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": "In the West Lake of Goose City, one lake has a pair of swans plus two more swans, and one lake has three swans minus three swans. How many swans are there in total?",
"role":... | math | {
"ground_truth": "12",
"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": "Each student inputs a natural number into a calculator, starting with 1 for the first student, 2 for the second student, and so on. The calculator's keys for numbers 4 and 8 are ... | math | {
"ground_truth": "155",
"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": "A 2-kilogram model of a sports car body made of aluminum was created in a 1:8 scale. What is the mass of the actual car body, assuming it is also made entirely of aluminum?",
... | math | {
"ground_truth": "1024 \\, \\text{kg}",
"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": "A number is formed by repeating a three place number, find the common divisor for any number of this form.",
"role": "user"
}
] | math | {
"ground_truth": "1001",
"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": "In the same right triangle $ABC$ with $\\angle A = 90^\\circ$, where $AB =16$ and $BC = 24$, find $\\tan B$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{2}",
"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": "Let \\(a, b,\\) and \\(c\\) be three distinct numbers. Solve the system\n\n$$\n\\left\\{\\begin{aligned}\nz + ay + a^{2}x + a^{3} &= 0 \\\\\nz + by + b^{2}x + b^{3} &= 0 \\\\\nz ... | math | {
"ground_truth": "2^{49}",
"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 that Mindy made four purchases for $\\textdollar 2.47$, $\\textdollar 7.51$, $\\textdollar 11.56$, and $\\textdollar 4.98$, find her total, to the nearest dollar.",
"ro... | math | {
"ground_truth": "27",
"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": "<details><summary>D stands for Dedekind, Z stands for Zermelo</summary>they had two problem sets under those two names</details> \n\n\n<u>Set 4</u>**D16.** The cooking club at B... | math | {
"ground_truth": "58",
"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 all functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ from $C^2$ (id est, $f$ is twice differentiable and $f''$ is continuous.) such that for every real number $t... | math | {
"ground_truth": "f(x) = e^{cx^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": "Let $S=\\{1,2,3,\\cdots,100\\}$ . Find the maximum value of integer $k$ , such that there exist $k$ different nonempty subsets of $S$ satisfying the condition: for any two ... | math | {
"ground_truth": "2^{99} - 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": "A 50-foot tree next to Bob is casting a 25-foot shadow. How tall, in feet, is Bob if he is casting a 6-foot shadow at the same time?",
"role": "user"
}
] | math | {
"ground_truth": "144",
"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": "Evaluate the expression $\\sqrt{80} - 3\\sqrt{20} + \\frac{\\sqrt{500}}{\\sqrt{5}} + 2\\sqrt{45}$.",
"role": "user"
}
] | math | {
"ground_truth": "4\\sqrt{5} + 10",
"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\\) and \\(b\\) are positive reals and \\(a > b\\). Let \\(C\\) be the plane curve given by \\(r = a - b \\cos \\theta\\). For what values of \\(\\frac{b}{a}\\) is \\(C\\) co... | math | {
"ground_truth": "\\frac{b}{a} \\leq \\frac{1}{2}",
"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 Cesàro sum of a 99-term sequence $(p_{1},p_{2},…,p_{99})$ is 1000, determine the Cesàro sum of the 100-term sequence $(9,p_{1},p_{2},…,p_{99})$.",
"role": "user"
}
] | math | {
"ground_truth": "999",
"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 $O$ is the origin, vector $\\overrightarrow{OA}=(-1,2)$, and $\\overrightarrow{BA}=(3,3)$, find the coordinates of point $B$.",
"role": "user"
}
] | math | {
"ground_truth": "(-4,-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": "What is the residue of $15^{1234}$, modulo 19?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"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": "Let $\\star$ be an operation defined in the set of nonnegative integers with the following properties: for any nonnegative integers $x$ and $y$ ,\n(i) $(x + 1)\\star 0 = (0... | math | {
