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": "If $2x^{|k|}+\\left(k-1\\right)y=3$ is a linear equation in $x$ and $y$, then the value of $k$ is ______.",
"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": "Let $a$, $b$, and $c$ be the roots of the cubic equation $$\n5x^3 - 2019x + 4029 = 0.\n$$ Compute $(a + b)^3 + (b + c)^3 + (c + a)^3.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{12087}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the integer $n$, $0 \\le n \\le 12$, that satisfies \\[n \\equiv -3457 \\pmod{13}.\\]",
"role": "user"
}
] | 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": "A pentagon is formed by placing an equilateral triangle on top of a square. The side of the square is equal to the side of the equilateral triangle. What percent of the area of t... | math | {
"ground_truth": "\\frac{100\\sqrt{3}}{4 + \\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": "Given quadrilateral $ABCD$ with $AB = 5$, $BC = 17$, $CD = 5$, and $DA = 9$, where $BD$ is an integer, calculate the length of $BD$.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mrs. Gomez has recorded the grades for 24 out of 25 students in her class for a math test. The average score for these 24 students is 76. When she added Oliver's test score, the ... | math | {
"ground_truth": "\\textbf{(C)}\\ 126",
"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 all integer $c\\in\\{0,1,...,2016\\}$ such that the number of $f:\\mathbb{Z}\\rightarrow\\{0,1,...,2016\\}$ which satisfy the following condition is minimal:\n(1) $f$ ... | math | {
"ground_truth": "c = 1, 2016, 1008, 1009",
"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 $n$ be a positive integer. How many polynomials $P$ with coefficients in the set $\\{0,1,2,3\\}$ satisfy $P(2)=n$?",
"role": "user"
}
] | math | {
"ground_truth": "\\left\\lfloor \\frac{n}{2} \\right\\rfloor + 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": "A picture 5 feet across is hung on a wall that is 25 feet wide with a 2-foot offset from being centered toward one end of the wall. Determine the distance from the end of the wal... | 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": "In a square \\(ABCD\\) with side length of 2 cm, draw quarter circles with a radius of 2 cm centered at points \\(A, B, C, D\\). The intersection points of these arcs are \\(E, F... | math | {
"ground_truth": "4.188",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x)$ satisfies $f(x) + f(2a - x) = 2b$ for any $x$ in its domain, the graph of the function $y = f(x)$ is symmetric about the point $(a, b)$.\n\n1. If t... | math | {
"ground_truth": "a \\in (-2\\sqrt{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": "A rectangular experimental field measures 200 meters in length and 100 meters in width. What is the area of this field on a map with a scale of 1:2000?",
"role": "user"
}
] | math | {
"ground_truth": "50 \\text{ square centimeters}",
"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 $L(x) = x - \\frac{x^2}{2}$ for every real number $x$. If $n$ is a positive integer, define $b_n$ by\n\\[\n b_n = L \\Bigl( L \\Bigl( L \\Bigl( \\cdots L \\Bigl( \\frac{2... | math | {
"ground_truth": "\\frac{40}{19}",
"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 plane, 4 points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) are given, and the distance between any two of them is at least 1. What is the maximum possible number of line segments \\... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The probability of snow on each of the first two days is $\\frac{2}{3}$, and the probability of snow on the third day is $\\frac{3}{5}$. What is the probability that it will not ... | math | {
"ground_truth": "\\frac{2}{45}",
"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 $x = -0.239$, then the value of $|x - 1| + |x - 3| + \\ldots + |x - 1997| - |x| - |x - 2| - \\ldots - |x - 1996|$ is equal to ____.",
"role": "user"
}
] | math | {
"ground_truth": "999",
"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": "Three numbers have sum $k$ (where $k\\in \\mathbb{R}$ ) such that the numbers are arethmetic progression.If First of two numbers remain the same and to the third number we add... | math | {
