data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest number of consecutive integers whose sum is $50$?",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Eyes are the windows of the soul. In order to protect students' eyesight, Qihang High School conducts eye examinations for students every semester. The table below shows the resu... | math | {
"ground_truth": "4.6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the area of a circle where the center is at point $P$ located at (2, 5) and the circle passes through point $Q$ at (6, -1). State your answer in terms of $\\pi$.",
... | math | {
"ground_truth": "52\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 $a$ workers can paint $d$ walls in $g$ days. We want to find the number of days it will take $g$ workers to paint $a$ walls, where each worker now paints with a rate... | math | {
"ground_truth": "\\frac{a^2}{1.25 \\times d}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The product of two factors is 65.08. If one factor is reduced by 100 times, to keep the product unchanged, the other factor should be __.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{increased by 100 times}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\(\\sin ^{2} x \\operatorname{tg} x+\\cos ^{2} x \\operatorname{ctg} x+2 \\sin x \\cos x=\\frac{4 \\sqrt{3}}{3}\\).",
"role": "user"
}
] | math | {
"ground_truth": "x=(-1)^k \\frac{\\pi}{6} + \\frac{\\pi}{2}, \\, k \\in \\mathbb{Z}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two vectors $\\overrightarrow {a}$ and $\\overrightarrow {b}$, where $| \\overrightarrow {a}|=2$ and $| \\overrightarrow {b}|=1$:\n\n1. If $( \\overrightarrow {a}+2 \\overr... | math | {
"ground_truth": "(-7，- \\frac { \\sqrt {14}}{2})∪(- \\frac { \\sqrt {14}}{2}，- \\frac {1}{2})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for $x$ in the equation $24 - 4 = 3 + x$.",
"role": "user"
}
] | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest common factor of all three-digit palindromes where each digit is the same? (Examples of such palindromes include 111, 222, ..., 999.)",
"role": "user"
... | math | {
"ground_truth": "111",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 measure of angle $ACB$ is 60 degrees. If ray $CA$ is rotated 300 degrees about point $C$ in a clockwise direction, what will be the positive measure of the new acute angle $A... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "During a different game session, Ramanujan and Hardy again picked complex numbers. This time, if the product of their numbers was $40-24i$, and Hardy picked $4+4i$, what number d... | math | {
"ground_truth": "2 - 8i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A line $l$ passing through the point $\\left(0, -\\frac{1}{2}\\right)$ intersects the parabola $y = -x^2$ at points $A$ and $B$, with $O$ being the origin. Find the value of $\\o... | math | {
"ground_truth": "-\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 sequence of natural numbers $ a_1 $ , $ a_2 $ , $ \\dots $ , $ a_ {1999} $ , $ a_n-a_ {n-1} -a_ {n-2} $ is divisible by $ 100 (3 \\leq n \\leq 1999) $ . It is known t... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 the correct order of the fractions $\\frac{-16}{12}, \\frac{-18}{14},$ and $\\frac{-20}{15},$ from least to greatest?\nA) $\\frac{-16}{12} < \\frac{-18}... | math | {
"ground_truth": "\\frac{-20}{15} = \\frac{-16}{12} < \\frac{-18}{14}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sherry is waiting for a train. Every minute, there is a $75\\%$ chance that a train will arrive.\nHowever, she is engrossed in her game of sudoku, so even if a train arrives sh... | math | {
"ground_truth": "0.718",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( N \\) be a natural number greater than 3 that has the following property: no matter how the set \\( S_n = \\{1, 2, \\cdots, n\\} \\) is partitioned into two groups, there... | math | {