"ground_truth": "579",
"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 that squares to $9$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\pm 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": "In triangle $DEF$, $DE = 4$, $DF = 6$, and $EF = 5$. The medians $DG$, $EH$, and $FI$ of triangle $DEF$ intersect at the centroid $J$. Let the projections of $J$ onto $EF$, $DF$,... | math | {
"ground_truth": "4.07888",
"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": "For which values of the parameter \\( a \\) does the equation \\( f(x) = p(x) \\) have one solution, if \\( f(x) = \\left|\\frac{2 x^{3}-5 x^{2}-2 x+5}{(1.5 x-3)^{2}-(0.5 x-2)^{2... | math | {
"ground_truth": "-10",
"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 $\\clubsuit(x)$ denote the sum of the digits of the positive integer $x$. For example, $\\clubsuit(8)=8$ and $\\clubsuit(123)=1+2+3=6$. For how many two-digit values of $x$ i... | math | {
"ground_truth": "10",
"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": "a) Derive Vieta's formula from the result of problem 137.\n\nb) What is the value of the infinite product\n\n$$\n\\begin{aligned}\n& \\frac{1}{2} \\cdot \\sqrt{\\frac{1}{2}+\\fra... | math | {
"ground_truth": "\\frac{3}{4\\pi}",
"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": "Determine the set of all $x$ for which the inequality $\\frac{x^3 - x^2 - 6x}{x^2 - 3x + 2} > 0$ holds.\nA) $x < -2$ or $-1 < x < 1$ or $x > 2$\nB) $x < -1$ or $x > 3$\nC) $-2 < ... | math | {
"ground_truth": "x > 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": "Is there a constant $m, n$ that makes the function $f(x) = (m^2-1)x^2 + (m-1)x + n + 2$ an odd function? If so, find the values of $m$ and $n$.",
"role": "user"
}
] | math | {
"ground_truth": "m = \\pm 1, n = 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": "A $ 1$ by $ 1$ square $ABCD$ is inscribed in the circle $m$ . Circle $n$ has radius $1$ and is centered around $A$ . Let $S$ be the set of points inside of $m$ bu... | math | {
"ground_truth": "\\frac{\\pi}{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 the equation of the directrix of the parabola $y = \\frac{x^2 - 4x + 3}{8}$.",
"role": "user"
}
] | math | {
"ground_truth": "y = -\\frac{9}{8}",
"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 $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If $a + b + c = 20$, the area of the triangle is $10\\sqrt{3}$, and $A = 60^{\\cir... | math | {
"ground_truth": "7",
"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 equation $\\frac{P}{8} = \\frac{8}{Q}$, where P and Q are positive integers, determine the number of ordered pairs (P, Q) that satisfy this equation.",
"role": "use... | math | {
"ground_truth": "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": "Find the number of pairs of integers \\((x, y)\\) that satisfy the system of inequalities\n\n$$\n\\left\\{\\begin{array}{l}\ny \\geqslant 80 + x - 7^{80} \\\\\ny \\leqslant \\log... | math | {
"ground_truth": "\\frac{1}{2} \\cdot 7^{160} - \\frac{2}{3} \\cdot 7^{80} + \\frac{487}{6}",
"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 area of a triangle with side lengths 7, 8, and 10.",
"role": "user"
}
] | math | {
"ground_truth": "39.335",
"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": "Compute \\(12 \\cdot \\left(\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{6}\\right)^{-1}\\).",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let $a$ and $b$ be positive integers such that $2a - 9b + 18ab = 2018$ . Find $b - a$ .",
"role": "user"
}
] | math | {
"ground_truth": "223",
"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": "Seven distinct integers are picked at random from $\\{1, 2, 3, \\ldots, 12\\}$. What is the probability that, among those selected, the third smallest is $5$?",
"role": "user... | math | {
"ground_truth": "\\frac{35}{132}",
"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 an integer $n \\ge 2$ , determine the number of ordered $n$ -tuples of integers $(a_1, a_2,...,a_n)$ such that\n(a) $a_1 + a_2 + .. + a_n \\ge n^2$ and\n(b) $a_1^2 ... | math | {
"ground_truth": "a_i = n \\text{ for all } 1 \\le i \\le n",
