data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Cut a piece of equal weight from each of two alloys, one weighing 10 kg and the other 15 kg, with different percentages of copper content. Then, melt each cut piece with the rema... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ with the following property:\n\nFor any integer $m$ with $0 < m < 2004$ , there exists an integer $k$ such that\n\n\\[\\frac{m}{2004... | math | {
"ground_truth": "4009",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the solutions to \\( z^6 = 8 \\). Enter the solutions separated by commas.",
"role": "user"
}
] | math | {
"ground_truth": "0 \\pm \\sqrt[3]{2}i, \\pm \\sqrt[3]{2}, 0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the integers \\( a, b, c \\) that satisfy \\( a + b + c = 2 \\), and\n\\[ \nS = (2a + bc)(2b + ca)(2c + ab) > 200,\n\\]\nfind the minimum value of \\( S \\).",
"role": ... | math | {
"ground_truth": "256",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let's modify the previous problem. Now, when Bernardo receives a number, he doubles it, and when he gives it to Silvia, she now adds 60 instead of 50. The number game between Ber... | math | {
"ground_truth": "B) 5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular vegetable garden is enclosed by a fence that is 36m long. What are the dimensions (length and width) of the rectangle when the area of the vegetable garden is maxim... | math | {
"ground_truth": "81 \\text{ square meters}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the largest prime divisor of $12! + 13! + 17$.",
"role": "user"
}
] | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\[ 4.65 \\sin ^{2}\\left(135^{\\circ}-2 \\alpha\\right)-\\sin ^{2}\\left(210^{\\circ}-2 \\alpha\\right)-\\sin 195^{\\circ} \\cos \\left(165^{\\circ}-4 \\alpha\\right) \\]",
... | math | {
"ground_truth": "\\sin(4\\alpha)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Is it possible to select two natural numbers $m$ and $n$ so that the number $n$ results from a permutation of the digits of $m$ , and $m+n =999 . . . 9$ ?",
"role": ... | math | {
"ground_truth": "m = 7272",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Round 9.6654 to two decimal places and to the nearest integer.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $2023^{0} = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three points, \\(A, B\\), and \\(C\\), are selected independently and uniformly at random from the interior of a unit square. Compute the expected value of \\(\\angle ABC\\).",
... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Andile and Zandre play a game on a $2017 \\times 2017$ board. At the beginning, Andile declares some of the squares *forbidden*, meaning the nothing may be placed on such a squ... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N$ be the sum of the divisors of $180$. What is the largest prime factor of $N$?",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine what percent of $y$ is equal to $60\\%$ of $30\\%$ of $y$.",
"role": "user"
}
] | math | {
"ground_truth": "18\\%",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A regular polygon has interior angles of 174 degrees. How many sides does the polygon have?",
"role": "user"
}
] | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ for which there exist non-negative integers $a_1, a_2, \\ldots, a_n$ such that\n\\[\n\\frac{1}{2^{a_1}} + \\frac{1}{2^{a_2}} + \\cdots + \\frac... | math | {
"ground_truth": "n \\equiv 1, 2 \\pmod{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any sets $X$ and $Y$, define: $①X-Y={x|x∈X$ and $x∉Y}$, $②X△Y=(X-Y)∪(Y-X)$. Given $A={y|y=x^{2},x∈R}$ and $B={y|-2≤slant y≤slant 2}$, find $A△B=$ _____.",
"role": "user"
... | math | {
"ground_truth": "[-3,0) ∪ (3,+∞)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the mean, median, and mode of the list $10,2,5,2,4,2,x$ are arranged in increasing order, they form a non-constant arithmetic progression. Calculate the sum of all possible ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence is $\\frac {1}{2}$, $\\frac {1}{2^{2}}$, $\\frac {1}{2^{2}}$, $\\frac {1}{2^{3}}$, $\\frac {1}{2^{3}}$, $\\frac {1}{2^{3}}$, $\\frac {1}{2^{4}}$, $\\frac {1}{2^{4}}$... | math | {
"ground_truth": "\\frac {1}{128}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the diagonals of a rhombus bisect each other at right angles, determine the area of a rhombus with sides of length $\\sqrt{130}$ units and diagonals that differ by 4 u... | math | {
"ground_truth": "126",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $k>1$ be a positive integer and $n>2018$ an odd positive integer. The non-zero rational numbers $x_1,x_2,\\ldots,x_n$ are not all equal and: $$ x_1+\\frac{k}{x_2}=x_2+... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An actor announces the program on a stage that is 10 meters long. If the actor should stand at the golden section of the stage, then how far from one end of the stage should the ... | math | {