"ground_truth": "\\left(\\frac{2k}{3}, \\frac{k}{3}, 0\\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": "Given the hyperbola $C$: $\\dfrac{x^2}{a^2} - \\dfrac{y^2}{b^2} = 1 \\ (a > 0, b > 0)$ has an asymptote equation $y = \\dfrac{\\sqrt{5}}{2}x$, and it shares a common focus with t... | math | {
"ground_truth": "\\dfrac{x^2}{4} - \\dfrac{y^2}{5} = 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": "If the digit 2 is placed after a three-digit number whose hundreds' digit is $h$, tens' digit is $t$, and units' digit is $u$, find the expression that represents the new number ... | math | {
"ground_truth": "1000h + 100t + 10u + 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": "If 81 is divided into three parts proportional to 3, 5, and 7, find the value of the smallest part.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{81}{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": "Two positive integers \\( m \\) and \\( n \\) are chosen such that \\( m \\) is the second smallest positive integer with only two positive divisors and \\( n \\) is the largest ... | math | {
"ground_truth": "172",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,$ $b,$ $c,$ and $d$ be nonzero real numbers. Find the number of real roots of the equation\n\\[\n\\begin{vmatrix} x & d & c \\\\ -d & x & b \\\\ -c & -b & x \\end{vmatrix}... | math | {
"ground_truth": "x = 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": "In the diagram below, points $A$, $B$, $C$, and $P$ are located so that $PA=3$, $PB=4$, $PC=5$, and $BC=6$. What is the maximum possible area of $\\triangle ABC$?\n[asy]\ndefault... | math | {
"ground_truth": "18.921",
"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 $f(x)$ be an even function defined on $\\mathbb{R}$ such that $f(x + \\pi) = f(x)$, and $f(x) = \\sin x$ when $x \\in \\left[0, \\frac{\\pi}{2}\\right]$. Find the value of $f... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{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": "Suppose $\\tan \\gamma$ and $\\tan \\delta$ are the roots of the quadratic equation $x^2 - mx + n = 0$, and $\\cot \\gamma$ and $\\cot \\delta$ are the roots of another quadratic... | math | {
"ground_truth": "\\frac{m}{n^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": "Find the number of unordered pairs $\\{ A,B \\}$ of subsets of an n-element set $X$ that satisfies the following:\r\n(a) $A \\not= B$ \r\n(b) $A \\cup B = X$",
"role": ... | math | {
"ground_truth": "\\frac{3^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": "Express \\(\\frac{47}{5^4 \\cdot 2}\\) as a terminating decimal.",
"role": "user"
}
] | math | {
"ground_truth": "0.0376",
"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": "Solve the system of linear equations using the Gaussian elimination method.\n\n$$\n\\begin{aligned}\n& 2 x_{1}+7 x_{2}+13 x_{3}=0 \\\\\n& 3 x_{1}+14 x_{2}+12 x_{3}=18 \\\\\n& 5 x... | math | {
"ground_truth": "x_{1} = -4, x_{2} = 3, x_{3} = -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": "Given the function $f(x) = \\begin{cases} x^{2}+2x & ,x<0 \\\\ x-1 & ,x\\geq 0 \\end{cases}$, if the equation $f(x) - a^2 + 2a = 0$ has three distinct real roots, then the range ... | math | {
"ground_truth": "0 < a < 1 \\text{ or } 1 < a < 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": "Julia had eaten a box of candies in 4 days. On the first day she ate \\(\\frac{1}{5}\\) of the total number of candies. On the second day she ate half of what was left after the ... | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the point $(1, t)$ is above the line $2x - y + 1 = 0$, and the inequality $x^2 + (2t-4)x + 4 > 0$ always holds, find the set of possible values for $t$.",
"role": ... | math | {
"ground_truth": "\\{t | 3 < t < 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": "Sofia and Viktor are playing the following game on a $2022 \\times 2022$ board:\n - Firstly, Sofia covers the table completely by dominoes, no two are overlapping and all are i... | math | {
"ground_truth": "1011^2",