"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": "Four circles of radius $r = 2$ are externally tangent to each other and internally tangent to a larger circle. What is the radius of the larger circle? Express your answer in sim... | math | {
"ground_truth": "4\\sqrt{2} + 2",
"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": "An isosceles trapezoid has legs each 20 cm, two diagonals each 25 cm, and the longer base is 30 cm. Calculate the area of the trapezoid in square centimeters.",
"role": "user... | math | {
"ground_truth": "315.82 \\text{ cm}^2",
"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": "Consider all line segments of length 4 with one end-point on the line $y=x$ and the other end-point on the line $y=2x$ . Find the equation of the locus of the midpoints of the... | math | {
"ground_truth": "25x^2 - 36xy + 13y^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 the equation of the line that passes through the point P(2,3) and has intercepts on the axes that are opposite in sign.",
"role": "user"
}
] | math | {
"ground_truth": "B: x-y+1=0 \\text{ or } 3x-2y=0",
"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": "How many positive factors of 180 are also multiples of 15?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"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": "Martha writes down a random mathematical expression consisting of 3 single-digit positive integers with an addition sign \" $+$ \" or a multiplication sign \" $\\times$ \" betwee... | math | {
"ground_truth": "50",
"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": "We spill the content of a box of paprika-flavored and a box of bear's garlic-flavored, eight-slice Maci cheese onto a table, then put the 16 small cheese slices (with their label... | math | {
"ground_truth": "234",
"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 all triples $ \\left(p,x,y\\right)$ such that $ p^x\\equal{}y^4\\plus{}4$ , where $ p$ is a prime and $ x$ and $ y$ are natural numbers.",
"role": "user"
}
] | math | {
"ground_truth": "(5, 1, 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": "Compute $2021 \\cdot 2022 \\cdot 2023 \\cdot 2024$ modulo 7.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 sides of a triangle are $35$, $85$, and $90$ units, find the length of the larger segment cut off by an altitude dropped upon the side of length $90$.",
"role": "user"... | math | {
"ground_truth": "78.33",
"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": "Determine the largest possible natural number \\( n \\) for which there are \\( n \\) different subsets of \\( S = \\{1,2, \\ldots, 2017\\} \\) such that the union of no two of t... | math | {
"ground_truth": "2^{2016}",
"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": "In how many ways can the number 1024 be factored into three natural factors such that the first factor is a multiple of the second, and the second is a multiple of the third?",
... | math | {
"ground_truth": "14",
"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": "What is the correct ordering of the three numbers, $10^9$, $5^{13}$, and $3^{15}$?",
"role": "user"
}
] | math | {
"ground_truth": "3^{15} < 10^9 < 5^{13}",
"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": "If Xiluva puts two oranges in each basket, four oranges are in excess. If she puts five oranges in each basket, one basket is in excess. How many oranges and baskets has Xiluva?"... | math | {
"ground_truth": "o = 10",
"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 LeRoy and Bernardo split costs equally, with LeRoy paying $A$ dollars and Bernardo paying $B$ dollars, calculate the amount LeRoy must give to Bernardo for them to sha... | math | {
"ground_truth": "\\frac{B - A}{2}",
"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": "A container in the shape of a right circular cone is 12 inches tall and its base has a 5-inch radius. The liquid that is sealed inside is 9 inches deep when the cone is held with... | math | {
"ground_truth": "52",
"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 parabola \\( C: x^{2} = 2py \\) with \\( p > 0 \\), two tangents \\( RA \\) and \\( RB \\) are drawn from the point \\( R(1, -1) \\) to the parabola \\( C \\). The poin... | math | {
