data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $1002^2 - 1000^2$?",
"role": "user"
}
] | math | {
"ground_truth": "4004",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the length of Crystal's final segment back to the starting point after running due north for 2 miles, then southeast for 1 mile, and northeast for 2 miles.",
"role"... | math | {
"ground_truth": "\\sqrt{10.75}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive integer $k$ . Find the condition of positive integer $m$ over $k$ such that there exists only one positive integer $n$ satisfying $$ n^m | 5^{n^k} + 1, ... | math | {
"ground_truth": "k + 2 \\leq m",
"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 picture $3$ feet across is hung in the center of a wall that is $19$ feet wide. Calculate the distance from the end of the wall to the nearest edge of the picture.",
"role"... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a rectangle, if one of its diagonals forms angles $\\alpha$ and $\\beta$ with the two sides starting from one vertex, then we have ${\\cos^2}\\alpha +{\\cos^2}\\beta = 1$. By ... | math | {
"ground_truth": "{\\cos^2}\\alpha +{\\cos^2}\\beta +{\\cos^2}\\gamma = 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": "For each positive integer $n$ , let $S(n)$ be the sum of the digits of $n$ . Determines the smallest positive integer $a$ such that there are infinite positive integers $n... | math | {
"ground_truth": "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": "Which digit will appear in the 845th place after the decimal point in the decimal representation of $\\frac{7}{29}$?",
"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": "Given the function $f(x)= \\sqrt {3}\\sin \\omega x+\\cos \\omega x (\\omega > 0)$, the distance between two adjacent axes of symmetry of its graph is $\\dfrac {\\pi}{2}$. Find a... | math | {
"ground_truth": "\\left[- \\dfrac {\\pi}{3}, \\dfrac {\\pi}{6}\\right]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A polygon has 150 sides. Calculate the number of diagonals that can be drawn if the diagonal should not connect vertices whose indices differ by a multiple of 4.\nA) 11025\nB) 56... | math | {
"ground_truth": "C) 5400",
"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 principal, the caretaker, and the parent-teacher committee, not consulting each other, each bought a carpet for the school auditorium of size \\(10 \\times 10\\). Deciding wh... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $\\frac{10^8}{2 \\times 10^5} - 50$.",
"role": "user"
}
] | math | {
"ground_truth": "450",
"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 college student drove his compact car 150 miles home for the weekend, averaging 30 miles per gallon. For the return trip, the student drove his parents' more fuel-efficient SUV... | math | {
"ground_truth": "C) 28",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x>0$, $y>0$, and $x+16y=xy$, find the minimum value of $x+y$.",
"role": "user"
}
] | math | {
"ground_truth": "25",
"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 numbers in the set $\\{9, 19, 29, 39, \\ldots\\}$ can be written as the difference of two primes?",
"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": "Given that $X$ is a subset of $\\{1,~2,~3,~4,~5,~6\\}$, find the number of subsets that satisfy the condition $\\{1,~2,~3\\}\\subseteq~X$.",
"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": "Let \\( A, B, C, \\) and \\( D \\) be four points lying in this order on a circle. Assume that there is a point \\( K \\) on the line \\( AB \\) such that \\( BD \\) bisects the ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest positive integer $x$ such that $2520x = M^3$, where $M$ is an integer.\nA) 3520 \nB) 3675 \nC) 7350 \nD) 8820",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(B)}\\ 3675",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of the parameter \\( p \\) such that the equation\n\n$$\nx^2 + px + p - 1 = 0\n$$\n\nsatisfies the requirement for its roots \\( x_1 \\) and \\( x_2 \\) given... | math | {
"ground_truth": "p = 1 \\text{ and } p = 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many right interior angles are in a right triangle?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a right square prism $ABCD-A_{1}B_{1}C_{1}D_{1}$ with a base edge length of $1$, and $AB_{1}$ forms a $60^{\\circ}$ angle with the base $ABCD$, find the distance from $A_{1... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all tuples of positive integers $(x, y, z, t)$ such that: $$ xyz = t! $$ $$ (x+1)(y+1)(z+1) = (t+1)! $$ \nholds simultaneously.",
"role": "user"
}
] | math | {
