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": "The difference between two positive integers is 8, and their product is 240. What is the sum of these integers?",
"role": "user"
}
] | math | {
"ground_truth": "32",
"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 $150 \\times 22.5 \\times (1.5)^2 \\times 10$. Which of the following is the correct result?\n- **Note**: This problem retains multiplication but modifies ... | math | {
"ground_truth": "75937.5",
"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": "How many pairs $(a, b)$ of positive integers $a,b$ solutions of the equation $(4a-b)(4b-a )=1770^n$ exist , if $n$ is a positive integer?",
"role": "user"
}
] | math | {
"ground_truth": "N_n = 9(n-1)^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, with sides $a$, $b$, $c$ that are opposite to angles $A$, $B$, $C$ respectively, it is given that $b^2 + c^2 - a^2 = bc$, $\\overrightarrow{AB} \\cdot \\overri... | math | {
"ground_truth": "b+c \\in \\left(\\frac{3}{2}, \\frac{3\\sqrt{3}}{2}\\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": "Let \\( ABCD \\) and \\( WXYZ \\) be two squares that share the same center such that \\( WX \\parallel AB \\) and \\( WX < AB \\). Lines \\( CX \\) and \\( AB \\) intersect at \... | math | {
"ground_truth": "\\sqrt{2} + 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": "The edges of a rectangular parallelepiped are $a$, $b$, and $c$. Find the angles between its diagonals.",
"role": "user"
}
] | math | {
"ground_truth": "\\alpha = 180^\\circ - \\arccos\\left(\\frac{b^2 - a^2 - c^2}{a^2 + b^2 + c^2}\\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 dam releases water into a pipe with an inside diameter of 8 inches. To distribute this water equally over various parts of a city, it is proposed to use smaller pipes each with... | 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": "Evaluate the expression: $\\frac{32 \\times 2 - 16}{8 - (2 \\times 3)}$",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the ellipse $mx^{2}+4y^{2}=1$ with an eccentricity of $\\frac{\\sqrt{2}}{2}$, find the real number $m$ equal to \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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 all prime numbers \\( p \\) such that there exist strictly positive integers \\( x \\) and \\( y \\) that satisfy:\n\n\\[ x(y^2 - p) + y(x^2 - p) = 5p \\]",
"role": "use... | math | {
"ground_truth": "2, 3, 7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the function value of $f(x) = 2x^4 + 3x^3 + 5x - 4$ at $x=2$ using Horner's Method.",
"role": "user"
}
] | math | {
"ground_truth": "62",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $y < 0$, find the range of all possible values of $y$ such that $\\lceil{y}\\rceil\\cdot\\lfloor{y}\\rfloor=132$. Express your answer using interval notation.",
"role": "u... | math | {
"ground_truth": "(-12, -11)",
"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": "Kelvin the Frog lives in the 2-D plane. Each day, he picks a uniformly random direction (i.e. a uniformly random bearing $\\theta\\in [0,2\\pi]$ ) and jumps a mile in that dire... | math | {
"ground_truth": "200",
"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 the function $f(x) = \\ln(-x^2 + x)$, then the domain of $f(x)$ is",
"role": "user"
}
] | math | {
"ground_truth": "(0, 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": "Given a sequence of length 15, determine the number of arrangements that have exactly one block of zeros and exactly one block of ones.",
"role": "user"
}
] | math | {
"ground_truth": "238",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, $|\\overrightarrow{AB}|=5$, $|\\overrightarrow{AC}|=4$, $|\\overrightarrow{BC}|=3$, then $\\overrightarrow{AB} \\cdot \\overrightarrow{BC}=$ _____ .",
"r... | math | {
"ground_truth": "-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": "Liza found the total of the interior angles of a convex polygon. She missed one of the angles and obtained the result $2017^\\circ$. Which of the following was the angle she miss... | math | {
"ground_truth": "143^\\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": "A five-digit integer is chosen at random. What is the probability that the integer ends in 0 and all its non-zero digits are distinct?\nA) $\\frac{18}{625}$\nB) $\\frac{21}{625}$... | math | {
"ground_truth": "\\textbf{(B)}\\ \\frac{21}{625}",
"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 $p, q, r, s$ be real numbers. If all the roots of the equation $w^4 + pw^3 + qw^2 + rw + s = 0$ are complex numbers, and they lie symmetrically about the real or imaginary ax... | 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": "Let \\( x = -\\sqrt{2} + \\sqrt{3} + \\sqrt{5} \\), \\( y = \\sqrt{2} - \\sqrt{3} + \\sqrt{5} \\), and \\( z = \\sqrt{2} + \\sqrt{3} - \\sqrt{5} \\). What is the value of the exp... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $i$ is the imaginary unit, and the complex number $z$ satisfies $z= \\frac {4}{1-i}$, calculate the imaginary part of the complex number $z$.",