"ground_truth": "243",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n\\geq 3$ be an integer. Find the number of ways in which one can place the numbers $1, 2, 3, \\ldots, n^2$ in the $n^2$ squares of a $n \\times n$ chesboard, one on... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a store advertises a promotion: \"Buy three bags at the regular price and get the fourth bag for $5\", and Jessica paid $305 for four bags during this sale, calculate ... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 polynomials $P_{n}(x)$ are defined by $P_{0}(x)=0,P_{1}(x)=x$ and \\[P_{n}(x)=xP_{n-1}(x)+(1-x)P_{n-2}(x) \\quad n\\geq 2\\] For every natural number $n\\geq 1$ , find a... | math | {
"ground_truth": "x = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 what point does the line containing the points $(2, 9)$ and $(5, 21)$ intersect the $y$-axis? Express your answer as an ordered pair.",
"role": "user"
}
] | math | {
"ground_truth": "(0, 1)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 base $5$ number $32$ is equal to the base $7$ number $23$ . There are two $3$ -digit numbers in base $5$ which similarly have their digits reversed when expressed i... | math | {
"ground_truth": "153",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 $g(x) = \\frac{x - 8}{\\sqrt{x^2 - 5x + 6}}$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 2) \\cup (3, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Fifteen percent of what number is sixty?",
"role": "user"
}
] | math | {
"ground_truth": "400",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 vectors $\\overrightarrow{a}=(1,2)$, $\\overrightarrow{b}=(0,-2)$, $\\overrightarrow{c}=(-1,\\lambda)$, determine the value of the real number $\\lambda$ if $(2\\overrighta... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 average running times of sixth graders, seventh graders, and eighth graders as 20, 18, and 22 minutes per day, respectively, where the ratio of the number of sixth grad... | math | {
"ground_truth": "19.67",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 right triangle has legs measuring 8 units and 15 units. What is the length of the hypotenuse?",
"role": "user"
}
] | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $\\frac{3^4 \\times 5^2 \\times 7^3 \\times 11}{7 \\times 11^2}$?",
"role": "user"
}
] | math | {
"ground_truth": "9025",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Values for \\(A, B, C, D,\\) and \\(E\\) are to be selected from \\(\\{1, 2, 3, 4, 5, 6, 7, 8\\}\\) without replacement, where \\(E\\) represents a horizontal shift. Determine ho... | math | {
"ground_truth": "The final answer, given the choices, is \\(C) 50.\\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $R_k$ is a number consisting of $k$ consecutive ones, calculate the number of zeros in the decimal representation of \\(Q + S\\) where \\(Q = \\frac{R_{32}}{R_8}\\) an... | math | {
"ground_truth": "E) 29",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 percent that $M$ is greater than $N$ is:\n$(\\mathrm{A})\\ \\frac{100(M-N)}{M} \\qquad (\\mathrm{B})\\ \\frac{100(M-N)}{N} \\qquad (\\mathrm{C})\\ \\frac{M-N}{N} \\qquad (\\m... | math | {
"ground_truth": "\\mathrm{(B)}\\ \\frac{100(M-N)}{N}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the sides of a right triangle with a perimeter equal to $2p$ and an area equal to $m^2$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{p^2 - m^2}{p}; \\frac{p^2 + m^2 \\pm \\sqrt{(p^2 + m^2)^2 - 8p^2m^2}}{2p}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\(O A\\) in the case of an equilateral triangle as a function of the side length.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{AB}{\\sqrt{3}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the following:<br/>$(1)$ Calculate: $-\\sqrt{16}÷|-2|+\\sqrt[3]{27}$;<br/>$(2)$ Solve the system of linear equations: $\\left\\{\\begin{array}{l}2x-y=7①\\\\ 3x+2y=0②\\end{ar... | math | {
"ground_truth": "\\left\\{\\begin{array}{l}x=2\\\\ y=-3\\end{array}\\right.}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 a nonnegative integer $n$ and a strictly increasing sequence of real numbers $t_0, t_1, \\ldots, t_n$ , let $f(t)$ be the corresponding real-valued function defined for ... | math | {