"ground_truth": "10 \\times \\left(\\frac{3-\\sqrt{5}}{2}\\right) \\text{ or } 10 \\times \\left(\\frac{1+\\sqrt{5}}{2}\\right) - 10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x \\) is an integer, and \\( y = \\frac{3x + 13}{x + 6} \\) is an integer, what is the sum of all possible values of \\( y \\)?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For every pair of reals $0 < a < b < 1$ , we define sequences $\\{x_n\\}_{n \\ge 0}$ and $\\{y_n\\}_{n \\ge 0}$ by $x_0 = 0$ , $y_0 = 1$ , and for each integer $n \\ge 1$... | math | {
"ground_truth": "100m + n = 100 \\cdot 1 + 3 = 103",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Please fill in the subsequent letter or number in the blank space from a theoretical or logical perspective. \n①A, D, G, J, . ②21, 20, 18, 15, 11, . \n③8, 6,... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For each positive integer \\( n \\) let \\( S_{n} \\) denote the set \\( \\{1,2,3, \\ldots, n\\} \\). Compute the number of triples of subsets \\( A, B, C \\) of \\( S_{2006} \\)... | math | {
"ground_truth": "2^{4012}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(a) Three lines $l,m,n$ in space pass through point $S$ . A plane perpendicular to $m$ intersects $l,m,n $ at $A,B,C$ respectively. Suppose that $\\angle ASB = \\angle ... | math | {
"ground_truth": "PQ = 1, QR = \\sqrt{2}, PR = \\sqrt{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the set \\( A = \\{a_{1}, a_{2}, a_{3}, a_{4}\\} \\). If the set of sums of elements from all possible three-element subsets of \\( A \\) is \\( B = \\{-1, 3, 5, 8\\} \\), th... | math | {
"ground_truth": "\\{-3, 0, 2, 6\\}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that -2, a_1, a_2, -8 form an arithmetic sequence, and -2, b_1, b_2, b_3, -8 form a geometric sequence, determine the value of \\(\\dfrac {a_{2}-a_{1}}{b_{2}}\\).",
"ro... | math | {
"ground_truth": "\\dfrac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the digits left and right of the decimal point in the decimal form of the number \\[ (\\sqrt{2} + \\sqrt{3})^{1980}. \\]",
"role": "user"
}
] | math | {
"ground_truth": "7.9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We have two gears. When they are connected, the ratio of the drive gear to the driven gear (the gear ratio) is $7:9$ or $9:7$. If we replace one gear with a gear having 3 fewer t... | math | {
"ground_truth": "9 \\text{ teeth, } 7 \\text{ teeth, } 12 \\text{ teeth, } 4 \\text{ teeth}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, the sides $AB$ and $AC$ are $\\sqrt{10}$ and $\\sqrt{2}$ respectively, and the radius of the circumscribed circle around triangle $ABC$ is $\\sqrt{5}$. Find th... | math | {
"ground_truth": "BC = 4, \\angle ACB = 45^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $M$ be the positive integer $8888\\ldots888$, a $200$-digit number where each digit is an $8$. Let $g(r)$ be the leading digit of the $r{ }$th root of $M$. Calculate\\[g(2) +... | math | {
"ground_truth": "D) 10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In quadrilateral $EFGH$, $EF = 6$, $FG = 18$, $GH = 6$, and $HE = x$ where $x$ is an integer. Calculate the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the radius of the largest circle that can be covered by three circles with radii $R$. Additionally, solve the problem for the general case when the radii are $R_{1}, R_{2}, ... | math | {
"ground_truth": "\\max \\left( \\frac{2R_1}{\\sqrt{3}}, \\frac{2R_2}{\\sqrt{3}}, \\frac{2R_3}{\\sqrt{3}}, R_1, R_2, R_3 \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are knights who always tell the truth and liars who always lie living on an island. One day, 30 residents of this island sat around a round table. Each of them said one of ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $c$ and $d$ are nonzero integers such that two of the roots of\n\\[x^3 + cx^2 + dx + 15c\\] coincide, and all three roots are integers. Find $|cd|$.",
"role": "u... | math | {
"ground_truth": "840",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Petya came home from school today at 16:45, looked at the clock, and wondered: after how much time will the clock hands align for the seventh time since he arrived home from scho... | math | {
"ground_truth": "435 \\text{ minutes}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice decided to enclose her rectangular lawn using 24 fence posts. She put one post at each corner and evenly spaced the remaining posts along the edges with a distance of 5 yar... | math | {