"ground_truth": "3 \\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": "Given the proposition \"$\\exists x \\in \\mathbb{R}$, $x^{2}+2ax+1 < 0$\" is true, the range of values for the real number $a$ is _______.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty,-1)\\cup(1,+\\infty)",
"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": "How many minutes before 16:00 was the angle between the hour and minute hands exactly the same as it is at 16:00?",
"role": "user"
}
] | math | {
"ground_truth": "21 \\frac{9}{11} \\approx 21.82 \\text{ minutes}",
"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": "Consider parabolas $C_a: y=-2x^2+4ax-2a^2+a+1$ and $C: y=x^2-2x$ in the coordinate plane.\nWhen $C_a$ and $C$ have two intersection points, find the maximum area enclosed... | math | {
"ground_truth": "\\frac{27}{4\\sqrt{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": "We know that there exists a positive integer with $7$ distinct digits which is multiple of each of them. What are its digits?\n\n(Paolo Leonetti)",
"role": "user"
}
] | math | {
"ground_truth": "\\{1, 2, 3, 6, 7, 8, 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": "What is the area enclosed by the graph of the equation $(x - 1)^2 + (y - 1)^2 = |x - 1| + |y - 1|$?\nA) $\\frac{\\pi}{4}$\nB) $\\frac{\\pi}{2}$\nC) $\\frac{\\pi}{3}$\nD) $\\pi$",... | math | {
"ground_truth": "\\frac{\\pi}{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": "Calculate: \\((128)^{\\frac47}\\).",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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": "Six test scores have a mean of 85, a median of 88, and a mode of 90. The highest score exceeds the second highest by 5 points. Find the sum of the three highest scores.",
"ro... | math | {
"ground_truth": "275",
"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": "Passing through the origin of the coordinate plane are $180$ lines, including the coordinate axes,\nwhich form $1$ degree angles with one another at the origin. Determine the... | math | {
"ground_truth": "8950",
"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 proposition $p$: For $m \\in [-1,1]$, the inequality $a^{2}-5a-3 \\geqslant \\sqrt{m^{2}+8}$ always holds; proposition $q$: The inequality $x^{2}+ax+2 < 0$ has a solution. ... | math | {
"ground_truth": "-2\\sqrt{2} \\leqslant a \\leqslant -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 set $A=\\{-1, 1, 3\\}$ and set $B = \\{a + 2, a^2 + 4\\}$. If $A \\cap B = \\{3\\}$, then the real number $a = \\_\\_\\_\\_\\_.$",
"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": "In $\\triangle ABC$, the ratio $AC:CB$ is $2:3$. The bisector of the internal angle at $C$ intersects $AB$ at point $D$. Find the ratio $AD:DB$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{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": "If the inequality $mx^{2}+mx-4 \\lt 2x^{2}+2x-1$ holds for any real number $x$, determine the range of real number $m$.",
"role": "user"
}
] | math | {
"ground_truth": "(-10,2]",
"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": "If $3$ is a solution (root) of $x^3 + hx + 5 = 0$, determine the value of $h$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{32}{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": "The sum of three integers is $36$. When three more integers are added to the first three, the sum becomes $60$. Finally, when two more integers are added to the sum of the previo... | 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": "Given the sum of three numbers is 30, where one number is twice the sum of the other two, and the second number is five times the third, find the product of all three numbers.",
... | math | {
"ground_truth": "\\frac{2500}{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": "If the sum of two numbers is 1 and their product is 1, calculate the sum of their cubes.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"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 $g(x) = 3^x + 2$, find the value of $g(x+1) - g(x)$.\nA) $2g(x) - 2$\nB) $g(x) + 2$\nC) $3g(x) - 2$\nD) $2g(x) + 2$",