"ground_truth": "89",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of $$ \\sum_{1\\le a<b<c} \\frac{1}{2^a3^b5^c} $$ (i.e. the sum of $\\frac{1}{2^a3^b5^c}$ over all triples of positive integers $(a, b, c)$ satisfying $a<... | math | {
"ground_truth": "\\frac{1}{406}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the Dogwood Animal Shelter received 100 adult cats of which 40% were female, and two-thirds of the adult female cats were accompanied by a litter of kittens with an av... | math | {
"ground_truth": "181",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $f(x)=ax-\\frac{2a}{x}-3\\ln x$.\n\n(1) Find the value of the real number $a$ if the function $f(x)$ has an extreme value at $x=1$.\n\n(2) Under the condition ... | math | {
"ground_truth": "f(1)=-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let's define integers $X$, $Y$, and $Z$ which are relatively prime such that:\n\\[X \\log_{500} 5 + Y \\log_{500} 2 = Z.\\]\nFind the value of $X + Y + Z$.\nA) 4\nB) 5\nC) 6\nD) ... | math | {
"ground_truth": "C) 6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 triangle $ABC$ with incenter $I$ and circumcircle $\\Gamma$ satisfy $AB = 6\\sqrt{3}, BC = 14,$ and $CA = 22$ . Construct points $P$ and $Q$ on rays $BA$ and ... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of $1000$ elves has a hat, red on the inside and blue on the outside or vise versa. An elf with a hat that is red outside can only lie, and an elf with a hat that is blue ... | math | {
"ground_truth": "998",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $\\sqrt{2}(\\sqrt{2}+2)-\\sqrt[3]{8}$",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 $\\log_8 x=3$, calculate the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "512",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The product of the two $101$-digit numbers $707,070,707,...,070,707$ and $909,090,909,...,090,909$ has hundreds digit $C$ and units digit $D$. What is the sum of $C$ and $D$?\nA)... | math | {
"ground_truth": "B) 7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points $A$ and $B$ are selected on the graph of $y = -x^2$ so that triangle $ABO$ is isosceles with $AB = AO = BO$. Determine the length of one side of triangle $ABO$.",
"rol... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 least possible value of the natural number $n$ such that $n!$ ends in exactly $1987$ zeros.\n\n<details><summary>Note</summary>Note. Here (and generally in Ma... | math | {
"ground_truth": "7960",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $\\dfrac{\\frac{1}{4}-\\frac{1}{6}}{\\frac{1}{3}-\\frac{1}{4}}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for $y$: $6(4y - 1) - 3 = 3(2 - 5y)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 $3x + 6x + 9x + 12x + 15x + 18$.",
"role": "user"
}
] | math | {
"ground_truth": "45x + 18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of 8 balls is randomly and independently painted either black or white with equal probability. Calculate the probability that every ball is different in color from at least ... | math | {
"ground_truth": "\\frac{35}{128}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $f(\\sin x) = \\cos 3x$, find the value of $f(\\cos 10^\\circ)$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bill plays a game in which he rolls two fair standard six-sided dice with sides labeled one through six. He wins if the number on one of the dice is three times the number on the... | math | {
"ground_truth": "\\frac{217}{729}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 the legs of a right triangle are in the ratio $3:4$, find the ratio of the areas of the two triangles created by dropping an altitude from the right-angle vertex to the hypote... | math | {
"ground_truth": "\\frac{9}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 prime number $p$ . A positive integer $x$ is divided by $p$ with a remainder, and the number $p^2$ is divided by $x$ with a remainder. The remainders turned out ... | math | {