"ground_truth": "\\textbf{(C)}\\ 825",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the set $S$ of primes such that $p \\in S$ if and only if there exists an integer $x$ such that $x^{2010} + x^{2009} + \\cdots + 1 \\equiv p^{2010} \\pmod{p^{2011}}$ ... | math | {
"ground_truth": "S = \\{ p : p \\equiv 1 \\pmod{2011} \\land p \\in \\mathbb{P} \\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular solid has one vertex where the three edge lengths are $3$, $4$, and $5$, respectively, and all of its $8$ vertices lie on the same spherical surface. Given that the... | math | {
"ground_truth": "50\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three mutually perpendicular lines intersect at a point \\( O \\). Points on one of these lines that are at a distance of 1 unit from \\( O \\) are denoted by \\( X_{1} \\) and \... | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "2010 consecutive natural numbers are arranged in a row in increasing order. The average of the numbers in the odd positions is 2345. Then the average of the numbers in the even p... | math | {
"ground_truth": "2346",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the maximum number of diagonals of a regular $12$ -gon which can be selected such that no two of the chosen diagonals are perpendicular?\n\nNote: sides are not diagonals... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nick is taking a $10$ question test where each answer is either true or false with equal prob\u0002ability. Nick forgot to study, so he guesses randomly on each of the $10$ p... | math | {
"ground_truth": "\\frac{63}{256}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the leading coefficient of the polynomial $5(x^5 - 2x^4 + 3x^3) - 8(x^5 + x^4 - x^2 + 1) + 3(3x^5 - x^4 + x)$ after simplifying.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Convex quadrilateral $ABCD$ has $AB = 15$ and $CD = 20$. Diagonals $AC$ and $BD$ intersect at $E$, $AC = 18$, and $\\triangle AED$ and $\\triangle BEC$ have equal areas. What is ... | math | {
"ground_truth": "\\frac{54}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "289. A remarkable number. Find a number such that its fractional part, its integer part, and the number itself form a geometric progression.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1+\\sqrt{5}}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bakery offers three different kinds of bread rolls. Tom wants to buy a total of eight rolls and ensure he has at least one of each kind. Determine how many different combinatio... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(y = -x^2 + 4x + 3\\) and \\(x\\) is a real number, then what is the maximum value possible for \\(y\\)?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$ be $S_n$. If $S_8 = 2S_4$, then $\\frac{a_3}{a_1} = \\boxed{\\text{\\_\\_\\_\\_\\_\\_}}$.",
"role": "us... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Which numbers leave a remainder of 5 when dividing 2007?",
"role": "user"
}
] | math | {
"ground_truth": "7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, \\text{ and } 2002",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the product of all positive integers \\( b \\geq 2 \\) for which the base \\( b \\) number \\( 111111_b \\) has exactly \\( b \\) distinct prime divisors.",
"role": "... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A number is composed of 10 ones, 9 tenths (0.1), and 6 hundredths (0.01). This number is written as ____, and when rounded to one decimal place, it is approximately ____.",
"... | math | {
"ground_truth": "11.0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Expand the expression $4(5x^3 - 3x^2 + 7x - 2)$.",
"role": "user"
}
] | math | {
"ground_truth": "20x^3 - 12x^2 + 28x - 8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x > 0$, $y > 0$, and $\\frac{1}{x} + \\frac{2}{y} = 1$, if $x + 2y > a^2 + 8a$ always holds, find the range of the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "-4 - 2\\sqrt{6} < a < -4 + 2\\sqrt{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three positive integers have an arithmetic mean of 24 and a median of 25. If the median is 6 less than the largest number, what is the smallest number?",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest five-digit negative integer congruent to $2 \\pmod{17}$?",
"role": "user"
}
] | math | {
"ground_truth": "-10011",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( N \\) be the smallest positive integer for which \n\\[ x^2 + x + 1 \\quad \\text{divides} \\quad 166 - \\sum_{d \\mid N, d>0} x^d. \\]\nFind the remainder when \\( N \\) ... | math | {