"role": "user"
}
] | math | {
"ground_truth": "2g(x) - 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 regular tetrahedron $OABC$ with side length 1. Let $D,\\ E$ be the midpoints of the sides $AB,\\ OC$ respectively.\nFind the scalar product of two vectors $\\overr... | math | {
"ground_truth": "\\frac{7}{6}",
"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": "(1) The negation of the proposition: \"There exists $x_0 > -1$ such that $x_0^2+x_0-2018 > 0$\" is _______________.\n\n(2) The standard equation of the ellipse passing through $A... | math | {
"ground_truth": "5",
"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": "What is the value of $\\frac{3a^{-2} + \\frac{a^{-3}}{3}}{a^2}$ when $a = 3$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{28}{729}",
"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": "Determine the number of angles between 0 and $2 \\pi,$ excluding integer multiples of $\\frac{\\pi}{2},$ such that $\\sin^2 \\theta,$ $\\cos \\theta$, and $\\tan \\theta$ form a ... | math | {
"ground_truth": "2",
"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": "Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike, and bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on h... | math | {
"ground_truth": "11:00",
"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": "In $\\triangle ABC$, the side lengths opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $a^2$, $b^2$, and $c^2$ form an arithmetic sequenc... | math | {
"ground_truth": "2 \\text{ or } \\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": "For a more concentrated lemonade, I use a ratio of $4$ parts water to $1$ part lemon juice. If I want to make $3$ gallons of lemonade, and there are four quarts in each gallon, h... | math | {
"ground_truth": "9.6",
"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 that Ella has 18 coins, all of which are nickels and dimes, and two more dimes than nickels results in a ratio of nickels to dimes, find the total worth of Ella's coins in ... | math | {
"ground_truth": "130",
"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 $A$, $B$, and $C$ are distinct points on the graph of $y=x^2$ such that line $AB$ is parallel to the $x$-axis and $\\triangle ABC$ is a right triangle with area $2008$... | math | {
"ground_truth": "18",
"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": "Let $m\\ge 3$ and $n$ be positive integers such that $n>m(m-2)$ . Find the largest positive integer $d$ such that $d\\mid n!$ and $k\\nmid d$ for all $k\\in\\{m,m+1,\... | math | {
"ground_truth": "m-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": "For a positive integer $n$ consider all its divisors $1 = d_1 < d_2 < \\ldots < d_k = n$ . For $2 \\le i \\le k-1$ , let's call divisor $d_i$ good, if $d_{i-1}d_{i+1}$ is... | math | {
"ground_truth": "n = 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": "For what value of $m$ does the line represented by the equation $2m - 3x = 5y + 1$ contain the point $(-1, 3)$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{2}",
"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 positive integers $ a$ and $ b$ are such that the numbers $ 15a \\plus{} 16b$ and $ 16a \\minus{} 15b$ are both squares of positive integers. What is the least possi... | math | {
"ground_truth": "481^2",
"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": "A height $A H$ is drawn from the vertex $A$ to the base $BC$ of isosceles triangle $ABC$. A point $P$ is marked on the side $A B$ such that $C P = BC$. The segment $C P$ intersec... | math | {
"ground_truth": "30^\\circ, 75^\\circ, 75^\\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": "Let nonzero complex numbers \\( x \\) and \\( y \\) satisfy \\( x^{2} + xy + y^{2} = 0 \\). Calculate the value of the algebraic expression \\(\\left(\\frac{x}{x+y}\\right)^{1990... | math | {
"ground_truth": "-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 $ S$ be the set of nonnegative integers. Find all functions $ f,g,h: S\\rightarrow S$ such that\r\n\r $ f(m\\plus{}n)\\equal{}g(m)\\plus{}h(n),$ for all $ m,n\\in S$ , ... | math | {
