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": "Assuming buses from Dallas to Houston leave every hour on the hour and buses from Houston to Dallas leave every hour on the half hour, and the trip from one city to the other tak... | 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": "Given the function \\( f(x) = \\lg \\left[\\left(a^{2}-1\\right)x^{2} + (a+1)x + 1\\right] \\):\n1. If the domain of \\( f(x) \\) is \\(\\mathbf{R}\\), determine the range of val... | math | {
"ground_truth": "- \\textbf{ a in} \\ (-\\infty, -1] \\cup \\left( \\frac{5}{3}, +\\infty \\right) \\textbf{ for Domain } , \\left[1, \\frac{5}{3}\\right] \\textbf{ for Range }",
"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 rectangle is inscribed in a circle of area $32\\pi$ and the area of the rectangle is $34$ . Find its perimeter.\n\n*2017 CCA Math Bonanza Individual Round #2*",
"role": ... | math | {
"ground_truth": "28",
"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 function $f(x) = |ax + x^2 - x \\cdot \\ln a - m| - 2$, ($a > 0$ and $a \\neq 1$) has two zeros, determine the range of values for $m$.",
"role": "user"
}
] | math | {
"ground_truth": "(-1, 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": "Consider the set $M=\\{1,2,3,...,2020\\}.$ Find the smallest positive integer $k$ such that for any subset $A$ of $M$ with $k$ elements, there exist $3$ distinct numb... | math | {
"ground_truth": "1011",
"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 $\\mathcal S$ be a set of $16$ points in the plane, no three collinear. Let $\\chi(S)$ denote the number of ways to draw $8$ lines with endpoints in $\\mathcal S$ , ... | math | {
"ground_truth": "1430",
"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 hyperbola $\\frac{x^2}{3} - \\frac{y^2}{6} = 1$, let $F_2$ be its right focus and let $A$ and $B$ be the points at which the line with a slope of $30^\\circ$ intersects... | math | {
"ground_truth": "\\frac{16}{5}\\sqrt{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": "A certain ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are located at $(3, -4 + \\sqrt{8})$ and $(3, -4 - \\sqrt{8}).$ Determine the length of the major... | math | {
"ground_truth": "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": "Given any \\( n \\) points \\( P_{1}, P_{2}, \\cdots, P_{n} \\) on a plane, where no three points are collinear, each point \\( P_{i} \\) (\\(1 \\leqslant i \\leqslant n \\)) is ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define the sequence $(a_n)_{n=1}^\\infty$ of positive integers by $a_1=1$ and the condition that $a_{n+1}$ is the least integer such that \\[\\mathrm{lcm}(a_1, a_2, \\ldots... | math | {
"ground_truth": "\\{1\\} \\cup \\{p^{\\alpha} \\mid p \\text{ prime}, \\ \\alpha \\geq 1\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given 11 distinct positive integers \\(a_{1}, a_{2}, \\cdots, a_{11}\\) with a total sum less than 2007. On the blackboard, the numbers 1, 2, ..., 2007 are written in sequence. A... | math | {
"ground_truth": "\\prod_{j=1}^{11} a_{j}",
"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 $B$ be a $1 \\times 2 \\times 4$ box (rectangular parallelepiped). Let $R$ be the set of points that are within distance 3 of some point in $B$ . (Note that $R$ co... | math | {
"ground_truth": "92 + 144\\pi",
"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, \\ldots, 100\\} \\). Find the smallest positive integer \\( n \\) such that every \\( n \\)-element subset of \\( S \\) contains 4 pairwise coprime number... | math | {
"ground_truth": "75",
"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 non-negative real numbers $a, b, c$ satisfying the condition $a^2 + b^2 + c^2 = 2$ . Find the maximum value of the following expression $$ P=\\frac{\\sqrt{b^2+c^2}... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all triangles such that the lengths of the three sides and its area are given by four consecutive natural numbers.",
"role": "user"
}
] | math | {
"ground_truth": "3, 4, 5",
"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 $ABCD$ be an isosceles trapezoid with $AB$ and $CD$ as parallel bases, and $AB > CD$. A point $P$ inside the trapezoid connects to the vertices $A$, $B$, $C$, $D$, creating f... | math | {