"ground_truth": "(8, 3, 3, 1), (5, 4, 3, 1), (3, 2, 2, 2), (7, 6, 2, 1), (9, 5, 2, 1), (15, 4, 2, 1), (1, 1, 1, 7), (2, 1, 1, 5), (3, 2, 1, 3), (8, 3, 1, 2), (5, 4, 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": "Given a sequence ${a_n}$ with the sum of its first $n$ terms denoted as $S_n$, the \"optimal value\" $H$ of ${a_n}$ is defined as $H = \\frac{a_1 + 2a_2 + \\dots + 2^{n-1}a_n}{n}... | math | {
"ground_truth": "S_n = \\frac{n(n+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": "Let $p = 2017,$ a prime number. Let $N$ be the number of ordered triples $(a,b,c)$ of integers such that $1 \\le a,b \\le p(p-1)$ and $a^b-b^a=p \\cdot c$ . Find the rem... | math | {
"ground_truth": "2016",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 36 contestants in the CMU Puyo-Puyo Tournament, each with distinct skill levels. \n \n The tournament works as follows:\n First, all $\\binom{36}{2}$ pairing... | math | {
"ground_truth": "\\frac{22085}{36}",
"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 non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ that satisfy $|\\overrightarrow{b}| = \\sqrt{2}$, and $(\\overrightarrow{a} - \\overrightarrow{b}) \\cdot (... | math | {
"ground_truth": "45^{\\circ}",
"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 sequence of polynomials $\\left( P_{n}(X)\\right)_{n\\in Z_{>0}}$ is defined as follows: $P_{1}(X)=2X$ $P_{2}(X)=2(X^2+1)$ $P_{n+2}(X)=2X\\cdot P_{n+1}(X)-(X^2-1)P_{n}(X)... | math | {
"ground_truth": "n \\equiv 2 \\pmod{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Which of the following is not the sum of two primes?\nA) 5\nB) 7\nC) 9\nD) 11\nE) 13",
"role": "user"
}
] | math | {
"ground_truth": "11",
"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 circles of radius $a$ are drawn on the surface of a sphere of radius $r$ . Each pair of circles touches externally and the three circles all lie in one hemisphere. Find ... | math | {
"ground_truth": "R = r \\sin\\left(\\arcsin\\left(\\frac{a}{r}\\right) - \\arcsin\\left(\\frac{a\\sqrt{3}}{3r}\\right)\\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": "Find the solution set for the inequality $\\frac{x-1}{x+2} > 0$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x \\mid x < -2 \\text{ or } x > 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": "Find the smallest positive integer $n$ that satisfies the following two properties:\n\n1. $n$ has exactly 144 distinct positive divisors.\n2. Among the positive divisors of $n$, ... | math | {
"ground_truth": "110880",
"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 the sequence \\\\(\\{a_n\\}\\) be defined as \\\\(a_1=2\\\\), \\\\(a_{n+1}= \\dfrac{2}{a_n+1}\\\\), \\\\(b_n=\\left| \\dfrac{a_n+2}{a_n-1} \\right|\\), \\\\(n\\in\\mathbb{N}^... | math | {
"ground_truth": "2^{n+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": "Consider five strips of paper, each of 8 units long and 2 units wide, laid flat on a table. Three strips are placed horizontally, and two are placed vertically, overlapping in a ... | math | {
"ground_truth": "B) 56 square units",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A=\\{x|x^{2}-4\\leqslant 0\\}$, $B=\\{x\\left|\\right.2x+a\\leqslant 0\\}$, and $A\\cap B=\\{x\\left|\\right.-2\\leqslant x\\leqslant 1\\}$. Find the value of $a$.",
"ro... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer and let $P(x)$ be a monic polynomial of degree $n$ with real coefficients. Also let $Q(x)=(x+1)^2(x+2)^2\\dots (x+n+1)^2$ . Consider the mini... | math | {
"ground_truth": "4318",
"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's solve the following system of equations:\n\n$$\n\\begin{aligned}\n& x + y^{2} = a \\\\\n& y + x^{2} = a\n\\end{aligned}\n$$\n\nFor which values of \\(a\\) do we obtain real... | math | {
"ground_truth": "a\\geq \\frac{3}{4}",
"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 the function $f(x) = \\overrightarrow{m} \\cdot \\overrightarrow{n}$, where vector $\\overrightarrow{m} = (2\\cos x, 1)$, $\\overrightarrow{n} = (\\cos x, \\sqrt{3}\\sin 2x)$... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the $x$-intercept and $y$-intercept of a line are both positive prime numbers, calculate the number of lines passing through the point $(6,5)$.",
"role": "user"
... | math | {
"ground_truth": "0",
"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 have a triangle $\\triangle ABC$ and a point $L$ on $BC$ such that $AL$ is an altitude of $\\triangle ABC$. If $AC = 15$, $BL = 9$, and $BC = 17$, what is the area of $\\trian... | math | {
"ground_truth": "\\frac{17 \\sqrt{161}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a number $x$ is randomly selected from the interval $[-1,1]$, calculate the probability that the value of $x^2$ falls between $0$ and $\\frac{1}{4}$.",
"role": "user"
... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the matrix $\\mathbf{M}$ if it satisfies $\\mathbf{M} \\mathbf{i} = \\begin{pmatrix} 5 \\\\ 4 \\\\ -9 \\end{pmatrix},$ $\\mathbf{M} \\mathbf{j} = \\begin{pmatrix} -3 \\\\ 6 ... | math | {