"role": "user"
}
... | 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 1 can of soup can feed $4$ adults or $6$ children, calculate the number of adults that $4$ cans of soup can feed.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the least common multiple of 5, 6, 8, and 18?",
"role": "user"
}
] | math | {
"ground_truth": "360",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=2x+1$, if $f_{1}(x)=f(x)$, $f_{n+1}(x)=f[f_{n}(x)]$, $n\\in\\mathbb{N}^{*}$. Then the expression for $f_{5}(x)$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "32x+31",
"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 parallelogram has adjacent sides of lengths $s$ units and $2s$ units forming a 60-degree angle. Determine the value of $s$ if the area of the parallelogram is given to be $6\\s... | math | {
"ground_truth": "\\sqrt{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": "If $z=2+3i$, then calculate $|{z-\\overline{z}}|$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer, $n$ , which can be expressed as the sum of distinct positive integers $a,b,c$ such that $a+b,a+c,b+c$ are perfect squares.",
"role": ... | math | {
"ground_truth": "55",
"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": "Circles $C_1$ and $C_2$ intersect at points $X$ and $Y$ . Point $A$ is a point on $C_1$ such that the tangent line with respect to $C_1$ passing through $A$ inter... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For each integer $n \\geq 2$, define $B(n)$ as the area of the region in the coordinate plane determined by the inequalities $2 \\leq x \\leq n$ and $0 \\leq y \\leq x \\lceil \\... | math | {
"ground_truth": "850",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The maximum value of the function $f(x) = x(4-x)$, where $x \\in (0, 4)$, is ____.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "N > 3 is an odd integer. Find all positive integers a, b, c such that a^N = b^N + 2^N + abc, and c ≤ 5 * 2^(N-1).",
"role": "user"
}
] | math | {
"ground_truth": "\\{ N = 5, a = 3, b = 1, c = 70 \\}",
"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": "Investigate the asymptotic behaviour of the solutions $y$ of the equation $x^5 + x^2y^2 = y^6$ that tend to zero as $x\\to0$ .",
"role": "user"
}
] | math | {
"ground_truth": "y = \\pm x^{1/2} + o(x^{1/2})",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A school has $100$ students divided among $5$ classes taught by $5$ teachers, with each teacher teaching one class. The student distribution across the classes is $40, 40, 10, 5,... | math | {
"ground_truth": "-13.5",
"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": "Let $\\{a_n\\}$ be a geometric sequence with a positive common ratio, where $a_1=2$ and $a_3=a_2+4$. \n(I) Find the general formula for $\\{a_n\\}$. \n(II) Let $\\{b_n\\}$ be a... | math | {
"ground_truth": "S_n=2^{n+1}+n^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": "Every spring, the sea of rapeseed flowers in Wuyuan attracts tens of thousands of tourists, making rapeseed flowers a characteristic landscape of \"China's most beautiful country... | math | {
"ground_truth": "\\frac{7}{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": "For every positive integer $n$ less than $3000$, define\n\\[\na_n = \\left\\{\\begin{array}{lr}\n15, & \\text{if } n \\text{ is divisible by } 15 \\text{ and } 16; \\\\\n16, & \\... | math | {
"ground_truth": "A) 543",
"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 half of the pink flowers are roses, half of the red flowers are carnations, three fifths of the flowers are pink, and one fifth of the flowers are white, determine the... | math | {
"ground_truth": "60\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A telephone number has the form $\\text{ABC-DEF-GHIJ}$, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, $A... | math | {
"ground_truth": "8",
"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": "Find the smallest period of the function \\( y = \\cos^{10} x + \\sin^{10} x \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x)$ is an odd function defined on $(-\\infty, 0) \\cup (0, +\\infty)$, and $f(-1) = 0$. If for any two real numbers $x_1$, $x_2 \\in (0, +\\infty)$ and... | math | {
"ground_truth": "(-\\infty, -1) \\cup (1, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given Amy, Beth, and Jo listen to five different songs and discuss which ones they like, determine the total number of ways this is possible if no song is liked by no one.",
... | math | {
"ground_truth": "300",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the fractional equation $\\frac{2x-m}{x+1}=1$ with respect to $x$, solve for the range of the real number $m$ such that the solution is negative.",
"role": "user"
}