"ground_truth": "\\frac{7}{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": "a) Given a convex quadrilateral \\(ABCD\\), let \\(r_1 \\leq r_2 \\leq r_3 \\leq r_4\\) be the radii of the inscribed circles of triangles \\(ABC\\), \\(BCD\\), \\(CDA\\), and \\... | math | {
"ground_truth": "r_2 \\leq 2r_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": "Three fair coins are to be tossed once. For each tail that results, one fair die is to be rolled. Determine the probability that the sum of the die rolls is odd.",
"role": "u... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for x:\n$$3^{x + 6} = 81^{x + 1}.$$",
"role": "user"
}
] | math | {
"ground_truth": "x = \\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": "Let $U$ be the set of all positive integer divisors of $36,000.$ How many numbers are the product of two distinct elements of $U$?\nA) 303\nB) 307\nC) 311\nD) 315\nE) 318",
"... | math | {
"ground_truth": "C) 311",
"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 AIME Triathlon consists of a half-mile swim, a 30-mile bicycle ride, and an eight-mile run. Tom swims, bicycles, and runs at constant rates. He runs fives times as fast as he... | math | {
"ground_truth": "150",
"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": "Given that \\( a, b, \\) and \\( c \\) are distinct integers, determine the minimum value of the expression\n\\[ 4\\left(a^{2}+b^{2}+c^{2}\\right)-(a+b+c)^{2} \\]",
"role": "... | math | {
"ground_truth": "8",
"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 you walk for 30 minutes at a rate of 3 mph, then run for 20 minutes at a rate of 8 mph, and finally cycle for 25 minutes at a rate of 12 mph, how many miles will you have cove... | math | {
"ground_truth": "The correct answer is B) 9.17 miles.",
"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 \\(\\frac{1}{5}\\) of the team's total points were scored by Linda, \\(\\frac{3}{8}\\) were scored by Maria, and Kelly scored 18 points, and the other 8 teammates scor... | 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": "Considering all three-digit whole numbers, find the number of integers whose digits sum to 27 and are odd.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A car dealer sold an average of 7 cars per day over a certain period. Ignoring the day with the lowest sales, the average number of cars sold on the remaining days was 8. Excludi... | math | {
"ground_truth": "42",
"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 each positive integer \\( n \\), define the point \\( P_{n} \\) to have coordinates \\(\\left((n-1)^{2}, n(n-1)\\right)\\) and the point \\( Q_{n} \\) to have coordinates \\(... | math | {
"ground_truth": "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 all pairs of functions $f; g : R \\to R$ such that for all reals $x.y \\ne 0$ : $$ f(x + y) = g \\left(\\frac{1}{x}+\\frac{1}{y}\\right) \\cdot (xy)^{2008} $$",
"ro... | math | {
"ground_truth": "f(x) = g(x) = f(1) x^{2008}",
"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 $f(n)=\\frac{n}{3}$ if $n$ is divisible by $3$ and $f(n)=4n-10$ otherwise. Find the sum of all positive integers $c$ such that $f^5(c)=2$ . (Here $f^5(x)$ means... | math | {
"ground_truth": "235",
"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 line $l: 2x + y + 4 = 0$ and the circle $C: x^2 + y^2 + 2x - 4y + 1 = 0$, let the two intersection points be A and B.\n\n(1) Find the coordinates of A and B.\n\n(2) Poi... | math | {
"ground_truth": "\\left(- \\frac{11}{5} - \\frac{2 \\sqrt{19}}{5}, 0\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Petya added several consecutive odd numbers. It turned out that the resulting sum is 20 times greater than the largest term and 60 times greater than the smallest term. Find out ... | math | {
"ground_truth": "29, 31, 33, \\ldots, 87",
"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 function $f(x)=e^{x}(\\sin x+\\cos x)+a$, $g(x)=(a^{2}-a+10)e^{x}$ ($a\\in\\mathbb{R}$ and $a$ is a constant). \n(I) If the tangent line of the curve $y=f(x)$ at $(0,f... | math | {
