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": "The longest professional tennis match ever played lasted a total of $11$ hours and $5$ minutes. Calculate the total number of minutes.",
"role": "user"
}
] | math | {
"ground_truth": "665",
"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 an odd function $f(x)$ with the domain of $\\mathbb{R}$, which is a decreasing function on $[0, +\\infty)$, determine the monotonicity of $f(x)$ on $(-\\infty, 0)$ and prov... | math | {
"ground_truth": "\\text{f(x) is a decreasing function on } (-\\infty, 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a regular tetrahedron \\(ABCD\\), points \\(E\\) and \\(F\\) are on edges \\(AB\\) and \\(AC\\) respectively, satisfying \\(BE=3\\) and \\(EF=4\\), and \\(EF \\parallel\\) pla... | math | {
"ground_truth": "2 \\sqrt{33}",
"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": "Outstanding Brazilian footballer Ronaldinho Gaúcho will be $X$ years old in the year $X^{2}$. How old will he be in 2018, when the World Cup is held in Russia?",
"role": "use... | math | {
"ground_truth": "38",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For every positive real pair $(x,y)$ satisfying the equation $x^3+y^4 = x^2y$, find the value of $A/B$ where $A$ is the greatest value of $x$ and $B$ is the greatest v... | math | {
"ground_truth": "\\frac{729}{1024}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute\n\\[\n\\prod_{n=1}^{15} \\frac{n+4}{n}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "3876",
"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 minimal absolute difference \\(|a_1 - b_1|\\) where the number $2030$ is expressed as $\\frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!}$, where $a_1 \\ge a_2 \\ge \\cdots \\ge a... | math | {
"ground_truth": "\\textbf{(B)}\\ 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression $\\sqrt{\\frac{9}{4}} - \\sqrt{\\frac{4}{9}} + \\left(\\sqrt{\\frac{9}{4}} + \\sqrt{\\frac{4}{9}}\\right)^2$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{199}{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": "For the binomial $(1-x)^{10}$, find: \n(1) Which term is the middle term in its expansion? Write down this term; \n(2) Find the sum of the coefficients of all terms in the expa... | math | {
"ground_truth": "210x^{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": "In a checked $ 17\\times 17$ table, $ n$ squares are colored in black. We call a line any of rows, columns, or any of two diagonals of the table. In one step, if at least $ ... | math | {
"ground_truth": "27",
"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 $(a, b)$ and $(c, d)$ are two points on the line whose equation is $y=mx+k$, calculate the distance between $(a, b)$ and $(c, d)$ in terms of $a, c,$ and $m$.",
"role": "u... | math | {
"ground_truth": "|a - c|\\sqrt{1 + m^2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the intersection point of the line \\( y = 3x + 4 \\) and the line perpendicular to it that passes through the point \\( (3, 2) \\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\left(-\\frac{3}{10}, 3.1\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The difference between two numbers is 7, and the sum of the squares of these numbers is 85. What is the value of the product of the two numbers?",
"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": "Find the imaginary part of the complex number $\\frac{3i+4}{1+2i}$.",
"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": "The volume of a right square prism is $8$. Find the minimum volume of the circumscribed sphere of this right square prism.",
"role": "user"
}
] | math | {
"ground_truth": "4 \\sqrt {3}\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive integer factors of $3080$ have more than $5$ factors?\nA) 3\nB) 4\nC) 5\nD) 6\nE) 7",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(B) }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": "Find distinct positive integers $n_1<n_2<\\dots<n_7$ with the least possible sum, such that their product $n_1 \\times n_2 \\times \\dots \\times n_7$ is divisible by $2016$... | math | {
"ground_truth": "31",
"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": "$25$ checkers are placed on $25$ leftmost squares of $1 \\times N$ board. Checker can either move to the empty adjacent square to its right or jump over adjacent right check... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a square \\( A B C D \\) with a side length of 1, point \\( E \\) is located on side \\( A B \\). Draw \\( E F \\) perpendicular to \\( D E \\), intersecting \\( B C \\) at... | math | {
"ground_truth": "\\frac{1}{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": "Below is a diagram showing a $6 \\times 8$ rectangle divided into four $6 \\times 2$ rectangles and one diagonal line. Find the total perimeter of the four shaded trapezoids.... | math | {
