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": "A triangle with side lengths $DB=EB=2$ is cut from an equilateral triangle ABC of side length $5$. Calculate the perimeter of the remaining quadrilateral.",
"role": "user"
... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $n$ is an integer $\\geq 2$ . Determine the first digit after the decimal point in the decimal expansion of the number \\[\\sqrt[3]{n^{3}+2n^{2}+n}\\]",
"role": "u... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x$ is the fifth power of a positive integer, determine the number of positive integers that are divisors of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "301",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The Evil League of Evil is plotting to poison the city's water supply. They plan to set out from their headquarters at $(5, 1)$ and put poison in two pipes, one along the line ... | math | {
"ground_truth": "4\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $(2+i)^{12}-(2-i)^{12}$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 the polar coordinate system, it is known that $A(2, \\frac{\\pi}{6}), B(4, \\frac{5\\pi}{6})$. Then, the distance between points A and B, $|AB|=$ ______.",
"role": "user"
... | math | {
"ground_truth": "2\\sqrt{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagram shows a $3\\times3$ rectangular array of points, where each point is $1$ unit away from its nearest vertical or horizontal neighbors.\n[asy] \nunitsize(0.25inch); \nd... | math | {
"ground_truth": "36",
"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": "Every fourth-grade classroom at Pine Hill Elementary has $20$ students, $2$ pet rabbits, and $1$ pet hamster. Calculate the total number of students minus the total number of pet... | math | {
"ground_truth": "85",
"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 snail starts at point $A$ on a rubber rope of length $10 \\mathrm{~m}$ with point $B$ fixed to the ground. The snail moves towards $B$ at a speed of $1 \\mathrm{~cm} / \\mathrm... | math | {
"ground_truth": "1.97 \\times 10^{434} \\ \\text{seconds}",
"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 a calculator with a reciprocal key $\\boxed{\\frac{1}{x}}$, if the display initially shows $\\boxed{00012}$, what is the fewest number of times you must press the $\\boxed{... | math | {
"ground_truth": "B) 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 $\\frac{bx(a^2x^2 + 2a^2y^2 + b^2y^2) + ay(a^2x^2 + 2b^2x^2 + b^2y^2)}{bx + ay}$, simplify this expression.",
"role": "user"
}
] | math | {
"ground_truth": "(ax + by)^2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An ellipse has foci at $(5, 15)$ and $(40, 45)$ in the $xy$-plane and is tangent to the $x$-axis. What is the length of its major axis?",
"role": "user"
}
] | math | {
"ground_truth": "10\\sqrt{193}",
"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": "For how many integers $n$ with $1 \\le n \\le 2012$ is the product\n\\[\n \\prod_{k=0}^{n-1} \\left( \\left( 1 + e^{2 \\pi i k / n} \\right)^n + 1 \\right)\n\\]\nequal to ze... | math | {
"ground_truth": "335",
"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 natural numbers \\( n \\) such that \\(\\frac{1}{n}=\\frac{1}{p}+\\frac{1}{q}+\\frac{1}{p q}\\) for some prime numbers \\( p \\) and \\( q \\).",
"role": "user"
}
... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\(14 \\cdot 31\\) and \\(\\left\\lfloor\\frac{2+\\sqrt{2}}{2}\\right\\rfloor + \\left\\lfloor\\frac{3+\\sqrt{3}}{3}\\right\\rfloor + \\left\\lfloor\\frac{4+\\sqrt{4}}{... | math | {
"ground_truth": "1989",
"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 number of real solutions of the equation\n\\[\n\\frac{x}{50} = \\sin x.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the polynomial $x^3 - 6x^2 + 11x - 6 = 0$, and let $y = x + \\frac{1}{x}$. Express the polynomial in terms of $y$.",
"role": "user"
}
] | math | {
"ground_truth": "x^2(y^2 + y - 6) = 0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If point $O$ and point $F$ are respectively the center and the left focus of the ellipse $\\frac{x^2}{2} + y^2 = 1$, and point $P$ is any point on the ellipse, then the minimum v... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(\\log (x^2y^5)= 2\\) and \\(\\log (x^3y^2) = 2\\), what is \\(\\log (xy)\\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{11}",
"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": "Give two regular polygons, where the ratio of the interior angles is $4:3$ and both polygons have more than 5 sides. How many such pairs of polygons exist?\nA) 0 \nB) 1 \nC) 2 ... | math | {
"ground_truth": "\\textbf{(C)}\\ 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": "Let \\(a > 1\\) be a positive real number and \\(n \\geq 2\\) be a natural number. The equation \\(\\lfloor a x \\rfloor = x\\) has exactly \\(n\\) different solutions. Find the ... | math | {