"ground_truth": "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": "A box contains 1 grey ball, 2 white balls, and 3 black balls. Calculate the probability that the ball chosen is not grey.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{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": "In an arithmetic sequence, the third term is 14 and the sixth term is 32. What is the tenth term of this sequence? Also, find the common difference.",
"role": "user"
}
] | math | {
"ground_truth": "56",
"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": "Admiral Ackbar needs to send a 5-character message through hyperspace to the Rebels. Each character is a lowercase letter, and the same letter may appear more than once in a mess... | math | {
"ground_truth": "26",
"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": "Attach a single digit to the left and right of the eight-digit number 20222023 so that the resulting 10-digit number is divisible by 72. (Specify all possible solutions.)",
"... | math | {
"ground_truth": "3202220232",
"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 bug crawls along a number line, starting at $-2$. It crawls to $-6$, and then turns around and crawls to $5$. What is the total distance traveled by the bug?",
"role": "use... | math | {
"ground_truth": "15",
"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": "The angle bisector $AL$ and the median $BM$ of triangle $ABC$ intersect at point $X$. The line $CX$ intersects side $AB$ at point $Y$. Find the area of triangle $CYL$, given that... | math | {
"ground_truth": "\\frac{x^2}{4 \\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": "<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 1</u>**D1 / Z1.** What is $1 + 2 \\... | math | {
"ground_truth": "16",
"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 increasing sequence of positive integers $b_1,$ $b_2,$ $b_3,$ $\\dots$ has the property that\n\\[b_{n + 2} = b_{n + 1} + b_n\\]for all $n \\ge 1.$ If $b_6 = 60,$ then find $b... | math | {
"ground_truth": "97",
"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": "Find the points that can help construct the curve\n\n$$\n4 x^{3}-8 x y+4 y^{2}+8 x-16 y+3=0\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\left(-\\frac{11}{8}, \\frac{1}{8}\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ be chosen at random from the interval $(0,1)$. What is the probability that $\\lfloor\\log_{10}5x\\rfloor - \\lfloor\\log_{10}x\\rfloor = 0$?\nHere, $\\lfloor x\\rfloor$ ... | math | {
"ground_truth": "\\frac{8}{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": "Let $s$ be the result of tripling the base and squaring the exponent of $a^b$, where $a, b > 0$. If $s$ is equal to $5$ times the product of $a^b$ and $y^b$, determine the value ... | math | {
"ground_truth": "\\frac{9a}{5}",
"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": "Inside a given circle, there is another circle; \\( C A E \\) and \\( D B F \\) are two chords of the larger circle (not intersecting), tangent to the smaller circle at points \\... | math | {
"ground_truth": "18^\\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": "In rectangle \\(ABCD\\), \\(A B: AD = 1: 2\\). Point \\(M\\) is the midpoint of \\(AB\\), and point \\(K\\) lies on \\(AD\\), dividing it in the ratio \\(3:1\\) starting from poi... | math | {
"ground_truth": "45^\\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 \\( O = (0,0) \\), \\( Q = (13,4) \\), \\( A = (a, a) \\), \\( B = (b, 0) \\), where \\(a\\) and \\(b\\) are positive real numbers with \\(b \\geq a\\). The point \\( Q \\) i... | math | {
"ground_truth": "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": "A musical has three different male roles, three different female roles, and two different roles that can be either gender. Only a man can be assigned to a male role, and only a w... | math | {
"ground_truth": "5080320",
"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": "Calculate the value of $2^3 + 4 \\cdot 5 - 6 + 7$.",
"role": "user"
}
] | math | {
"ground_truth": "29",
"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 a bill for $\\textdollar{12,000}$, calculate the difference in dollars between a discount of $35\\%$ and two successive discounts of $30\\%$ and $6\\%$.",