"ground_truth": "672",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagram shows a square divided into strips of equal width. Three strips are black and two are grey. What fraction of the perimeter of the square is grey? \n\nA) $\\frac{1}{5}... | math | {
"ground_truth": "\\frac{2}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all primes $p$ and $q$ such that $3p^{q-1}+1$ divides $11^p+17^p$ Proposed by Stanislav Dimitrov,Bulgaria",
"role": "user"
}
] | math | {
"ground_truth": "(p, q) = (3, 3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When passengers boarded an empty tram, half of them took seats. How many passengers boarded initially if, after the first stop, their number increased by exactly $8 \\%$ and it i... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider an even number larger than 7 and the representation of this number as the sum of two different prime numbers. For the number 172, what is the largest possible difference... | math | {
"ground_truth": "The correct answer is **C) 162**.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Fold a piece of coordinate paper once so that the point $(10,0)$ coincides with $(-6,8)$. What are the coordinates of the point that coincides with $(-4,2)$?",
"role": "user"... | math | {
"ground_truth": "(4,-2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define the operation $\\#$ for real numbers $a$, $b$, $c$, and $d$ as $\\#(a, b, c, d) = b^2 - 4ac + d^2$. What is the value of $\\#(2, 3, 1, 4)$?",
"role": "user"
}
] | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points \\( A, B, C, D \\) are on the same circle, and \\( BC = CD = 4 \\). Let \\( E \\) be the intersection of \\( AC \\) and \\( BD \\), with \\( AE = 6 \\). If the lengths of ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest possible value of the expression $$\\frac{(a+b)^2+(b-c)^2+(c-a)^2}{a^2},$$ where \\(a > b > c\\) are real numbers, and \\(a + c = 2b\\), with \\(a \\neq 0.\\)",... | math | {
"ground_truth": "\\frac{7}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Numbers $\\frac{49}{1}, \\frac{49}{2}, ... , \\frac{49}{97}$ are writen on a blackboard. Each time, we can replace two numbers (like $a, b$ ) with $2ab-a-b+1$ . After $96$ ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square with side length $2$ has an isosceles right triangle placed at each of its corners, with the legs of each triangle lying along the sides of the square. The sum of the ar... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the odd function $f(x)$ is defined on the domain $\\mathbb{R}$ and satisfies $f(x) = f(2 - x)$ for any real number $x$. When $x \\in (0, 1)$, $f(x) = 2^x + 1$. Find th... | math | {
"ground_truth": "-\\frac{31}{15}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Piravena must make a trip from $D$ to $E$, then from $E$ to $F$, and finally from $F$ to $D$. Each of these three parts of the trip is either entirely by bus or entirely by airpl... | math | {
"ground_truth": "\\$1627.44",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A plane is passed through a side of the base of a cube, dividing the volume of the cube in the ratio $m: n$ when measured from the base. Find the angle between this plane and the... | math | {
"ground_truth": "\\alpha = \\arctan \\left(\\frac{2m}{m+n}\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Meteorological records for a certain area indicate that during a certain period of time, there was 1 day of continuous rain; 9 days when it rained during the day and was clear at... | math | {
"ground_truth": "12, 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the books of Novgorod scribes from the 15th century, the following liquid measures are mentioned: a barrel, a nasadka, and a bucket. From these same books, it became known tha... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given points $P_{1}(a,5)$ and $P_{2}(2,b)$ are symmetric about the $y$-axis, find the value of $a+b$.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $n\\geq 3$ cities in a country and between any two cities $A$ and $B$ , there is either a one way road from $A$ to $B$ , or a one way road from $B$ to $A$ (... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function f(x) = cos²x + $\\sqrt{3}$sinxcosx, where $x \\in (0, \\frac{\\pi}{2})$, determine the interval where f(x) is monotonically increasing.",
"role": "user"
... | math | {
"ground_truth": "(0, \\frac{\\pi}{6})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assuming $t \\neq 0$, the point $P(t, 0)$ is a common point of the graphs of the functions $f(x) = x^3 + ax$ and $g(x) = bx^2 + c$. If the graphs of the two functions have the sa... | math | {
"ground_truth": "c = -t^3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number 1000 can be written as the product of two positive integers, neither of which contains zeros. Find the sum of these two integers.",
