutions \\((x, y)\\) satisfy \\(\\frac{1}{x+1} + \\frac{1}{y} + \\frac{1}{(x+1) y} = \\frac{1}{1991}\\)?",
"role": "user"
}
] | 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": "Given the daily sales volume of a product, $y$ (in tons), in relation to its sale price, $x$ (in ten thousand yuan per ton, $1 < x \\leq 5$), follows the relationship: When $1 < ... | math | {
"ground_truth": "x = 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": "Chichikov is playing with Nozdryov. Initially, Nozdryov distributes 1001 nuts into three boxes. After viewing the distribution, Chichikov names any integer \\( N \\) from 1 to 10... | math | {
"ground_truth": "71",
"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": "Karlsson is counting 200 buns baked by Fröken Bock: \"one, two, three, ..., one hundred ninety-eight, one hundred ninety-nine, two hundred.\" How many words will he say in total?... | math | {
"ground_truth": "443",
"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 school has between 150 and 200 students enrolled. Every afternoon, all the students come together to participate in gym class. The students are separated into seven distinct se... | math | {
"ground_truth": "1232",
"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 $(a_1,a_2,a_3,\\ldots,a_{18})$ be a permutation of $(1,2,3,\\ldots,18)$ for which\n$a_1>a_2>\\cdots>a_9$ and $a_9<a_{10}<\\cdots<a_{18}.$\nDetermine how many such permutation... | math | {
"ground_truth": "24310",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For \\( a, b \\in \\mathbb{R} \\), define \\(\\max \\{a, b\\}=\\left\\{\\begin{array}{ll}a, & a \\geq b \\\\ b, & a < b \\end{array}\\right.\\). The minimum value of the function... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given Sarah earns $2$ dollars for doing her tasks, $4$ dollars for doing them well, or $6$ dollars for doing them exceptionally over a period of $15$ days, and she accumulated a ... | 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": "If the terminal side of angle $\\alpha$ passes through $P(\\sin \\frac{2\\pi}{3}, \\cos \\frac{2\\pi}{3})$, then the smallest positive value of angle $\\alpha$ is ______.",
"... | math | {
"ground_truth": "\\frac{11\\pi}{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = ax^2 + 2x + c$ (where $a, c \\in \\mathbb{N}^*$), it satisfies the following conditions:\n1. $f(1) = 5$;\n2. $6 < f(2) < 11$.\n - Find the values of ... | math | {
"ground_truth": "m \\geq 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": "Given a triangle ABC with vertices at \\( A = (0, 4) \\), \\( B = (0, 0) \\), and \\( C = (10, 0) \\), find the value of \\( x = d \\) where a vertical line \\( x = d \\) divides... | math | {
"ground_truth": "C) \\, x = 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 that the local park is $2$ miles away from Jack's and Jill's house, and Jill rides her bicycle at a speed of $10$ miles per hour while Jack walks at a speed of $5$ miles pe... | math | {
"ground_truth": "12",
"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": "We are given a real number $a$ , not equal to $0$ or $1$ . Sacho and Deni play the following game. First is Sasho and then Deni and so on (they take turns). On each turn, a p... | math | {
"ground_truth": "a > 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": "For the function $ f(x) = ax^3 - 3x + 1 $ where $ x \\in [-1, 1] $, it is always true that $ f(x) \\geq 0 $. Determine the value of $ a $.",
"role": "user"
}
] | math | {
"ground_truth": "a = 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": "Calculate the number of solutions to $\\{1,~2,~3\\}\\subseteq~X~\\subseteq~\\{1,~2,~3,~4,~5,~6\\}$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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 area of one lateral face of a right pyramid with an equilateral triangular base is 90 square meters. If the slant height is 15 meters, calculate the length of the side of its... | 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": "Twenty-five coins are divided into piles in the following way. First, they are randomly split into two groups. Then any of the existing groups is split into two groups again, and... | math | {
"ground_truth": "300",
"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 $f(x)= \\begin{cases} x, & x < 1 \\\\ x^{2}-2x-5, & x\\geqslant 1 \\end{cases}$, find the solution set for the inequality $f(x)\\geqslant -2$.",
"role": "u... | math | {
"ground_truth": "\\{x|-2\\leqslant x < 1 \\text{ or } x\\geqslant 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 Odell and Kershaw run for $30$ minutes on a circular track, Odell runs clockwise at $250 m/min$ and uses the inner lane with a radius of $50$ meters, while Kershaw runs cou... | math | {
"ground_truth": "47",
"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 sum of two nonzero real numbers is 5 times their product. Calculate the sum of the reciprocals of the two numbers.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five consecutive two-digit positive integers, each less than 50, are not prime. What is the largest of these six integers?",
"role": "user"
}
] | math | {
"ground_truth": "43",
"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 $\\frac{5}{8} = \\frac{P}{56} = \\frac{80}{Q}$, and $R = P - 4$, find the value of $Q + R$.",
"role": "user"
}
] | math | {
"ground_truth": "159",
"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 function $f(x)= \\begin{cases} -x^{2}-ax-5,x\\leqslant 1 \\\\ \\frac {a+1}{x},x > 1\\end{cases}$ is an increasing function on $\\mathbb{R}$, find the range of values fo... | math | {
"ground_truth": "[- \\frac {7}{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": "Define an operation $*$ on the set of positive real numbers, such that when $a \\geqslant b$, $a * b = b^a$; and when $a < b$, $a * b = b^2$. According to this rule, find the sol... | math | {
"ground_truth": "3, 3\\sqrt{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 a triangle with integral sides and an isosceles perimeter of 11, calculate the area of the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5\\sqrt{2.75}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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