"role": "user... | math | {
"ground_truth": "\\textdollar{96}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the set of triples $(a,b,c)$ of non-negative integers with $a+b+c$ even. The value of the sum\n \\[\\sum_{(a,b,c)\\in S}\\frac{1}{2^a3^b5^c}\\]\n can be ex... | math | {
"ground_truth": "37",
"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 \n$$\n\\sin \\alpha + \\sqrt{3} \\sin \\beta = 1,\n\\quad \n\\cos \\alpha + \\sqrt{3} \\cos \\beta = \\sqrt{3}.\n$$\n\nFind the value of $\\cos (\\alpha - \\beta)$.",
"... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the algebraic expression $\\sqrt{3x-5}$ is meaningful within the real number range, then the range of values for $x$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "x \\geqslant \\frac{5}{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": "A cuboid becomes a cube if its height is reduced by 2 cm, and its volume decreases by 50 cubic centimeters. What is the surface area of this cube in square centimeters?",
"ro... | math | {
"ground_truth": "150",
"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": "Two dice are rolled simultaneously. Calculate the probability that the absolute difference between the numbers facing up is $4$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{1}{9}",
"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": "Find the closest value to $\\sqrt{91} - \\sqrt{88}$.",
"role": "user"
}
] | math | {
"ground_truth": "0.158",
"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 $ABCD$ be a square with side length $2$ , and let a semicircle with flat side $CD$ be drawn inside the square. Of the remaining area inside the square outside the semi-c... | math | {
"ground_truth": "4 - 2\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the numerator of the fraction $\\frac {29}{43}$ is decreased by $a$, and the denominator is increased by $a$, and the new fraction simplifies to $\\frac {3}{5}$, the natural n... | math | {
"ground_truth": "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 rectangle with dimensions $1\\times 3$ and a right triangle with legs of length $1$ and $\\sqrt{8}$ are inscribed in a semicircle. The longer side of the rectangle lies along t... | math | {
"ground_truth": "\\frac{9\\pi}{8}",
"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": "Ten identical skateboards weigh the same as four identical canoes. If one of the canoes weighs a total of 45 pounds, how many pounds does one of the skateboards weigh?",
"rol... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a 10 km stretch of highway, void of intersections, a bus stops only for passengers to get on and off. It makes a total of 6 intermediate stops, each lasting 1 minute, and it a... | math | {
"ground_truth": "24 \\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": "Two real numbers $x$ and $y$ satisfy $x+y=9$ and $x^3+y^3=351$. Compute $xy$.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"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 \\[ \\left\\lfloor \\dfrac {2010^3}{2008 \\cdot 2009} - \\dfrac {2008^3}{2009 \\cdot 2010} \\right\\rfloor,\\] where $\\lfloor x \\rfloor$ denotes the greatest integer le... | math | {
"ground_truth": "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": "Given that the coordinates of the direction vector of the line $l$ are $(2, 2\\sqrt{3})$, find the inclination angle of the line $l$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{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 a right triangle, the lengths of the two legs are 30 inches and 45 inches. What is the area of the triangle, and what is its perimeter assuming the hypotenuse needs to be calc... | math | {
"ground_truth": "129 \\text{ inches}",
"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": "Jack walked up a hill at a speed of $(x^2 - 13x - 30)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2 - 5x - 84)$ miles in $(x+7)$ hours. If Jack and Jill walke... | 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": "For every $4^\\circ$ rise in temperature, the volume of a certain gas expands by $5$ cubic centimeters. Initially, the gas had a volume of $35$ cubic centimeters at a temperature... | math | {