"ground_truth": "48",
"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 rope is cut at a random point along its length of 1 meter. What is the probability that the longer piece is at least three times as large as the shorter piece?",
"role": "u... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=\\sin \\left(2x+\\dfrac{\\pi }{6}\\right)$, determine the horizontal shift required to obtain the graph of the function $y=\\sin 2x$.",
"role": "user"
... | 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": "If $\\frac{8^x}{4^{x+y}}=16$ and $\\frac{16^{x+y}}{4^{7y}}=1024$, find $x+y$.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A $4 \\times 4$ square is divided into $16$ unit squares. Each unit square is painted either white or black, each with a probability of $\\frac{1}{2}$, independently. The square ... | math | {
"ground_truth": "\\frac{6561}{65536}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the point $P$ is inside equilateral triangle $ABC$ such that $PA=8$, $PB=6$, and $PC=10$, calculate the area of triangle $ABC$.",
"role": "user"
}
] | math | {
"ground_truth": "79",
"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 plane, two large rectangles intersect each other perpendicularly. The first rectangle has dimensions $4 \\times 15$ and the second one $5 \\times 12$. A smaller third rectan... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the product of the sequence $\\frac{6}{4} \\times \\frac{7}{6} \\times \\frac{8}{7} \\times \\cdots \\times \\frac{2010}{2009}$.\nA) 501.5\nB) 502\nC) 502.5\nD) 503\nE)... | math | {
"ground_truth": "\\textbf{(C)}\\ 502.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the arithmetic sequence $\\{a_n\\}$, the sum of the first $n$ terms is $S_n$. If $S_4=1$ and $S_8=4$, find the value of $a_9+a_{10}+a_{11}+a_{12}$.",
"role": "user"
}... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Isabella's home has 4 bedrooms, each with dimensions 14 feet long, 11 feet wide, and 9 feet high, where doorways and windows occupy 70 square feet and fixed furniture ... | math | {
"ground_truth": "520",
"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 boys and girls must sit alternately, and there are 3 boys. The number of such arrangements is the product of the number of ways to choose 3 positions out of a total of 7, and... | math | {
"ground_truth": "144",
"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 vectors $\\overrightarrow{a} = (1, x)$ and $\\overrightarrow{b} = (x, 4)$, determine the condition for $\\overrightarrow{a} \\parallel \\overrightarrow{b}$ in terms of the ... | 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 sets $A=\\{x|x^2-2x-3>0\\}$, $B=\\{x|x^2+ax+b\\leq0\\}$, if $A\\cup B=\\mathbb{R}$ and $A\\cap B=\\{x|3<x\\leq4\\}$, then the value of $a+b$ equals to.",
"role": "user"... | math | {
"ground_truth": "-7",
"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 arithmetic sequences $\\left(a_n\\right)$ and $\\left(b_n\\right)$ have integer terms with $a_1=b_1=1<a_2 \\le b_2$ and $a_n b_n = 1764$ for some $n$, find the largest... | math | {
"ground_truth": "44",
"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 that becomes a perfect square either by adding 5 or by subtracting 11.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"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 \\(x\\) is a positive number such that \\[\\sqrt{12x}\\cdot\\sqrt{5x}\\cdot\\sqrt{7x}\\cdot\\sqrt{21x}=21,\\] find all possible values for \\(x\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{21}{97}",
"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 derivative of the following functions: \n(1) $y=(x+1)(x+2)(x+3)$ \n(2) $y=2x\\cdot\\tan(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "y'=\\frac{2\\sin(x)\\cos(x)+2x}{\\cos^2(x)}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each positive integer number $n \\ ge 1$ is assigned the number $p_n$ which is the product of all its non-zero digits. For example, $p_6 = 6$ , $p_ {32} = 6$ , $p_ {203} =... | math | {
"ground_truth": "103",
"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": "Moe uses a mower to cut his rectangular $100$-foot by $200$-foot lawn. The swath he cuts is $30$ inches wide, but he overlaps each cut by $6$ inches to ensure no grass is missed.... | 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": "In triangle $XYZ,$ $\\sin X = \\frac{4}{5}$ and $\\cos Y = \\frac{3}{5}.$ Find $\\cos Z.$",
"role": "user"
}
] | math | {
"ground_truth": "\\cos Z = \\frac{7}{25}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ ($a > b > 0$) with one vertex at $A(2,0)$ and an eccentricity of $\\frac{\\sqrt{2}}{2}$. The line $y = x - 1$ inte... | math | {
"ground_truth": "|MN| = \\frac{4\\sqrt{5}}{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": "One hundred musicians are planning to organize a festival with several concerts. In each concert, while some of the one hundred musicians play on stage, the others remain in the ... | math | {