"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": "In triangle \\(XYZ\\), \\(YZ = 30\\) and \\(\\angle Y = 60^\\circ\\). Let the perpendicular bisector of \\(YZ\\) intersect \\(YZ\\) and \\(XZ\\) at \\(P\\) and \\(Q\\), respectiv... | math | {
"ground_truth": "7.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The point $A$ is located at $(5, 3)$. Reflect $A$ over the y-axis to get point $B$. Then, reflect $B$ over the line $y=x$ to get point $C$. Calculate the area of triangle $ABC$."... | 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": "If $81^6 = 9^q$, what is $q$?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $1-\\frac{4}{x}+\\frac{4}{x^2}=0$, find the value of $\\frac{2}{x}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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": "David has a collection of 40 rocks, 30 stones, 20 minerals and 10 gemstones. An operation consists of removing three objects, no two of the same type. What is the maximum number ... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation \\( 3\\log x - 4 \\log 5 = -1 \\), solve for \\( x \\).\nA) \\( \\sqrt[3]{60} \\)\nB) \\( \\sqrt[3]{62.5} \\)\nC) \\( \\sqrt[3]{65} \\)\nD) \\( \\sqrt[3]{70} \... | math | {
"ground_truth": "B) \\( \\sqrt[3]{62.5} \\)",
"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": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $b\\sin ^{2} \\frac {A}{2}+a\\sin ^{2} \\frac ... | math | {
"ground_truth": "2 \\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If a worker receives a $20$% cut in wages, calculate the exact percentage or dollar amount of a raise needed for the worker to regain their original pay.",
"role": "user"
}... | math | {
"ground_truth": "25\\%",
"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 nonzero numbers \\( x, y \\), and \\( z \\) satisfy the equations\n\\[\nxy = 2(x + y), \\quad yz = 4(y + z), \\quad \\text{and} \\quad xz = 8(x + z).\n\\]\nSolve for \\( x \\... | math | {
"ground_truth": "\\frac{16}{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": "In $\\vartriangle ABC$ points $D, E$ , and $F$ lie on side $\\overline{BC}$ such that $\\overline{AD}$ is an angle bisector of $\\angle BAC$ , $\\overline{AE}$ is a m... | math | {
"ground_truth": "94",
"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 function \\( f(x) = 1 - \\frac{1}{2} \\cos 2x + a \\sin \\frac{x}{2} \\cos \\frac{x}{2} \\) (where \\( a \\in \\mathbf{R} \\)), if the maximum value of the function is ... | math | {
"ground_truth": "3 \\text{ or } -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 that the point $({1,\\frac{3}{2}})$ lies on the ellipse $E$: $\\frac{{{x^2}}}{{{a^2}}}+\\frac{{{y^2}}}{{{b^2}}}=1(a＞b＞0)$, and the eccentricity of $E$ is $\\frac{1}{2}$. \... | math | {
"ground_truth": "|PQ| = 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The side $AC$ of triangle $ABC$ is extended at segment $CD = AB = 1$ . It is known that $\\angle ABC = 90^o$ , $\\angle CBD = 30^o$ . Calculate $AC$ .",
"role": "user... | math | {
"ground_truth": "\\sqrt[3]{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": "Find the value of the function \\( f(x) \\) at the point \\( x_{0} = 1000 \\), given that \\( f(0) = 1 \\) and for any \\( x \\), the equality \\( f(x+2) = f(x) + 4x + 2 \\) hold... | math | {
"ground_truth": "999001",
"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 number, $n$, is added to the set $\\{4, 8, 12, 15\\}$ to make the mean of the set of five numbers equal to its median. Find the smallest possible value of $n$.",
"role": "u... | math | {
"ground_truth": "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": "A circle is circumscribed around a unit square \\(ABCD\\), and a point \\(M\\) is selected on the circle.\n\nWhat is the maximum value that the product \\(MA \\cdot MB \\cdot MC ... | math | {
"ground_truth": "0.5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the sequence $\\{a_n\\}$, $a_1= \\sqrt{2}$, $a_n= \\sqrt{a_{n-1}^2 + 2}\\ (n\\geqslant 2,\\ n\\in\\mathbb{N}^*)$, let $b_n= \\frac{n+1}{a_n^4(n+2)^2}$, and let $S_n$ be the su... | math | {
"ground_truth": "\\frac{5}{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": "Find two numbers such that their sum is 20 and their product is 96.",
"role": "user"
}
] | math | {