"ground_truth": "17.5",
"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": "Compute the dot product of $3 \\begin{pmatrix} -2 \\\\ 0 \\end{pmatrix}$ and $4 \\begin{pmatrix} 3 \\\\ -5 \\end{pmatrix}$.",
"role": "user"
}
] | math | {
"ground_truth": "-72",
"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 $y$ is a real number and $y^2 = 81$, what is the sum of all possible values of $y$?",
"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": "A cube has a surface area of 150 square centimeters. What is the volume of this cube, in cubic centimeters?",
"role": "user"
}
] | math | {
"ground_truth": "125 \\text{ cm}^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": "Let $n\\geq 3$ be an integer. Find the largest real number $M$ such that for any positive real numbers $x_1,x_2,\\cdots,x_n$ , there exists an arrangement $y_1,y_2,\\cdots,... | 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": "Triangle $ABC$ is the right angled triangle with the vertex $C$ at the right angle. Let $P$ be the point of reflection of $C$ about $AB$ . It is known that $P$ and two... | math | {
"ground_truth": "30^\\circ",
"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 distinct triangles $ABC$ are tjere, up to simplilarity, such that the magnitudes of the angles $A, B$ and $C$ in degrees are positive integers and satisfy $$ \\co... | math | {
"ground_truth": "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": "The sequence \\(\\left(a_{n}\\right)\\) satisfies the conditions:\n\n\\[ a_{1} = 0, \\quad a_{n+1} = \\frac{n}{n+1}\\left(a_{n} + 1\\right) \\]\n\nFind the formula for \\(a_{n}\\... | math | {
"ground_truth": "a_{n} = \\frac{n-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": "A bug travels from A to B along the segments in the hexagonal lattice pictured, following the direction of the arrows, without repeating any segment. How many different paths are... | math | {
"ground_truth": "2400",
"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": "How many positive integers less than $50$ have an odd number of positive integer divisors?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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": "William is taking the 30-question, multiple-choice American Mathematics Competition. Each question has five answer choices. William guesses random answers for the last six questi... | math | {
"ground_truth": "\\frac{11529}{15625}",
"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": "Review the decimal representation of \\[\\dfrac{1}{30^{15}}\\]. This fraction in decimal form consists of a series of zeros after the decimal point, followed by a number other th... | math | {
"ground_truth": "22",
"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 an arithmetic sequence $\\{a_n\\}$ with common difference $d \\neq 0$ and $a_1 = 2d$, find the value of $k$ if $a_k$ is the geometric mean of $a_1$ and $a_{2k+1}$.",
"r... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of positive integer solutions $(a,b,c,d)$ to the equation \\[(a^2+b^2)(c^2-d^2)=2020.\\] \nNote: The solutions $(10,1,6,4)$ and $(1,10,6,4)$ are considered ... | math | {
"ground_truth": "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": "Given a sequence $\\{x_n\\}$ that satisfies $x_{n+3} = x_n$, $x_{n+2} = |x_{n+1} - x_n|$ ($n \\in \\mathbb{N}^*$), and $x_1 = 1$, $x_2 = a$ ($a \\leq 1$, $a \\neq 0$), find the s... | math | {
"ground_truth": "1340",
"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 number results when 80 is decreased by $85\\%$?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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 positive real numbers $s$, let $\\tau(s)$ denote the set of all obtuse triangles that have area $s$ and two sides with lengths $4$ and $10$. The set of all $s$ for which $\\t... | math | {
"ground_truth": "736",
"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": "Scientists released rats into a maze and observed whether they reached the goal. They found that 56% of black rats and 84% of white rats reached the goal. At the goal, the ratio ... | math | {