"ground_truth": "(x, p) = (p, p), (p^2, p), (p + 1, p)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each student in Mr. Gray's class is tasked to draw a rectangle with integer side lengths and a perimeter of 60 units. Students then calculate the area of the rectangles they have... | math | {
"ground_truth": "\\textbf{(D)}\\ 196",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 Bank of Pittsburgh issues coins that have a heads side and a tails side. Vera has a row of 2023 such coins alternately tails-up and heads-up, with the leftmost coin tails-up.... | math | {
"ground_truth": "4044",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 quadrilateral is inscribed in a circle with a radius of $150\\sqrt{3}$. Three sides of this quadrilateral are each $150$ units long. Find the length of the fourth side.",
"... | math | {
"ground_truth": "450",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $f(x)$ be an odd function defined on $[-1,1]$. The function $g(x)$ is symmetric with $f(x)$ about the $y$-axis, and when $x \\in (0,1)$, $g(x)=\\ln x - ax^2$.\n\n1. Find the ... | math | {
"ground_truth": "a \\geqslant \\frac{e}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $120^{\\circ}$, and their magnitudes are $|\\overrightarrow{a}|=2$ and $|\\overrightarrow{... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 diagonals of the inscribed quadrilateral $ABCD$ intersect at the point $P$, and the triangle $APD$ is acute-angled. Points $E$ and $F$ are the midpoints of sides $AB$ and $CD... | math | {
"ground_truth": "90^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers $1, 2, 3, 4, 6$ are to be arranged in a circle. An arrangement is considered $\\textit{bad}$ if it is not true that for every $n$ from $1$ to $20$ one can find a subs... | math | {
"ground_truth": "C) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 sum of the series $1 - 2 + 3 - 4 + \\cdots - 100 + 101$.\n- **A)** 49\n- **B)** 50\n- **C)** 51\n- **D)** 52\n- **E)** 53",
"role": "user"
}
] | math | {
"ground_truth": "**C)** 51",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $XYZ$, $XY = XZ = 120$, and $YZ = 80$. Circle $R$ has radius $20$ and is tangent to $\\overline{XZ}$ and $\\overline{YZ}$. Circle $S$ is externally tangent to $R$ and... | math | {
"ground_truth": "224",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an equilateral triangle $ABC$ with side length $1$, point $E$ is on $AC$, and $\\overrightarrow{AC}=4\\overrightarrow{AE}$. Point $P$ is on $BE$, and it satisfies $\\overright... | math | {
"ground_truth": "\\frac{ \\sqrt{7}}{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 base of a pyramid is a rectangle with an area of \\( S \\). Two of the lateral faces are perpendicular to the base, and the other two are inclined at angles of \\( 30^{\\circ... | math | {
"ground_truth": "\\frac{S \\sqrt{S}}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Fifty slips are placed into a hat, each bearing a number from 1 to 10, with each number entered on five slips. Five slips are drawn from the hat at random and without replacement... | math | {
"ground_truth": "450",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 the ellipse $\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1$ find the point $T=(x_0,y_0)$ such that the triangle bounded by the axes of the ellipse and the tangent at that point has ... | math | {
"ground_truth": "\\left( \\pm \\frac{a}{\\sqrt{2}}, \\pm \\frac{b}{\\sqrt{2}} \\right)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 $\\log_3 x^3 + \\log_9 x + \\log_{27} x = 10,$ compute $x.$",
"role": "user"
}
] | math | {
"ground_truth": "3^{\\frac{60}{23}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the equations \\(x^{2} + ax + b = 0\\) and \\(x^{2} + px + q = 0\\) have a non-zero common root, find the quadratic equation with their distinct roots as its roots.",
"rol... | math | {