] | math | {
"ground_truth": "m < -1 \\text{ and } m\\neq -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": "Clara and Dave are tiling a floor. The ratio of the amount of work Clara does to the amount of work Dave does is $4:7$. If the floor requires a total of $330$ square meters to be... | math | {
"ground_truth": "210",
"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": "**p1.** What is the maximum possible value of $m$ such that there exist $m$ integers $a_1, a_2, ..., a_m$ where all the decimal representations of $a_1!, a_2!, ..., a_m!$ ... | math | {
"ground_truth": "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 \\( x, y, z \\) be positive numbers that satisfy the following system of equations:\n\n$$\n\\left\\{\\begin{array}{l}\nx^{2}+x y+y^{2}=12 \\\\\ny^{2}+y z+z^{2}=16 \\\\\nz^{2}... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a rhombus with angle $\\angle A = 60^\\circ$ . Let $E$ be a point, different from $D$ , on the line $AD$ . The lines $CE$ and $AB$ intersect at $F$ . Th... | math | {
"ground_truth": "120^\\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": "Compute\n\\[\\left( 1 + \\cos \\frac{\\pi}{10} \\right) \\left( 1 + \\cos \\frac{3\\pi}{10} \\right) \\left( 1 + \\cos \\frac{7\\pi}{10} \\right) \\left( 1 + \\cos \\frac{9\\pi}{... | math | {
"ground_truth": "\\frac{3 - \\sqrt{5}}{32}",
"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": "Among the following statements: ① The function relationship is a deterministic relationship; ② The correlation relationship is a non-deterministic relationship; ③ Regression anal... | math | {
"ground_truth": "\\text{①②④}",
"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 greatest common divisor of $8!$ and $9!$.",
"role": "user"
}
] | math | {
"ground_truth": "40320",
"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": "(1) Simplify: $\\dfrac{\\cos 2\\alpha }{2\\tan (\\dfrac{\\pi }{4}-\\alpha ){{\\sin }^{2}}(\\dfrac{\\pi }{4}+\\alpha )}$;\n\n(2) Evaluate: $\\dfrac{\\cos {{10}^{\\circ }}(\\sqrt{3... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n_1,n_2,\\ldots,n_s$ be distinct integers such that $$ (n_1+k)(n_2+k)\\cdots(n_s+k) $$ is an integral multiple of $n_1n_2\\cdots n_s$ for every integer $k$ . For each... | math | {
"ground_truth": "\\{n_1, n_2, \\ldots, n_s\\} = \\{1, 2, \\ldots, s\\}",
"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": "In an opaque box, there are a total of $40$ identical black and white balls except for color. Xiao Ming conducts a ball-picking experiment. After stirring the balls in the box, h... | math | {
"ground_truth": "10",
"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 a circle with radius $r$ tangent to sides $AB,AD$, and $CD$ of rectangle $ABCD$ and passing through the midpoint of diagonal $AC$, find the area of the rectangle in terms o... | math | {
"ground_truth": "8r^2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(y = \\frac{x^2 - 3x + 10}{x - 5}\\), determine the \\(x\\) value where there is a vertical asymptote.",
"role": "user"
}
] | math | {
"ground_truth": "x = 5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the rational number $p/q$ be closest to but not equal to $22/7$ among all rational numbers with denominator $< 100$ . What is the value of $p - 3q$ ?",
"role": "use... | math | {
"ground_truth": "14",
"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 integers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 < 16 \\), and \\( xy > 4 \\). Determine the maximum value of \\( x^2 - 2xy - 3y \\).",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We call a positive integer $N$ *contagious* if there are $1000$ consecutive non-negative integers such that the sum of all their digits is $N$ . Find all contagious positive... | math | {
"ground_truth": "N = 13500, 13501, \\ldots",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the operation $\\spadesuit (x,y)$ is defined as $x-\\dfrac{1}{y}$ for positive numbers $x$ and $y$, calculate $\\spadesuit (2,\\spadesuit (2,2))$.",
"role": "user"... | math | {
"ground_truth": "\\frac{4}{3}",
"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)=\\ln (x+ \\sqrt {x^{2}+1})$, if real numbers $a$ and $b$ satisfy $f(a)+f(b-1)=0$, find the value of $a+b$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $PQR,$ points $M$ and $N$ are on $\\overline{PQ}$ and $\\overline{PR},$ respectively, such that $PM = 2$ and $MQ = 6$, while $PN = 3$ and $NR = 9$. The angle bisector... | math | {
"ground_truth": "\\frac{5}{20} = \\frac{1}{4}",
"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 semicircle. Consider the triangles whose one side contains the diameter of the semicircle and whose other two sides touch the semicircle. Which of these triangles has the... | math | {
"ground_truth": "T \\geq 2r^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": "Consider a sequence \\(y_1, y_2, y_3, \\dots\\) defined by:\n\\[\ny_1 = \\sqrt[4]{4}, \\\\\ny_2 = (\\sqrt[4]{4})^{\\sqrt[4]{4}},\n\\]\nand in general,\n\\[\ny_n = (y_{n - 1})^{\\... | math | {