"ground_truth": "1 + \\frac{1}{n} \\leq a < 1 + \\frac{1}{n-1}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the remainder of the Euclidean division of \\( 2018^{2019^{2020}} \\) by 11.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A $20$-gallon tank is filled with oil. Each time, $5$ gallons are removed and replaced with detergent. This process is repeated five times in total. What is the fractional part o... | math | {
"ground_truth": "\\frac{243}{1024}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\( a \\in \\mathbf{R} \\) and the function \\( f(x) = a x^{2} - 2 x - 2a \\). If the solution set of \\( f(x) > 0 \\) is \\( A \\) and \\( B = \\{ x \\mid 1 < x < 3 \\} \\... | math | {
"ground_truth": "(-\\infty, -2) \\cup \\left( \\frac{6}{7}, +\\infty \\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": "Find $\\frac{9}{23} - \\frac{5}{69}$ and reduce your answer to the simplest form.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{22}{69}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the units digit of the sum $64_8 + 75_8$ in base 8.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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": "For each natural number $n\\geq 2$ , solve the following system of equations in the integers $x_1, x_2, ..., x_n$ : $$ (n^2-n)x_i+\\left(\\prod_{j\\neq i}x_j\\right)S=n^3-n^2,... | math | {
"ground_truth": "x_i = 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": "Bella has two tanks. Initially, the first tank is $\\frac{3}{4}$ full of oil and the second tank is completely empty. Bella pours all the oil from the first tank into the second ... | math | {
"ground_truth": "\\frac{8}{15}",
"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": "On a certain function calculator, there is a display and two operation buttons. If the first button is pressed, it changes the number on the display to $\\left[\\frac{x}{2}\\righ... | math | {
"ground_truth": "233",
"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 addition is incorrect. Find the largest digit that can be changed to make the addition correct.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What value of $x$ will give the minimum value for the quadratic $x^2 - 8x + 18$?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"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 company sells a product, which costs 8 RMB per unit, at 10 RMB per unit, and they can sell 100 units per day. For each 1 RMB increase in the selling price, the selling ... | math | {
"ground_truth": "360",
"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 \\( a^3 - a - 1 = 0 \\), \\( a + \\sqrt{2} \\) is a root of some polynomial with integer coefficients. Find this polynomial with leading coefficient 1 and the lowest degree ... | math | {
"ground_truth": "x^6 - 8x^4 + 13x^2 - 2x^3 - 10x - 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\cos (\\frac{π}{4}-x)= \\frac{3}{5}$, find the value of $\\sin 2x$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{7}{25}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that point \\( P \\) moves on the circle \\( C: x^{2}+(y+2)^{2}=\\frac{1}{4} \\), and point \\( Q \\) moves on the curve \\( y=a x^{2} \\) (where \\( a > 0 \\) and \\( -1 \... | math | {
"ground_truth": "\\frac{\\sqrt{3} - 1}{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 proposition $p$: There exists some $x_{0} \\in \\mathbb{R}$ such that $mx_{0}^{2} + 1 < 1$, and proposition $q$: For all $x \\in \\mathbb{R}$, $x^2 + mx + 1 \\geq 0$. D... | math | {
"ground_truth": "[-2, 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": "The following propositions are given: \n① The values of trigonometric functions with the same name for angles with the same terminal side are equal; \n② The values of trigonome... | 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": "Given that $x < 1$ and\n\\[\n(\\log_{10} x)^2 - \\log_{10}(x^2) = 48,\n\\]\ncompute the value of \n\\[\n(\\log_{10}x)^5 - \\log_{10}(x^5).\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "-7746",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the New Year's table, there are 4 glasses arranged in a row: the first and third contain orange juice, and the second and fourth are empty. In anticipation of guests, Valya ab... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many unordered pairs of edges of a given square pyramid determine a plane?",
"role": "user"
}
] | math | {
"ground_truth": "22",
"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": "Consider a regular 18-gon. It has $L$ lines of symmetry, and the smallest positive angle for which it has rotational symmetry is $R$ degrees. Determine the value of $L+R$.\nA) 34... | math | {