"ground_truth": "\\frac{3}{4}",
"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": "Suppose $\\mathcal{T}=A_0A_1A_2A_3$ is a tetrahedron with $\\angle A_1A_0A_3 = \\angle A_2A_0A_1 = \\angle A_3A_0A_2 = 90^\\circ$ , $A_0A_1=5, A_0A_2=12$ and $A_0A_3=9$ . ... | math | {
"ground_truth": "\\frac{180}{71}",
"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 side of the lower base of a regular truncated quadrangular pyramid is 5 times the side of the upper base. The lateral surface area of the pyramid is equal to the square of it... | math | {
"ground_truth": "\\operatorname{arctan} \\sqrt{9 + 3\\sqrt{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": "Determine the coefficient of the $x^3$ term in the expansion of $(2x-\\frac{1}{x})^5$.",
"role": "user"
}
] | math | {
"ground_truth": "-80",
"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": "Quadrilateral $ABCD$ is inscribed in a circle with $\\angle BAC=60^{\\circ}, \\angle ADB=50^{\\circ}, AD=3,$ and $BC=5$. Calculate the length of $AC$.",
"role": "user"
}
] | math | {
"ground_truth": "5.5",
"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 point D is a point on side BC such that AD = DC and angle DAC measures 50 degrees, calculate the degree measure of angle ADB.",
"role": "user"
}
] | math | {
"ground_truth": "100^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the system of equations $\\left\\{\\begin{array}{l}x+\\sqrt{x+2 y}-2 y=\\frac{7}{2}, \\\\ x^{2}+x+2 y-4 y^{2}=\\frac{27}{2}\\end{array}\\right.$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left( \\frac{19}{4}, \\frac{17}{8} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A frog is at the point \\((0,0)\\). Every second, he can jump one unit either up or right. He can only move to points \\((x, y)\\) where \\(x\\) and \\(y\\) are not both odd. How... | math | {
"ground_truth": "330",
"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 inequality\n\\[\n\\frac{(x - 1)(x - 4)(x - 5)^2}{(x - 3)(x^2 - 9)} > 0.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "(-3, 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": "In the rectangular coordinate system $(xOy)$, the point $P(t^{2},2t)$ is parameterized by $t$. If the origin $O$ is taken as the pole and the positive semi-axis of the $x$-axis a... | math | {
"ground_truth": "d = \\frac{\\sqrt{2}}{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": "$\\sin \\frac{{35π}}{6}=\\left(\\ \\ \\right)$",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an arithmetic sequence $\\{a_{n}\\}$ such that $a_{2}+a_{8}=10$. If $S_{n}$ represents the sum of the first $n$ terms of $a_{n}$, then find the value of $S_{9}$.",
"rol... | math | {
"ground_truth": "45",
"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": "Find the number of pairs of positive integers $(m; n)$ , with $m \\le n$ , such that the ‘least common multiple’ (LCM) of $m$ and $n$ equals $600$ .",
"role": "user"
... | math | {
"ground_truth": "53",
"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 pairs $(a,b)$ of real numbers such that $\\lfloor an + b \\rfloor$ is a perfect square, for all positive integer $n$ .",
"role": "user"
}
] | math | {
"ground_truth": "(0, k^2 + u)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a function $ f(x)=ax^3-3x^2+1 $, if $ f(-a) $, $ f(a) $, and $ f(3a) $ form an arithmetic sequence with a non-zero common difference, determine the number of tangent lines ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the solution set of $\\left(m-1\\right)x \\gt m-1$ is $x \\lt 1$, determine the range of $m$.",
"role": "user"
}
] | math | {
"ground_truth": "m < 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 rectangular box measures $a \\times b \\times c$, where $a$, $b$, and $c$ are integers and $2 \\leq a \\leq b \\leq c$. The volume of the box is one third of its surface area. ... | math | {
"ground_truth": "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": "Find all prime numbers $p$ such that there exists a unique $a \\in \\mathbb{Z}_p$ for which $a^3 - 3a + 1 = 0.$",
"role": "user"
}
] | math | {
"ground_truth": "p = 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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