"ground_truth": "\\begin{pmatrix} 5 & -3 & 8 \\\\ 4 & 6 & -2 \\\\ -9 & 0 & 5 \\end{pmatrix}",
"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 distances from the vertices of a triangle to a certain plane are 5, 6, and 7. Find the distance from the centroid of the triangle to the same plane. Indicate all possible val... | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\cos^2 \\omega x + \\sqrt{3}\\sin \\omega x\\cos \\omega x - \\frac{1}{2}$ ($\\omega > 0$), its smallest positive period is $\\pi$.\n\n(1) Find the valu... | math | {
"ground_truth": "\\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": "Given the values of the algebraic expression $-ax^{2}+bx$ as shown below, infer the solutions of the quadratic equation $-ax^{2}+bx+2=0$ in terms of $x$.",
"role": "user"
}... | math | {
"ground_truth": "\\text{C: } x_{1}=-2, x_{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": "The distance between consecutive fence posts is 210 feet, and Harry covers this distance in 30 equal hops, and Gary covers the same distance in 8 equal bounds.",
"role": "use... | math | {
"ground_truth": "19.36",
"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": "John's flight departed from Los Angeles at 9:15 AM and arrived in New York at 6:25 PM. Los Angeles is in the Pacific Time Zone (PT), and New York is in the Eastern Time Zone (ET)... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Seven distinct pieces of candy are to be distributed among three bags, with the red bag and the blue bag each receiving at least one piece of candy, while the white bag may remai... | math | {
"ground_truth": "12",
"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": "For a parabola with the x-axis as the axis of symmetry and the origin as the vertex, the distance from a point P(1, m) on the parabola to the focus is 3. Determine the equation o... | math | {
"ground_truth": "y^2 = 8x",
"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 hyperbola $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ with one focus $F(c, 0)$ and one endpoint of the conjugate axis $B(0, b)$, find the eccentricit... | math | {
"ground_truth": "\\frac{\\sqrt{5} + 1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The edge of each square is one tile longer than the edge of the previous square. Determine the difference between the number of tiles in the seventh square and the number of tile... | 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": "Given that $x$ is the arithmetic square root of $16$, and $y$ is the square root of $9$, find the value of $x^{2}+y^{2}+x+2023$.",
"role": "user"
}
] | math | {
"ground_truth": "2052",
"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 equation $x^{2}-2x+k=0$ has two equal real roots with respect to $x$, 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": "How many 6-digit numbers contain at least one zero?",
"role": "user"
}
] | math | {
"ground_truth": "368,\\!559",
"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 all 4-tuples ( $a, b,c, d$ ) of real numbers satisfying the following four equations: $\\begin{cases} ab + c + d = 3 \nbc + d + a = 5 \ncd + a + b = 2 \nda + b + c = 6... | math | {
"ground_truth": "(a, b, c, d) = (2, 0, 0, 3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=\\sin (3x- \\frac {\\pi}{3})$, express the horizontal translation of the graph of the function $y=\\sin 3x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {π}{9}",
"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 vectors $\\overrightarrow{a}=(\\sin x,\\cos x)$, $\\overrightarrow{b}=(1,1)$.\n\n$(1)$ When $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, find the value of $\\tan x$... | math | {
"ground_truth": "m < - \\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": "Find the number of ways in which the nine numbers \\(1, 12, 123, 1234, \\ldots, 123456789\\) can be arranged in a row so that adjacent numbers are relatively prime.",
"role":... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with center $O$ is tangent to the x-axis and to one leg of the $45^\\circ$-$45^\\circ$-$90^\\circ$ triangle $ABC$, where $AB=2$. Point $A$ is at the origin, and $BC$ is ... | math | {
"ground_truth": "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": "The constant term of the expansion of $$(x- \\frac {1}{x})^{n}$$ is \\_\\_\\_\\_\\_\\_ , given that only the fifth term of the binomial coefficient is the largest.",
"role": ... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that point $D$ is a point on the ellipse $C: \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$, and $F_1, F_2$ are the left and right foci of $C$ respectively, with $|F_... | math | {
"ground_truth": "x - y - 1 = 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": "Broady The Boar is playing a boring board game consisting of a circle with $2021$ points on it, labeled $0$ , $1$ , $2$ , ... $2020$ in that order clockwise. Broady is rol... | math | {