"ground_truth": "12 \\text{ and } 8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\sqrt{4 + \\left(\\frac{x^3 - 2}{x}\\right)^2}$, simplify the expression.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{x^6 - 4x^3 + 4x^2 + 4}}{x}",
"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": "You flip a fair coin once and roll two six-sided dice. What is the probability that the coin will show heads and the combined total from the dice will either be exactly 5 or exac... | math | {
"ground_truth": "\\frac{1}{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": "In a positive geometric sequence $\\{a_n\\}$, $a_1$ and $a_{19}$ are the two roots of the equation $x^2 - 10x + 16 = 0$. Find the value of $a_8 \\cdot a_{12}$.",
"role": "use... | math | {
"ground_truth": "16",
"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 room containing $N$ people, where $N > 4$, and at least two people have not shaken hands with everyone else in the room, find the maximum number of people in the room tha... | math | {
"ground_truth": "N-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": "We consider two circles $k_1(M_1, r_1)$ and $k_2(M_2, r_2)$ with $z = M_1M_2 > r_1+r_2$ and a common outer tangent with the tangent points $P_1$ and $P2$ (that is, they... | math | {
"ground_truth": "P_1P_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": "Determine the positive numbers $a{}$ for which the following statement true: for any function $f:[0,1]\\to\\mathbb{R}$ which is continuous at each point of this interval and ... | math | {
"ground_truth": "a = \\frac{1}{n}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a tournament with $ n \\ge 3$ participants, every two participants played exactly one match and there were no draws. A three-element set of participants is called a *draw-tr... | math | {
"ground_truth": "\\binom{n}{3} - \\frac{n^3 - 4n^2 + 3n}{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 the positive integer $2020$, find the number of its positive integer factors that have more than $3$ factors.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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": "A wizard thinks of a number from $1$ to $n$ . You can ask the wizard any number of yes/no questions about the number. The wizard must answer all those questions, but not neces... | math | {
"ground_truth": "n-1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the length of the classroom is 15 feet and the width is 18 feet, calculate the area of the rectangular classroom in square feet.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"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 number of sets of two or more consecutive positive integers whose sum is 150.",
"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 Heidi can paint a wall in 45 minutes and Tim can paint the same wall in 30 minutes, what fractional part of the wall can they paint together in 9 minutes?",
"role": "user"... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( A = \\{1,2,3, \\ldots, n\\} \\), and let \\(\\{a_{1}, a_{2}, a_{3}\\}\\left(a_{1}<a_{2}<a_{3}\\right)\\) be a three-element subset of \\( A \\). If it satisfies \\(a_{3} ... | math | {
"ground_truth": "C_{n+2}^{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A jar initially contains $150$ gumdrops in $5$ different colors. $25\\%$ are blue, $25\\%$ are brown, $20\\%$ are red, $10\\%$ are yellow, and the remaining gumdrops are green. I... | math | {
"ground_truth": "C) 60",
"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 all triples $(a, b, p)$ of positive integers, where $p$ is a prime number, such that $a^p - b^p = 2013$ .",
"role": "user"
}
] | math | {
"ground_truth": "(337, 334, 2)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a parabola $y^2=2px$ ($p>0$) with a moving point $P$ on it, and a point $A(3, 2)$ inside the parabola. Let $F$ be the focus. The minimum value of $|PA|+|PF|$ is $\\frac{7}{... | math | {
"ground_truth": "(4, -2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the real values of $x$ satisfying the equality $|x+2|=2|x-2|$.",
"role": "user"
}
] | math | {