"ground_truth": "C) 38",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the coefficients in the expansion of the binomial $({a \\over x} + 3)^n$ is $256$. Find the value(s) of $a$.",
"role": "user"
}
] | math | {
"ground_truth": "a = -1 \\text{ or } a = -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": "Let $\\mathbb{R}^{+}$ be the set of positive real numbers. Find all real numbers $a$ for which there exists a function $f :\\mathbb{R}^{+} \\to \\mathbb{R}^{+}$ such that ... | math | {
"ground_truth": "a \\le 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": "Given that point $P(x,y)$ moves on the line segment $AB$, with $A(4,0)$ and $B(0,2)$, find the maximum value of $T=\\log_{2}x+\\log_{2}y$.",
"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": "Given that $s$ and $d$ are positive integers, such that $\\frac{1}{s} + \\frac{1}{2s} + \\frac{1}{3s} = \\frac{1}{d^2 - 2d}$, find the smallest possible value of $s + d$.",
"... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A *festive* number is a four-digit integer containing one of each of the digits $0, 1, 2$ , and $4$ in its decimal representation. How many festive numbers are there?",
"r... | math | {
"ground_truth": "18",
"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": "Convert $512_{10}$ to base 5.",
"role": "user"
}
] | math | {
"ground_truth": "4022_5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all triples $(p, q, r)$ of positive integers, where $p, q$ are also primes, such that $\\frac{r^2-5q^2}{p^2-1}=2$ .",
"role": "user"
}
] | math | {
"ground_truth": "(3, 2, 6)",
"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 $f(x)=|x-1|+|x-a|$ where $a\\in \\mathbb{R}$.\n\n$(1)$ If $a=4$, find the solution set of the inequality $f(x) \\geqslant 5$;\n\n$(2)$ If there exists $x \\in ... | math | {
"ground_truth": "-3 \\leqslant a \\leqslant 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": "How many one-thirds are there in $\\frac{9}{2}$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{27}{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": "The maximum value of the function $f(x)=\\ln 3x-3x$ in the interval $(0,e]$ is $\\boxed{\\text{answer}}$.",
"role": "user"
}
] | math | {
"ground_truth": "- \\ln 3-1",
"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": "A jacket originally priced at $120$ is put on sale with a $30\\%$ discount. After applying the discount, an $8\\%$ sales tax is added to the discounted price, along with a fixed ... | math | {
"ground_truth": "95.72",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive integer \\( n \\) that is a multiple of 5, and the least common multiple of \\( n \\) and \\( 5! \\) equals 5 times the greatest common divisor of \\( n \\) and ... | math | {
"ground_truth": "48",
"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 function $f(x)=({2\\cos \\omega x-1})\\sin({\\omega x-\\frac{\\pi}{4}}),\\omega>0$ has $6$ zeros in the interval $(0,3\\pi)$. Determine the range of values for $\\omega$.",
... | math | {
"ground_truth": "(\\frac{7}{9}, \\frac{13}{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": "Compare the sizes of $\\frac{99}{100}, \\frac{100}{101},$ and $\\frac{199}{201}$ and order them from smallest to largest.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{100}{101} > \\frac{199}{201} > \\frac{99}{100}",
"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 10-digit number whose sum of digits is not less than that of any smaller number.",
"role": "user"
}
] | math | {
"ground_truth": "1899999999",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\frac{z}{1-i} = 3+i$, where $i$ is the imaginary unit, then the imaginary part of the complex number $z$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two tour guides are leading six tourists. Each tourist must choose one of the guides, and each guide must take at least one tourist. Determine the number of different groupings o... | math | {
"ground_truth": "62",
"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": "Consider the additive group $\\mathbb{Z}^{2}$ . Let $H$ be the smallest subgroup containing $(3,8), (4,-1)$ and $(5,4)$ .\nLet $H_{xy}$ be the smallest subgroup containin... | math | {
"ground_truth": "(x, y) = (7, 5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = b \\cdot a^x$ (where $a$ and $b$ are constants, $a > 0$, $a \\neq 1$) and its graph passes through points A(1, $\\frac{1}{6}$) and B(3, $\\frac{1}{24}$... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two equilateral triangles $ABC$ and $CDE$ have a common vertex (see fig). Find the angle between straight lines $AD$ and $BE$ .\n![Image](https://1.bp.blogspot.com/-OWpqpA... | math | {