"role": "user"
}
] | math | {
"ground_truth": "133",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sum of $335$ pairwise distinct positive integers equals $100000$ .\na) What is the least number of uneven integers in that sum?\nb) What is the greatest number of uneven int... | math | {
"ground_truth": "n \\geq 20 \\text{ and } n \\leq 314",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ such that $$ \\phi(n) + \\sigma(n) = 2n + 8. $$",
"role": "user"
}
] | math | {
"ground_truth": "n = 343 \\text{ and } n = 12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ ABCD$ be a quadrilateral in which $ AB$ is parallel to $ CD$ and perpendicular to $ AD; AB \\equal{} 3CD;$ and the area of the quadrilateral is $ 4$ . if a circle ... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangles $PIQ$ and $PQR$ are right triangles in the quadrilateral $PIQR$ with $IP = 16$ units, $PQ = 20$ units, and $PR = 25$ units. Calculate the area of quadrilateral $PIQR$."... | math | {
"ground_truth": "246 \\text{ square units}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain shopping mall sells desk lamps at a price of $40$ yuan, which were purchased for $30$ yuan each. On average, $600$ lamps are sold each month. A survey shows that for ev... | math | {
"ground_truth": "12250 \\text{ yuan}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ f : \\mathbf {R} \\to \\mathbf {R} $ be a smooth function such that $ f'(x)^2 = f(x) f''(x) $ for all $x$ . Suppose $f(0)=1$ and $f^{(4)} (0) = 9$ . Find all possib... | math | {
"ground_truth": "\\pm \\sqrt{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points \\( M \\) and \\( N \\) are located on the sides \\( AB \\) and \\( AD \\) of the parallelogram \\( ABCD \\), such that \\( AM : MB = 1 : 2 \\) and \\( AN : ND = 3 : 2 \\)... | math | {
"ground_truth": "6:11 \\text{ for } DK:KM \\text{ and } 15:2 \\text{ for } CK:KN",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the solution set of the inequality: $-x^2+4x+5<0$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|x<-1 \\text{ or } x>5\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the distance between the center of the circle defined by the equation $x^2 + y^2 = 4x + 6y + 3$ and the point $(10,5)$?",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{17}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a real number $a \\neq 1$, the function $f(x)=\\begin{cases} 4^{x}, & x\\geqslant 0, \\\\ 2^{a-x}, & x < 0 \\end{cases}$, then $f(1-a)=f(a-1)$, the value of $a$ is ______."... | math | {
"ground_truth": "\\dfrac {1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integers \\( n > 1 \\) such that any prime divisor of \\( n^6 - 1 \\) is a divisor of \\((n^3 - 1)(n^2 - 1)\\).",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sets M = {x | 0 ≤ x ≤ 1} and N = {x ||x| ≥ 1}, find the intersection of sets M and N.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression: $4 \\times (5^2 + 5^2 + 5^2 + 5^2) =$\nA) $400$\nB) $325$\nC) $625$\nD) $800$",
"role": "user"
}
] | math | {
"ground_truth": "400",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the sum of the reciprocals of the first 1000 triangular numbers:\n\\[ \\frac{1}{t_1} + \\frac{1}{t_2} + \\frac{1}{t_3} + \\ldots + \\frac{1}{t_{1000}} \\]\nwhere $t_n$ i... | math | {
"ground_truth": "\\frac{2000}{1001}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence 1, -4, 9, -16, 25, determine the general term formula.",
"role": "user"
}
] | math | {
"ground_truth": "a_n = (-1)^{n+1} n^2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a convex hexagon $ABCDEF$, angles $A$, $B$, and $C$ are congruent, and angles $D$, $E$, and $F$ are congruent. If the measure of angle $A$ is $30^\\circ$ less than the measure... | math | {
"ground_truth": "135^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all 4-digit numbers that are 8802 greater than the number formed by reversing its digits.",
"role": "user"
}
] | math | {
"ground_truth": "1099",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Form a 4-digit number without repeating digits using the numbers 1, 2, 3, 4. How many of these 4-digit numbers are odd?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A triangular array of numbers has a first row consisting of the odd integers $ 1,3,5,\\ldots,99$ in increasing order. Each row below the first has one fewer entry than the row... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Working together, Jack and Jill can paint a house in 3 days; Jill and Joe can paint the same house in 4 days; or Joe and Jack can paint the house in 6 days. If Jill, Joe, and Jac... | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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