"ground_truth": "2021",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At 7:15 p.m., what is the measure of the smaller angle formed by the minute and hour hands on a clock?",
"role": "user"
}
] | math | {
"ground_truth": "127.5 \\text{ degrees}",
"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": "Climbing the first flight of stairs takes Jimmy 30 seconds, and each following flight takes 8 seconds more than the preceding one. How many total seconds does it take to climb th... | math | {
"ground_truth": "300",
"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 the inequality $|x-3|+|x-2|<a$ to have no real solutions, determine the range of $a$.",
"role": "user"
}
] | math | {
"ground_truth": "a\\leq1",
"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 fair 8-sided die is rolled. If I roll \\(n\\), then I win \\(n^3\\) dollars. What is the expected value of my win? Express your answer as a dollar value rounded to the nearest ... | math | {
"ground_truth": "\\$162.00",
"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 smallest positive real number $d,$ such that for all nonnegative real numbers $x$ and $y,$\n\\[\n\\sqrt{xy} + d (x^2 - y^2)^2 \\ge x + y.\n\\]",
"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": "Determine the largest possible radius of a circle that is tangent to both the \\( x \\)-axis and \\( y \\)-axis, and passes through the point \\((9,2)\\).",
"role": "user"
... | math | {
"ground_truth": "17",
"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 $a\\circ b=a+b-ab$ . Find all triples $(x,y,z)$ of integers such that\n\\[(x\\circ y)\\circ z +(y\\circ z)\\circ x +(z\\circ x)\\circ y=0\\]",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0, 0), (0, 2, 2), (2, 0, 2), (2, 2, 0)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The cafe \"Burattino\" operates 6 days a week with a day off on Mondays. Kolya made two statements: \"from April 1 to April 20, the cafe worked 18 days\" and \"from April 10 to A... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the radius of a circle is increased by $50\\%$, by what percentage is the area increased?\nA) 75%\nB) 100%\nC) 125%\nD) 150%\nE) 200%",
"role": "user"
}
] | math | {
"ground_truth": "C) 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": "Let \\( F = \\log \\frac{1+x}{1-x} \\). Define a new function \\( G \\) by replacing each \\( x \\) in \\( F \\) by \\( \\frac{2x - x^2}{1+2x^2} \\) and simplify. What does the s... | math | {
"ground_truth": "C) \\( 2F \\)",
"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 red ball and a blue ball are randomly and independently tossed into bins numbered with the positive integers starting from 2, so that for each ball, the probability that it is ... | math | {
"ground_truth": "\\frac{5}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**Begin with the integer 1,000,000,000. The sequence is formed by repeatedly dividing the number by 3. What is the last integer in this sequence?**",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the points (1, 2), (3, -2), and (4, k/3), determine the value(s) of k such that these points lie on the same straight line.",
"role": "user"
}
] | 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": "On the coordinate plane is given the square with vertices $T_1(1,0),T_2(0,1),T_3(-1,0),T_4(0,-1)$ . For every $n\\in\\mathbb N$ , point $T_{n+4}$ is defined as the midpoint o... | math | {
"ground_truth": "(0, 0)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The shooter shoots at a target until the first hit, with the probability of hitting the target each time being 0.6. Find the expected number of remaining bullets $\\xi$ after hit... | math | {
"ground_truth": "2.376",
"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": "Suzanna rides her bike at a constant rate. Every 10 minutes, she covers 3 miles. Calculate how many miles she would have ridden if she rides for a total of 40 minutes.",
"rol... | 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": "Suppose that $x$ is a positive multiple of $4$. If $x$ raised to the fifth power is less than $2000$, what is the greatest possible value of $x$?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the constant term in the expansion of the binomial $(4^{x} - 2^{-x})^{6}$ when $x\\in R$.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On each median of an equilateral triangle, a point is taken that divides the median in the ratio $3:1$, starting from the vertex. How much smaller is the area of the triangle wit... | 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 that a three-digit number has digits that sum to exactly $15$ and its last digit is $4$, calculate the number of such numbers that are not divisible by $7$.",