"ground_truth": "\\frac{\\pi}{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": "Given the equation $x^2 + 18x + 30 = 2 \\sqrt{x^2 + 18x + 45}$, find the product of the real roots.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three congruent isosceles triangles $DAO$, $AOB$, and $OBC$ have $AD=AO=OB=BC=15$ and $AB=DO=OC=20$. These triangles are arranged to form trapezoid $ABCD$. Point $P$ is on side $... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function \\( f \\) is defined on the set of integers and satisfies:\n\\[ \nf(n)=\\left\\{\n\\begin{array}{ll}\nn-3 & \\text{if } n \\geq 1000 \\\\\nf[f(n+5)] & \\text{if } n ... | math | {
"ground_truth": "997",
"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": "Circle $C$ is in the interior of circle $D$. The diameter of circle $D$ is 20 cm. What is the diameter of circle $C$ for which the ratio of the shaded area to the area of circle ... | math | {
"ground_truth": "4\\sqrt{5}\\text{ cm}",
"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": "Two points are moving uniformly in the same direction along a circumference of 60 meters. One of the points makes a full revolution 5 seconds faster than the other. The points co... | math | {
"ground_truth": "3 \\, \\text{m/s} \\ \\text{and} \\ 4 \\, \\text{m/s}",
"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 sphere with center $O$ has radius $10$. A right triangle with sides $8, 15,$ and $17$ is situated in 3D space such that each side is tangent to the sphere. What is the distance... | math | {
"ground_truth": "\\sqrt{91}",
"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 a soccer match, based on the attacking and defending situation on the field, the goalkeeper will move back and forth in front of the goal. If we take the goal line as the refe... | 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": "Find all natural numbers $k$ which can be represented as the sum of two relatively prime numbers not equal to $1$ .",
"role": "user"
}
] | math | {
"ground_truth": "k = 5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Isosceles triangle $\\triangle{ABC}$ has $\\angle{BAC}=\\angle{ABC}=30^\\circ$ and $AC=BC=2$ . If the midpoints of $BC$ and $AC$ are $M$ and $N$ , respectively, and t... | math | {
"ground_truth": "\\frac{3\\sqrt{3}}{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": "The numbers from $1$ to $n^2$ are written in order in a grid of $n \\times n$ , one number in each square, in such a way that the first row contains the numbers from $1$ t... | math | {
"ground_truth": "\\frac{3n^2}{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": "Kevin Kangaroo starts at 0 on a number line and wants to reach 2, but he can hop only $\\frac{1}{4}$ of the distance still to travel. Each subsequent hop is $\\frac{1}{4}$ of the... | math | {
"ground_truth": "\\frac{1031769}{2359296}",
"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": "Real numbers $a$, $b$, and $c$ satisfy the inequalities $0 < a < 2$, $-2 < b < 0$, and $0 < c < 3$. Determine which of the following expressions is necessarily positive:\n1. $b +... | math | {
"ground_truth": "b + a^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": "Two circles touch each other internally at point \\( A \\). A radius \\( OB \\) is drawn from the center of the larger circle, touching the smaller circle at point \\( C \\). Det... | math | {
"ground_truth": "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": "Given is a triangle $ABC$ where angle $B$ is $30^{\\circ}$, $AB = 4$, and $BC = 6$. The bisector of angle $B$ intersects side $AC$ at point $D$. Find the area of triangle $ABD$."... | math | {
"ground_truth": "2.4",
"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 the function f(x) satisfies for all real numbers x and y, the equation f(x) + f(2x + y) + 5xy = f(3x - y) + 2x^2 + 1, calculate the value of f(10).",
"role": "user"
}... | math | {
"ground_truth": "-49",
"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 $3n$ -table is a table with three rows and $n$ columns containing all the numbers $1, 2, …, 3n$ . Such a table is called *tidy* if the $n$ numbers in the first row appear... | math | {
"ground_truth": "\\frac{(3n)!}{6^n \\cdot n!}",
"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": "Suppose that the roots of the quadratic $x^2 + ax + b$ are $\\alpha$ and $\\beta$ . Then $\\alpha^3$ and $\\beta^3$ are the roots of some quadratic $x^2 + cx + d$ . Fi... | math | {
"ground_truth": "a^3 - 3ab",
"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": "Evaluate the expression $[4 - 7(4 - 7(4 - 7)^{-1})^{-1}]^{-1}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{19}{35}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The average age of 40 sixth-graders is 12. The average age of 60 of their parents is 35. What is the average age of all these parents and sixth-graders?",
"role": "user"
}
... | math | {
"ground_truth": "25.8",