"ground_truth": "6\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Palindromic primes are two-digit prime numbers such that the number formed when the digits are reversed is also prime. What is the sum of all palindromic primes less than 60?",
... | math | {
"ground_truth": "55",
"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 game of Colonel Blotto, you have 100 troops to distribute among 10 castles. Submit a 10-tuple $(x_1, x_2, \\dots x_{10})$ of nonnegative integers such that $x_1 + x_2 +... | math | {
"ground_truth": "(12, 12, 12, 12, 12, 12, 12, 9, 6, 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": "Tetrahedron $PQRS$ has $PQ=6$, $PR=5$, $PS=4$, $QR=7$, $QS=5$, and $RS=\\tfrac{15}4\\sqrt{2}$. What is the volume of the tetrahedron?\n**A)** $\\frac{5}{3}$ \n**B)** $\\frac{8}{... | math | {
"ground_truth": "\\textbf{(C)} \\frac{10}{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 $x$ cows give $x+1$ cans of milk in $x+2$ days, determine the number of days it will take $x+4$ cows to give $x+7$ cans of milk.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x(x+2)(x+7)}{(x+1)(x+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 product of two natural numbers that are reverse of each other is 92565. Find these two natural numbers. (For example, 102 and 201, 35 and 53, 11 and 11, etc., are considered ... | math | {
"ground_truth": "\\{165, 561\\}",
"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": "Genetic material DNA is composed of a chain of four compounds: $T, C, A, G$. The sequence of these compounds determines genetic information, known as genetic coding. In genetics,... | math | {
"ground_truth": "10^{1.26 \\times 10^{10}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive integers $ n$ such that it is possible to tile a $ 15 \\times n$ board with pieces shaped like this:\r\n\r\n[asy]size(100); draw((0,0)--(3,0)); draw((0... | math | {
"ground_truth": "n \\neq 1, 2, 4, 7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "After fully charging his phone, Alex used his phone for $30$ minutes. When he is not using his phone, the battery lasts for $18$ hours, and if he uses it constantly, the battery ... | math | {
"ground_truth": "C) 8 \\text{ hours}",
"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 a sequence $\\left\\{a_{1}, a_{2}, \\ldots, a_{n}\\right\\}$ of positive integers (where $n$ is a positive integer) has the property that the last digit of $a_{k}$ is the same... | math | {
"ground_truth": "46",
"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": "Three different positive integers have a mean of 7. What is the largest positive integer that could be one of them?\nA 15\nB 16\nC 17\nD 18\nE 19",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with $AC\\neq BC$ , and let $A^{\\prime }B^{\\prime }C$ be a triangle obtained from $ABC$ after some rotation centered at $C$ . Let $M,E,F$ be t... | math | {
"ground_truth": "60^\\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": "We cannot wind up our wall clock if either the hour hand or the minute hand is moving between 3 and 4, or between 8 and 9. How much time per day is available for winding the cloc... | math | {
"ground_truth": "18 \\text{ hours}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the day the Ice Palace opens, children agree to go together to escape the summer heat. There is a staircase in front of the Ice Palace. Alice took 120 seconds to walk 20 steps... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a regular tetrahedron, the midpoints of the six edges form the vertices of an octahedron. Determine the ratio of the volume of this octahedron to the volume of the original te... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_1,a_2,\\ldots,a_6$ be a sequence of integers such that for all $1 \\le i \\le 5$ , $$ a_{i+1}=\\frac{a_i}{3} \\quad \\text{or} \\quad a_{i+1}={-}2a_i. $$ Find the num... | math | {
"ground_truth": "142",
"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 $4y^2+4xy+x+6=0$, determine the complete set of values of $x$ for which $y$ is real.",
"role": "user"
}
] | math | {
"ground_truth": "x \\leq -2 \\text{ or } x \\geq 3",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=A\\sin (\\omega x+\\varphi)$ ($A > 0$, $\\omega > 0$) whose graph passes through point $P\\left(\\frac{\\pi}{12},0\\right)$, and the nearest highest point t... | math | {