"ground_truth": "x^2 - \\frac{(b+q)(a-p)}{q-b} x + \\frac{b q(a-p)^{2}}{(q-b)^{2}} = 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a>1$ be a constant. In the $xy$ -plane, let $A(a,\\ 0),\\ B(a,\\ \\ln a)$ and $C$ be the intersection point of the curve $y=\\ln x$ and the $x$ -axis. Denote by $... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $390$ can be written as the sum of an increasing sequence of two or more consecutive even integers, calculate the number of such ways.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many real roots does the polynomial $x^5 + x^4 - x^3 - x^2 - 2x - 2$ have? $ \n\\textbf{a)}\\ 1\n\\qquad\\textbf{b)}\\ 2\n\\qquad\\textbf{c)}\\ 3\n\\qquad\\textbf{d)}\\ 4\n... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 the equation \\(\\sqrt{a x^{2}+a x+2}=a x+2\\) has exactly one real root, what is the range of values for the real number \\(a\\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\{ -8 \\} \\cup [1, +\\infty)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the number of bijective functions $f:\\{0,1,\\dots,288\\}\\rightarrow\\{0,1,\\dots,288\\}$ such that $f((m+n)\\pmod{17})$ is divisible by $17$ if and only if ... | math | {
"ground_truth": "270",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 center of the base of a regular triangular pyramid as point $O$ and the points of intersection of a moving plane $QRS$ with the three lateral edges or their extensions ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define the operation \"*\":\n$$\na * b=\\log _{2}\\left(2^{a}+2^{b}\\right)(a 、 b \\in \\mathbf{R})\n$$\n\nLet \\( A = (1 * 3) * 5 \\) and \\( B = (2 * 4) * 6 \\). Find the value... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\\\(x_1\\\\) and \\\\(x_2\\\\) be the two real roots of the equation \\\\(5x^{2}-3x-2=0\\\\). The value of \\\\( \\dfrac {1}{x_1}+ \\dfrac {1}{x_2}\\\\) is \\_\\_\\_\\_\\_\\... | math | {
"ground_truth": "- \\dfrac {3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the simplest form of \\[1 - \\frac{2}{1 + \\frac{2a}{1 - 2a}}.\\]\n**A)** $2a - 1$ for all $a$\n**B)** $4a - 2$ if $a \\neq \\frac{1}{2}$\n**C)** $4a - 1$ if $a \\neq \\... | math | {
"ground_truth": "a \\neq \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 binary operation $\\diamondsuit$ defined by $a \\diamondsuit b = \\frac{a}{b}$ for all nonzero real numbers $a$ and $b$, solve the equation $504 \\diamondsuit (7 \\diamon... | math | {
"ground_truth": "\\frac{175}{84}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 circle $(x-1)^2+(y-2)^2=1$, find the value of the real number $b$ such that the circle is symmetric about the line $y=x+b$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 day, a truck driver drove through a tunnel and measured the time taken between the moment at which the truck started entering the tunnel and the moment at which the truck lef... | math | {
"ground_truth": "24 \\text{ meters}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the equation $x^{2}-4x+m=0$ has two equal real roots with respect to $x$, determine the value of $m$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 factory has several workshops. Today, a stratified sampling method is used to select a sample of 128 items from 2048 products produced by the entire factory for quality inspect... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sasha rides a scooter and Galya rides a hoverboard. Uphill, Sasha rides her scooter at a speed of 8 km/h, and downhill at a speed of 24 km/h. Galya rides her hoverboard uphill at... | math | {
"ground_truth": "\\text{On her 11-th lap, Galya overtakes Sasha on his 10-th lap.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(ABCD\\) be a square of side length 2. Points \\(X, Y, and Z\\) are constructed inside \\(ABCD\\) such that \\(ABX, BCY\\), and \\(CDZ\\) are equilateral triangles. Point \... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It is known that for every integer $n > 1$ there is a prime number among the numbers $n+1,n+2,...,2n-1.$ Determine all positive integers $n$ with the following property: Ev... | math | {
"ground_truth": "2, 4, 6, 8, 30",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 number $15!$ has a certain count of positive integer divisors. One of them is chosen at random. What is the probability that it is odd?\nA) $\\frac{1}{10}$\nB) $\\frac{1}{11}... | math | {