"ground_truth": "4",
"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 curve defined by the equation r = \\frac{2}{\\sin \\theta + \\cos \\theta}.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A town's population increased by $1,500$ people, and then this new population decreased by $20\\%$. After these changes, the town had $50$ more people than it did before the $1,5... | math | {
"ground_truth": "1,750",
"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": "An $m \\times n$ chessboard where $m \\le n$ has several black squares such that no two rows have the same pattern. Determine the largest integer $k$ such that we can alway... | math | {
"ground_truth": "n - m + 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a point $ M$ found in the same plane with the triangle $ ABC$ , but not found on any of the lines $ AB,BC$ and $ CA$ . Denote by $ S_1,S_2$ and $ S_3$ the area... | math | {
"ground_truth": "G \\left( \\frac{x_1 + x_2 + x_3}{3}, \\frac{y_1 + y_2 + y_3}{3} \\right)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "a) There are $n$ matches on a table. Starting with Aymeric, Aymeric and Maxime take turns taking 1, 2, or 3 matches. The player who takes the last match loses. Determine who has ... | math | {
"ground_truth": "\\text{Aymeric wins if } n \\not\\equiv 0 \\pmod{4}, \\text{ otherwise Maxime wins}",
"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 positive \\( x \\) and \\( y \\) for which the expression\n\n\\[ \n\\frac{x y}{2}+\\frac{18}{x y} \n\\]\n\ntakes the minimum value and among all such \\( x \\) and \\( y... | math | {
"ground_truth": "x=3, y=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": "Find all values of $ \\alpha$ for which the curves $ y\\equal{}\\alpha x^2\\plus{}\\alpha x\\plus{}\\frac1{24}$ and $ x\\equal{}\\alpha y^2\\plus{}\\alpha y\\plus{}\\frac1{2... | math | {
"ground_truth": "\\frac{13 \\pm \\sqrt{601}}{12}, \\frac{2}{3}, \\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An amount needs to be divided among $A, B, C,$ and $D$ such that the ratios of their shares are $3:4:5:6$. However, the amount was divided in the ratio $3:4:6:7$, resulting in $C... | math | {
"ground_truth": "36000",
"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}+x-1$, find the equation of the tangent line at the point $(1,f(1))$.",
"role": "user"
}
] | math | {
"ground_truth": "y = (e + 1)x - (e + 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": "The quadratic $x^2 + 500x + 1000$ can be written in the form $(x+b)^2+c$, where $b$ and $c$ are constants. What is $\\frac{c}{b}$?",
"role": "user"
}
] | math | {
"ground_truth": "-246",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the number of degrees in the acute angle formed by the hands of a clock at 3:37?",
"role": "user"
}
] | math | {
"ground_truth": "113.5^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The $2010$ positive numbers $a_1, a_2, \\ldots , a_{2010}$ satisfy\nthe inequality $a_ia_j \\le i+j$ for all distinct indices $i, j$.\nDetermine, with proof, the largest possible... | math | {
"ground_truth": "\\prod_{i=1}^{1005} (4i-1)",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given $a=1$, $\\angle B=45^{o}$, and the area of $\\triangle ABC$ is $S=2$, find t... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which integers $n = 1, \\ldots , 6$ does the equation $$ a^n + b^n = c^n + n $$ have a solution in integers?",
"role": "user"
}
] | math | {
"ground_truth": "n = 1, 2, 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": "Find the range of the real number $a$ such that for any real number $x$ and any $\\theta \\in\\left[0, \\frac{\\pi}{2}\\right]$, the inequality $(x+3+2 \\sin \\theta \\cos \\thet... | math | {
"ground_truth": "a \\geqslant \\frac{7}{2} \\text{ or } a \\leqslant \\sqrt{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": "Given vectors $\\vec{a}=(-3,1)$ and $\\vec{b}=(x,6)$, if $\\vec{a} \\perp \\vec{b}$, then $x$ equals",
"role": "user"
}
] | 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": "Two brigades together produced 8200 transformer coils. During inspection, $2\\%$ of the coils from one brigade and $3\\%$ from the other brigade were found to be improperly insul... | math | {
"ground_truth": "2940\\ \\text{and}\\ 5044",
"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": "Evaluate: $-\\left(18\\div 3\\cdot 8 - 48 + 4 \\cdot 6\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "-24",
"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": "$7z$ varies inversely as the cube of $x$. When $z=7, x=2$. Find the value of $z$ when $x=4$.\nA) $\\frac{7}{4}$\nB) $\\frac{7}{8}$\nC) $\\frac{8}{7}$\nD) $1$",
"role": "user"... | math | {