"ground_truth": "k\\pi-\\frac{5\\pi}{12}\\leqslant x\\leqslant k\\pi+\\frac{\\pi}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a cyclic quadrilateral with $AB = 1$ , $BC = 2$ , $CD = 3$ , $DA = 4$ . Find the square of the area of quadrilateral $ABCD$ .",
"role": "user"
}
] | 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": "Given six socks, each of a different color and easily stretchable. Turning them inside out is not allowed. In how many ways can you put three socks on each foot, considering the ... | math | {
"ground_truth": "720",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In her chemistry class, Samantha now needs to prepare a special solution that consists of chemical A, water, and a new substance, chemical B. The proportions in her initial test ... | math | {
"ground_truth": "0.60",
"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 quadratic function $f(x)=ax^{2}-bx+2$ where $a > 0$.\n(1) If the solution set of the inequality $f(x) > 0$ is ${x|x > 2$ or $x < 1}$, find the values of $a$ and $b$.\n(... | math | {
"ground_truth": "[\\frac {1}{a},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": "Determine the value of $a$ such that $9x^2 + 30x + a$ is the square of a binomial.",
"role": "user"
}
] | math | {
"ground_truth": "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": "A grid of points with 10 rows and 10 columns is given. Each point is colored either red or blue. Whenever two points of the same color are adjacent in the same row or column, the... | math | {
"ground_truth": "37",
"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 regular octagon is inscribed in a circle, and each side of the octagon is 5 units long. Find the circumference of the circle.\nA) $\\frac{4\\pi}{\\sin(22.5^\\circ)}$\nB) $\\fra... | math | {
"ground_truth": "\\frac{5\\pi}{\\sin(22.5^\\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": "Find the number of distinct points in the xy-plane common to the graphs of $(x+y-7)(3x-2y+6)=0$ and $(x-y-2)(4x+y-10)=0$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "In circle $\\odot O$, the distance from a point $P$ inside the circle to the nearest point on circle $\\odot O$ is $1$, and the distance to the farthest point is $7$. What is the... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a line $l$ passes through the point $(-2,1)$.\n\n$(1)$ If the line does not pass through the fourth quadrant, find the range of values for the slope $k$ of line $l$;\n\n$(2... | math | {
"ground_truth": "x-2y+4=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 a $2\\times 3$ grid where each entry is either $0$ , $1$ , or $2$ . For how many such grids is the sum of the numbers in every row and in every column a multiple of... | 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": "Given \\((a-i)^{2}=2i\\), where \\(i\\) is the imaginary unit, find the value of the real number \\(a\\).",
"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": "Your math friend Steven rolls five fair icosahedral dice (each of which is labelled $1,2, \\dots,20$ on its sides). He conceals the results but tells you that at least half the... | math | {
"ground_truth": "\\frac{1}{58}",
"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 $T_n = 1 + 2 + 3 + \\dots + n$ and \n\\[P_n = \\frac{T_2 + 1}{T_2 - 1} \\cdot \\frac{T_3 + 1}{T_3 - 1} \\cdot \\frac{T_4 + 1}{T_4 - 1} \\cdot \\dots \\cdot \\frac{T_n + 1}{T_n... | math | {
"ground_truth": "B) 187.5",
"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": "The total number of toothpicks used to build a rectangular grid 15 toothpicks high and 12 toothpicks wide, with internal diagonal toothpicks, is calculated by finding the sum of ... | math | {
"ground_truth": "567",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A particle starts moving, and from the second mile onwards, its speed is inversely proportional to the distance traveled in miles. If it takes 2 hours to travel the second mile, ... | math | {
"ground_truth": "2(n-1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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