"ground_truth": "9",
"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": "Devon, Ezra, Fiona, and Gabriel are volunteers in their community garden. Their volunteering schedule is as follows: Devon volunteers every second day, Ezra every fifth day, Fion... | math | {
"ground_truth": "990",
"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 area of a parallelogram is 32 square centimeters, and its height is 8 centimeters. Find the length of the base corresponding to this height in centimeters.",
"role": "use... | 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 that vectors $\\overrightarrow{e_{1}}$ and $\\overrightarrow{e_{2}}$ are not collinear, and vector $\\overrightarrow{a} = 2\\overrightarrow{e_{1}} - \\overrightarrow{e_{2}}... | math | {
"ground_truth": "- \\frac{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": "Thirty of King Arthur's knights are seated at their customary round table. Four of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dra... | math | {
"ground_truth": "799",
"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 complex number $z = (m^2 + m - 6) + (m^2 - 3m + 2)i$ where $m \\in \\mathbb{R}$.\n- (I) For what value(s) of $m$ is $z$ a purely imaginary number?\n- (II) If the point ... | math | {
"ground_truth": "-3 < m < 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=|x+1|+|x-1|$.\n(1) Solve the inequality $f(x) < 2x+3$.\n(2) If there exists $x\\_0∈R$ such that the inequality $f(x\\_0)≤m$ holds, find the minimum value... | 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": "A family of sets $ A_1, A_2, \\ldots ,A_n$ has the following properties:\r\n\r**(i)** Each $ A_i$ contains 30 elements.\r**(ii)** $ A_i \\cap A_j$ contains exactly one elem... | math | {
"ground_truth": "61",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the domain of the function $f(x) = \\log_5(\\log_3(\\log_4(x)))$?",
"role": "user"
}
] | math | {
"ground_truth": "(64, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that \\( n \\) is a positive integer and that the set \\( S \\) contains exactly \\( n \\) distinct positive integers. If the mean of the elements of \\( S \\) is equal t... | 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": "In each unit square of square $100*100$ write any natural number. Called rectangle with sides parallel sides of square $good$ if sum of number inside rectangle divided by $1... | math | {
"ground_truth": "10^4 - 16^2",
"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 a volleyball tournament with 5 teams, where there are no ties, each team plays against every other team. The team that finished in 1st place won all their matches. The teams t... | 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": "Two concentric spheres have radii of 4 units and 8 units, respectively. Calculate the volume, in cubic units, of the space that is inside the larger sphere but outside the smalle... | math | {
"ground_truth": "\\frac{1792}{3}\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The ratio of boys to girls in Mrs. Smith's history class is $3:4$. If there are $42$ students in the class, determine how many more girls than boys are in the class.",
"role"... | math | {
"ground_truth": "6",
"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": "Memories all must have at least one out of five different possible colors, two of which are red and green. Furthermore, they each can have at most two distinct colors. If all pos... | math | {
"ground_truth": "\\frac{2}{5}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a mob of kangaroos, the two lightest kangaroos together weigh 25% of the total weight of the mob. The three heaviest kangaroos together weigh 60% of the total weight. How many... | 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": "Let $b_1, b_2, \\dots$ be a sequence defined by $b_1 = 2, b_2 = 3$, and $b_{n+2} = b_{n+1} + 2b_n$ for $n \\geq 1$. Find \\[\n\\sum_{n=1}^\\infty \\frac{b_n}{3^{n+1}}.\n\\]",
... | math | {
"ground_truth": "\\frac{2}{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": "Given the equations of the parabola \\( y = x^2 + 2x - 3 \\) and the horizontal line \\( y = m \\), where \\( -8<m<5 \\), determine the value of \\( s \\) as \\( m \\) approaches... | math | {
"ground_truth": "\\frac{3}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The radius of the circle inscribed in a rhombus is \\( r \\), and the acute angle of the rhombus is \\( \\alpha \\). Find the side length of the rhombus.",
"role": "user"
}... | math | {
"ground_truth": "\\frac{2r}{\\sin(\\alpha)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For every integer \\( n \\geq 2 \\), let \\( f(n) \\) denote the number of distinct solutions of \\( \\sin(nx) = \\sin(x) \\) in the interval \\( [0, \\pi] \\), and \\( g(n) \\) ... | math | {