"ground_truth": "\\frac{7}{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": "Given a high school with $500$ students, $40\\%$ of the seniors play a musical instrument, while $30\\%$ of the non-seniors do not play a musical instrument. In all, $46.8\\%$ of... | math | {
"ground_truth": "154",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a science fair, 64 students are wearing green shirts, and another 68 students are wearing red shirts. The 132 students are grouped into 66 pairs. In exactly 28 of these pairs,... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the real coefficient equations \\( x^{2} - 2x + 2 = 0 \\) and \\( x^{2} + 2mx + 1 = 0 \\), the 4 distinct roots on the complex plane lie on the same circle. What is the ran... | math | {
"ground_truth": "-1 < m < 1 \\text{ or } m = -\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Bridget gave half of the apples to Ann and then gave Cassie 3 apples and kept 4 apples for herself, calculate the number of apples she originally bought.",
"role":... | math | {
"ground_truth": "14",
"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 out of 200 students, 70% like dancing and the remaining students dislike it, and among those who like dancing, 85% honestly say they like it while the rest say they di... | math | {
"ground_truth": "\\frac{12}{131}",
"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 ordered pair \\( (b, c) \\) of integers, each of which has absolute value less than or equal to seven, chosen randomly with each pair having an equal likelihood of being... | math | {
"ground_truth": "**C)** \\( \\frac{13}{15} \\)",
"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": "Machine P needs an additional 4 hours to do the job; Machine Q needs 2 additional hours; and Machine R now needs half the time it would take P and Q together to do the job alone.... | 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 cylinder with a height of `15` and a radius of `5` is topped with a cone that has the same radius and a height of `8`. Calculate the total surface area of this combined shape."... | math | {
"ground_truth": "175\\pi + 5\\pi \\sqrt{89}",
"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": "Two concentric circles have radii \\( r \\) and \\( R \\) where \\( R > r \\). Three new circles are drawn so that they are each tangent to the two large circles and to the other... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the complex number $z=i(3-2i)(i)$, where $i$ is the imaginary unit, evaluate $\\overline{z}$.",
"role": "user"
}
] | math | {
"ground_truth": "-3-2i",
"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 all pairs $(a,b)$ of integers satisfying: there exists an integer $d \\ge 2$ such that $a^n + b^n +1$ is divisible by $d$ for all positive integers $n$ .",
"rol... | math | {
"ground_truth": "(a, b) \\equiv (0, 1) \\pmod{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A company purchases 200 tons of a certain type of goods per year, divided into several equal purchases. The freight cost for each purchase is 20,000 yuan, and the annual storage ... | math | {
"ground_truth": "10",
"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 $\\sin(\\frac{\\pi}{2} + \\alpha) = \\frac{1}{3}$ where $0 < \\alpha < \\frac{\\pi}{2}$, find the value of $\\cos 2\\alpha$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{7}{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": "Given a circle of radius 3 centered at B(3,3) is dilated to a circle of radius 5, and the new center of the circle is at B'(7,10), determine the distance the origin O(0,0) moves ... | math | {
"ground_truth": "\\sqrt{29}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose 1 euro is equal to 1.5 dollars. If Christina has 750 dollars and Fabien has 450 euros, by what percent is the value of Fabien’s money greater than the value of Christina’... | math | {
"ground_truth": "E) 11.11%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $\\log_{8} 1000$, where $\\log$ has no base specified, therefore it is assumed to be $\\log_{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{\\log_{10} 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": "An eight-sided die is rolled, labeled with numbers 1 through 8. If $Q$ represents the product of the seven numbers that are visible, what is the largest number that is certain to... | math | {
"ground_truth": "48",
"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 machine can operate at different speeds, and some of the items it produces will have defects. The number of defective items produced per hour varies with the machine's operatin... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the hyperbola \\(\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)\\) has an eccentricity of \\(2\\), determine the equations of the asymptotes of the hyperbol... | math | {
"ground_truth": "y = \\pm \\sqrt{3}x",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
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