"role": "... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the minimum value of the expression \\(2x^2 + 2y^2 - 8x + 6y + 25\\).",
"role": "user"
}
] | math | {
"ground_truth": "12.5",
"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": "Calculate $\\langle\\langle\\langle 8\\rangle\\rangle\\rangle$ for a positive integer $n$, where $\\langle n\\rangle$ denotes the sum of all positive divisors of $n$ except for $... | math | {
"ground_truth": "A) 0",
"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)=\\log_{a}\\left(b-\\frac{2}{x+1}\\right)$ where $(a>0$ and $a\\neq 1)$ is an odd function.<br/>$(1)$ Find the solution set for the inequality $f(x) > 0$.... | math | {
"ground_truth": "(0, \\frac{3-2\\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": "In the Cartesian coordinate system xOy, it is known that the normal equation of line $l$ is $x-y-2=0$, and the parametric equation of curve $C$ is:\n$$\n\\begin{cases}\nx = 2\\sq... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the area, in square units, of a triangle with vertices at $(3, 2)$, $(3, -4)$, and $(9, -1)$.",
"role": "user"
}
] | 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": "There are 5 students in a queue. The questions are as follows:\n1) In how many ways can students A and B be adjacent to each other?\n2) In how many ways can students A, B, and C ... | math | {
"ground_truth": "60",
"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": "(2014 Jingzhou Mock Test) A ball is floating on a lake. After the water freezes, the ball is removed, leaving a hole in the ice with a diameter of 12 cm and a depth of 2 cm. Find... | math | {
"ground_truth": "400\\pi\\text{ cm}^2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a $35 \\cdot 44$ grid, calculate the total number of different rectangles (including squares).",
"role": "user"
}
] | math | {
"ground_truth": "87",
"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 quotient of dividing number A by number B is 0.514. If number A is increased by 10 times and number B is decreased by 100 times, the quotient will be \\_\\_\\_\\_\\_\\_.",
... | math | {
"ground_truth": "514",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two cylindrical poles, with diameters of 4 inches and 20 inches respectively, are aligned side by side and bound together with a wire. What is the length of the shortest wire tha... | math | {
"ground_truth": "\\textbf{(B)}\\ 8\\sqrt{5} + \\frac{44\\pi}{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": "A configuration of 4027 points in the plane is called Colombian if it consists of 2013 red points and 2014 blue points, and no three of these points are collinear. By drawing lin... | math | {
"ground_truth": "2013",
"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 ellipse $\\dfrac{x^2}{a^2} + \\dfrac{y^2}{b^2} = 1 (a > b > 0)$, with its left and right foci being $F_1$ and $F_2$ respectively, and its eccentricity being $e$. Point ... | math | {
"ground_truth": "2 - \\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": "Determine all possible values of $m+n$ , where $m$ and $n$ are positive integers satisfying \\[\\operatorname{lcm}(m,n) - \\gcd(m,n) = 103.\\]",
"role": "user"
}
] | math | {
"ground_truth": "21, 105, 309",
"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 $f(x)=\\ln x- \\frac {2}{x}$, locate the interval in which the zero point of the function $f(x)$ is located.",
"role": "user"
}
] | math | {
"ground_truth": "(2,3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle and $n$ a positive integer. Consider on the side $BC$ the points $A_1, A_2, ..., A_{2^n-1}$ that divide the side into $2^n$ equal parts, that i... | math | {
"ground_truth": "3 \\cdot 2^{2n} - 6 \\cdot 2^n + 6",
"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": "Simplify $(7-3i)-(2-5i)-(3+2i)$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square of side $2a$ , lying always in the first quadrant of the $xy$ -plane, moves so that two consecutive vertices\nare always on the $x$ - and $y$ -axes respectively. Fi... | math | {
"ground_truth": "X^2 + Y^2 = a^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the exterior angles of a pentagon is what value?",
"role": "user"
}
] | math | {
"ground_truth": "360^{\\circ}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an isosceles triangle \\(ABC (AB = BC)\\). Point \\(E\\) is marked on the ray \\(BA\\) beyond point \\(A\\), and point \\(D\\) is marked on side \\(BC\\). It is known that:... | math | {
"ground_truth": "4",
"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 45-45-90 triangle, the hypotenuse measures 16 inches. A median is drawn from the right-angle vertex to the midpoint of the hypotenuse. Calculate the area of one of the two t... | math | {
"ground_truth": "32 \\text{ square inches}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
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