"ground_truth": "504",
"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 \\(1501C - 3003A = 6006\\), \\(1501B + 4504A = 7507\\), and \\(A + B = 1\\), calculate the average of A, B, and C.",
"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": "Given a hyperbola and an ellipse with the same foci $F\\_1$, $F\\_2$, and a common point $P$. The eccentricity of the ellipse is $\\sin \\frac{\\pi}{4}$. If $\\cos \\angle F\\_1P... | math | {
"ground_truth": "\\frac{\\sqrt{6}}{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 $\\mathbf{a}, \\mathbf{b},$ and $\\mathbf{c}$ be vectors such that $\\|\\mathbf{a}\\| = \\|\\mathbf{b}\\| = 1,$ and $\\|\\mathbf{a} + \\mathbf{b}\\| = \\sqrt{2}$. If \n\\[\n\... | 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 that $a$ is a real number, $z\\_1=2-i$, and $z\\_2=a+i$ ($i$ is the imaginary unit),\n(1) If $a=1$, indicate the quadrant in which the point corresponding to $z\\_1+ \\over... | math | {
"ground_truth": "a=-\\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": "Each of $100$ boxes in a line contains a single red marble, and for $1 \\le k \\le 100$, the box in the $k\\text{th}$ position also contains $k$ white marbles. Karla begins at th... | math | {
"ground_truth": "B) 10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $k$ such that the sum of squares of the first $k$ positive integers, $1^2 + 2^2 + 3^2 + \\ldots + k^2$, is a multiple of $360$.",
"role": "... | math | {
"ground_truth": "72",
"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 $m \\angle A= 60^\\circ$, $BC=10$ units, $\\overline{BD} \\perp \\overline{AC}$, $\\overline{CE} \\perp \\overline{AB}$, and $m \\angle DBC = 4m \\angle ECB$, determin... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The stock of hay is such that 96 kg can be given daily to all the horses. In reality, the daily portion for each horse was increased by 4 kg because two horses were sold. How man... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the degree measure of an angle whose complement is 33.3% (one-third) of its supplement.",
"role": "user"
}
] | math | {
"ground_truth": "45",
"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 real numbers \\( x \\) such that \n\\[\n\\frac{x^3 - 3x^2}{x^2 - 4x + 3} + 2x = 0.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "0, \\frac{2}{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": "Simplify first, then evaluate: $(1-\\frac{1}{m})\\div \\frac{{m}^{2}-2m+1}{m}$, where $m=\\sqrt{3}+1$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{3}}{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": "Calculate the sum of all integers between 100 and 450 that end in 3.\nA) 9030\nB) 9375\nC) 9555\nD) 9740\nE) 9900",
"role": "user"
}
] | math | {
"ground_truth": "The correct answer is **C) 9555**.",
"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 swimmers, at opposite ends of a 120-foot pool, start to swim the length of the pool, one at the rate of 4 feet per second, the other at 3 feet per second. They swim back and ... | math | {
"ground_truth": "26",
"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 rectangular table $ 9$ rows $ \\times$ $ 2008$ columns is fulfilled with numbers $ 1$ , $ 2$ , ..., $ 2008$ in a such way that each number appears exactly $ 9$ times... | 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": "Let \\( c > 0 \\) be a given positive real number and \\( \\mathbb{R}_{>0} \\) be the set of all positive real numbers. Find all functions \\( f: \\mathbb{R}_{>0} \\rightarrow \\... | math | {
"ground_truth": "f(x) = 2x \\text{ for all } x > 0.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The 18-digit number written in the decimal system\n\n$x 3640548981270644 y$\n\nis divisible by 99. Determine the digits $x$ and $y$.",
"role": "user"
}
] | math | {
"ground_truth": "x = 9 \\quad \\text{and} \\quad y = 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 $0 < \\alpha < \\frac{\\pi}{2}$, and $\\sin\\alpha = \\frac{3}{5}$,\n(1) Find the value of $\\frac{2\\sin^{2}\\alpha + \\sin 2\\alpha}{\\cos 2\\alpha}$;\n(2) Find the value... | math | {
"ground_truth": "7",
"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 angle $x$ that satisfies this equation:\n\\[\\sin 4x \\sin 6x = \\cos 4x \\cos 6x\\]\nin degrees.",
"role": "user"
}
] | math | {
"ground_truth": "9^\\circ",
"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": "Consider a pyramid where each number below is the product of the two numbers directly above it. For example, if the topmost numbers are 3 and 2, and the next row down contains on... | math | {
"ground_truth": "\\frac{5}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of sets of three distinct, non-zero digits from the set $\\{1, 2, \\dots, 9\\}$ such that the digits in each set form an arithmetic sequence.",