"ground_truth": "\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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's define $n_a!$ where $n$ and $a$ are positive integers as \\[n_a! = n(n-a)(n-2a)...(n-ka)\\], where $k$ is the highest integer such that $n > ka$. Find the value of $\\frac{... | math | {
"ground_truth": "\\textbf{(B)}\\ 103680",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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)** Find all real numbers $a$ such that the parabola $y=x^2-a$ and the hyperbola $y=1/x$ intersect each other in three different points.**b)** Find the locus of centers ... | math | {
"ground_truth": "x = \\frac{1}{2}, y < \\frac{2 - 3\\sqrt[3]{2}}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 $x+y+z$ when $$ a_1x+a_2y+a_3z= a $$ $$ b_1x+b_2y+b_3z=b $$ $$ c_1x+c_2y+c_3z=c $$ Given that $$ a_1\\left(b_2c_3-b_3c_2\\right)-a_2\\left(b_1c_3-b_3c_1\\right... | math | {
"ground_truth": "\\frac{16}{9}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 geometric sequence with positive terms {an}, it is given that a6 - a4 = 24 and a3a5 = 64. Find the sum of the first 8 terms of {an}.",
"role": "user"
}
] | math | {
"ground_truth": "255",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $\\overrightarrow{a}=({-4,3})$, $\\overrightarrow{b}=({5,12})$, calculate the projection vector of vector $\\ov... | math | {
"ground_truth": "\\left( -\\frac{64}{5}, \\frac{48}{5} \\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Different letters represent different non-zero digits, and the same letters represent the same digits. If $\\overline{\\mathrm{AB}} \\times \\overline{\\mathrm{CB}} = \\overline{... | math | {
"ground_truth": "2, 7, 3, 9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$2023$ players participated in a tennis tournament, and any two players played exactly one match. There was no draw in any match, and no player won all the other players. If a p... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 sequence \\(\\{a_n\\}\\):\n\\[1,1,2,1,2,3,\\cdots, 1,2,\\cdots, n,\\cdots\\]\n\nLet \\(S_n\\) denote the sum of the first \\(n\\) terms of the sequence \\(\\{a_n\\}\\).... | math | {
"ground_truth": "\\left( \\frac{3}{2}, \\frac{\\sqrt{2}}{3} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x, y, z$ and $3x + \\frac{y}{3} + 2z$ are not zero, simplify the expression: $\\left(3x + \\frac{y}{3} + 2z\\right)^{-1} \\left[\\left(3x\\right)^{-1} + \\left(\\frac{y}{3... | math | {
"ground_truth": "\\frac{2y + 18xz + 3zx}{6xyz(9x + y + 6z)}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For positive integral $k>1$ , we let $p(k)$ be its smallest prime divisor. Given an integer $a_1>2$ , we define an infinite sequence $a_n$ by $a_{n+1}=a_n^n-1$ for each ... | math | {
"ground_truth": "\\text{all odd values of } a_1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 quadratic equation \\( 3x^2 + 4x + 5 = 0 \\) with roots \\( u \\) and \\( v \\), another quadratic equation \\( x^2 + mx + n = 0 \\) has roots \\( u^2+1 \\) and \\( v^2... | math | {
"ground_truth": "-\\frac{4}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 Ben spent x dollars on cookies, and for every dollar Ben spent, David spent 50 cents (or 0.5 dollars) less, how much did they spend in total?",
"role": "user"
}
... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 train passes a bystander in $t_{1}$ seconds, and at the same speed it crosses a bridge of length $a$ meters in $t_{2}$ seconds. Find the length and speed of the train.",
"r... | math | {
"ground_truth": "l = \\frac{t_{1} a}{t_{2} - t_{1}}, \\quad v = \\frac{a}{t_{2} - t_{1}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $F_1$ and $F_2$ be the left and right foci of the ellipse $\\frac{x^2}{3} + y^2 = 1$, respectively. Points $A$ and $B$ are on the ellipse. If $\\overrightarrow{F_1A} = 5\\ove... | math | {
"ground_truth": "(0, \\pm1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
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