"ground_truth": "f(n) = 2, g(n) = 1, h(n) = 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": "How many nonzero terms are in the expansion of $$(x^2 + 2)(3x^3 + 5x^2 + 2) - 2(x^4 - 3x^3 + 2x^2)?$$",
"role": "user"
}
] | math | {
"ground_truth": "5",
"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": "For the pair of positive integers \\((x, y)\\) such that \\(\\frac{x^{2}+y^{2}}{11}\\) is an integer and \\(\\frac{x^{2}+y^{2}}{11} \\leqslant 1991\\), find the number of such pa... | math | {
"ground_truth": "131",
"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": "Solve the system of equations \n\\[\n\\begin{cases}\n3x + \\sqrt{3x - y} + y = 6, \\\\\n9x^2 + 3x - y - y^2 = 36.\n\\end{cases}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "(2, -3), (6, -18).",
"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 that the major axis of an ellipse is $8$ and its eccentricity is $\\frac{3}{4}$, the standard equation of this ellipse is __________.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x^{2}}{16}+ \\frac{y^{2}}{7}=1 \\text{ or } \\frac{x^{2}}{7}+ \\frac{y^{2}}{16}=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": "A sequence of numbers is defined recursively by $a_1 = 1$, $a_2 = \\frac{3}{7}$, and \n\\[a_n=\\frac{a_{n-2} \\cdot a_{n-1}}{2a_{n-2} - a_{n-1}}\\]for all $n \\geq 3$. Find the v... | math | {
"ground_truth": "8078",
"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": "Ms. Thompson sold two books at $\\$4.50$ each. Determine the overall financial outcome when the profit on the first book is $25\\%$ and the loss on the second book is $25\\%$.",
... | math | {
"ground_truth": "-\\$0.60, or 60 cents lost",
"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 regular pentagon with side length 1, draw the two diagonals from one vertex. This creates a net for a tetrahedron with a regular triangular base. What is the volume of th... | math | {
"ground_truth": "\\frac{1 + \\sqrt{5}}{24}",
"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 $ABC$ be an equilateral triangle, and let $D$ and $F$ be points on sides $BC$ and $AB$ , respectively, with $FA=5$ and $CD=2$ . Point $E$ lies on side $CA$ s... | math | {
"ground_truth": "989",
"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": "Two regular tetrahedrons $A$ and $B$ are made with the 8 vertices of a unit cube. (this way is unique)\r\n\r\nWhat's the volume of $A\\cup B$ ?",
"role": "user"
}
] | 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": "The altitude drawn to the base of an isosceles triangle is $10$, and the perimeter is $40$. Find the area of the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "75",
"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": "Evaluate $\\lfloor 0.998 \\rfloor \\times \\lceil 1.999 \\rceil$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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": "Let us solve the following system of equations:\n\n\\[\n\\begin{aligned}\nx + y + z &= a \\\\\nx^2 + y^2 + z^2 &= b^2 \\\\\nxy &= z^2 \n\\end{aligned}\n\\]\n\nwhere \\(a\\) and \... | math | {
"ground_truth": "b^2 \\geq \\frac{a^2}{2}",
"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 the expression $\\left(30 - \\left(3010 - 310\\right)\\right) + \\left(3010 - \\left(310 - 30\\right)\\right)$, simplify the expression.",
"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": "What percentage of the area of a circle is occupied by a square inscribed in it? Give the answer in whole percent, rounding as necessary.",
"role": "user"
}
] | math | {
"ground_truth": "64",
"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": "We call a permutation $(a_1, a_2,\\cdots , a_n)$ of the set $\\{ 1,2,\\cdots, n\\}$ \"good\" if for any three natural numbers $i <j <k$ , $n\\nmid a_i+a_k-2a_j$ find all n... | math | {
"ground_truth": "n = 2^b",
"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 circumference of a particular circle is 36 cm. Calculate both the diameter and the area of the circle in square centimeters, expressing the area as a common fraction in terms... | math | {
"ground_truth": "\\frac{324}{\\pi} \\, \\text{square centimeters}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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