"role": "user"... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest integer $A$ for which in any permutation of the numbers $1, 2, \\ldots , 100$ there exist ten consecutive numbers whose sum is at least $A$ .",
"role":... | math | {
"ground_truth": "505",
"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": "Point $Q$ is located inside triangle $DEF$ so that angles $QDE, QEF,$ and $QFD$ are all congruent. The sides of the triangle have lengths $DE=15, EF=17,$ and $FD=18.$ Calculate $... | math | {
"ground_truth": "\\tan \\angle QDE = \\frac{216}{419}",
"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 $a$ if $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^{17} + bx^{16} + 1$ .",
"role": "user"
}
] | math | {
"ground_truth": "987",
"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 $ \\int_{ - 1}^1 {n\\choose k}(1 + x)^{n - k}(1 - x)^k\\ dx\\ (k = 0,\\ 1,\\ 2,\\ \\cdots n)$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2^{n+1}}{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": "Let \\( n \\geq 2 \\) be an integer and \\( X \\) be a set with \\( n \\) elements. For a sequence of non-empty subsets \\( A_{1}, A_{2}, \\ldots, A_{k} \\) of \\( X \\), if the ... | math | {
"ground_truth": "2n - 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": "A river is bounded by the lines $x=0$ and $x=25$ , with a current of 2 units/s in the positive y-direction. At $t=0$ , a mallard is at $(0, 0)$ , and a wigeon is at $(25, 0... | math | {
"ground_truth": "\\frac{100}{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": "Let $A_o =\\{1, 2\\}$ and for $n> 0, A_n$ results from $A_{n-1}$ by adding the natural numbers to $A_{n-1}$ which can be represented as the sum of two different numbers f... | math | {
"ground_truth": "a_n = 2^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": "Determine the domain of the function: \n$$k(x) = \\frac{1}{x+7} + \\frac{1}{x^2+1} + \\frac{1}{x^4+16}.$$",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, -7) \\cup (-7, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x = 1+3^p$ and $y = 1+3^{-p}$, determine the expression for $y$ in terms of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x}{x-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": "There are 2010 boxes labeled $B_1,B_2,\\dots,B_{2010},$ and $2010n$ balls have been distributed among them, for some positive integer $n.$ You may redistribute the balls by... | math | {
"ground_truth": "n \\geq 1005",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Expand \\((x^{25} - 5x^7 + 2x^{-3} - 10) \\cdot (-3x^6)\\).",
"role": "user"
}
] | math | {
"ground_truth": "-3x^{31} + 15x^{13} + 30x^6 - 6x^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": "On a Pacific beach, an electronic shark warning system, which on average triggers an alert once a month (specifically, 1 day out of 30), has been installed. The false alarms occu... | math | {
"ground_truth": "64.44\\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For real numbers $a$ and $b$, define $a\\spadesuit b = (a + b)(a - b)$. What is $7\\spadesuit(2\\spadesuit 3)$?\nA) 10\nB) -10\nC) 24\nD) -24\nE) 49",
"role": "user"
}
] | math | {
"ground_truth": "C) 24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the radius of circle $C$ is $5$, the center of the circle is on the $x$-axis, and it is tangent to the line $x=3$, then the equation of circle $C$ is __________.",
"role":... | math | {
"ground_truth": "(x-8)^{2}+y^{2}=25 \\text{ or } (x+2)^{2}+y^{2}=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": "Determine how many positive integers are divisors of both $60$ and $90$, and are also divisors of $30$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ABCD$ is a square where each side measures 4 units. $P$ and $Q$ are the midpoints of $\\overline{BC}$ and $\\overline{CD},$ respectively. Find $\\sin \\phi$ where $\\phi$ is the... | math | {
"ground_truth": "\\frac{3}{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": "How many integer quadruples $a, b, c, d$ are there such that $7$ divides $ab - cd$ where $0\\leq a, b, c, d < 7$?",
"role": "user"
}
] | math | {
"ground_truth": "385",
"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 all pairs of unequal integers \\( m \\) and \\( n \\) such that \\( m^n = n^m \\).",
"role": "user"
}
] | math | {
"ground_truth": "(2, 4), (4, 2), (-2, -4), (-4, -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": "Evaluate $(x - 2b + 5)$ if the value of $x$ is $(2b + 9)$.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"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 sum of the series \\(\\sum_{n=1}^{\\infty} \\frac{1}{n} \\sin(n x)\\).",
"role": "user"
}
] | math | {
"ground_truth": "0 \\text{ when } x = 2k\\pi \\text{ and } \\frac{\\pi - x}{2} + \\left\\lfloor \\frac{x}{2\\pi} \\right\\rfloor \\pi \\text{ in other cases}.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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