"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": "Calculate the value of the expression: \\[ \\frac{2 \\times 6}{12 \\times 14} \\times \\frac{3 \\times 12 \\times 14}{2 \\times 6 \\times 3} \\times 2 \\]",
"role": "user"
... | 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": "Find the number of ordered pairs of positive integers $(m,n)$ such that ${m^2n = 20 ^{20}}$.",
"role": "user"
}
] | math | {
"ground_truth": "231",
"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 continuous random variable \\( X \\) is defined by the probability density function \\( f(x) = \\frac{3}{2} \\sin 3x \\) in the interval \\( (0, \\frac{\\pi}{3}) \\); outside... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{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 the sequence $\\{a\\_n\\}$, where $a\\_1= \\frac {5}{6},a\\_2= \\frac {19}{36}$, and the sequence $\\{b\\_n\\}$ is an arithmetic sequence with a common difference of $(-1)$... | math | {
"ground_truth": "a\\_n=6\\[( \\frac {1}{2})^{n+1}-( \\frac {1}{3})^{n+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": "Compute $(23+12)^2 - (23-12)^2$.",
"role": "user"
}
] | math | {
"ground_truth": "1104",
"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 positive integer $N$ with three digits in its base ten representation is chosen at random, with each three-digit number having an equal chance of being chosen. Find the probabi... | math | {
"ground_truth": "\\frac{1}{300}",
"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": "Evaluate the expression: $\\frac{5}{1 - \\frac{1}{2}}$\nA) 2.5\nB) 5\nC) 7.5\nD) 10",
"role": "user"
}
] | 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": "John is purchasing eight items with prices listed as $10.49$, $7.49$, $5.99$, $3.49$, $6.99$, $4.99$, $2.49$, and $11.99$. However, due to a promotion, the item priced at $11.99$... | math | {
"ground_truth": "A) 0%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The project consists of the following processes, and the total number of days for the project is_______. \nProcess a b c d ... | math | {
"ground_truth": "11",
"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 lengths of two altitudes of a triangles are $8$ and $12$ . Which of the following cannot be the third altitude? $ \n\\textbf{a)}\\ 4\n\\qquad\\textbf{b)}\\ 7\n\\qquad\\tex... | 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": "For any positive integers \\( m \\) and \\( n \\), define \\( r(m, n) \\) as the remainder of \\( m \\div n \\) (for example, \\( r(8,3) \\) represents the remainder of \\( 8 \\d... | math | {
"ground_truth": "120",
"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 all words containing only letters $A$ and $B$ . For any positive integer $n$ , $p(n)$ denotes the number of all $n$ -letter words without four consecutive $A$ 's... | math | {
"ground_truth": "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": "Determine the 8th term of the Fibonacci sequence.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"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 60 pieces of wood in a black box, all of the same size and shape. Every 15 pieces are painted the same color. What is the minimum number of pieces that need to be taken... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $(a,b,c,d)$ be an ordered quadruple of not necessarily distinct integers, each one of them in the set ${1,2,3,4}$. Calculate the number of quadruples for which $a\\cdot b - c... | math | {
"ground_truth": "160",
"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 certain item was originally priced at $200$ yuan. After two consecutive price reductions, the selling price became $128$ yuan. Find the average rate of reduction per reduction.... | math | {
"ground_truth": "20\\%",
"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": "All students in a history class took a $100$-point test. Four students scored $100$, each student scored at least $50$, but two students scored at least $70$. The average score w... | math | {
"ground_truth": "The answer is B) 6.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a$ is an integer, and point $A(2a+1, 2+a)$ is in the second quadrant, then $a= \\boxed{-1}$.",
"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": "Given that the first container is $\\tfrac{3}{5}$ full of water, and the second container is $\\tfrac{1}{4}$ full, after transferring the water, the second container becomes $\\t... | math | {
"ground_truth": "\\frac{11}{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": "The seats in the Parliament of some country are arranged in a rectangle of $10$ rows of $10$ seats each. All the $100$ $MP$ s have different salaries. Each of them asks all... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
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