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": "Jack recorded times, in seconds, of 102, 107, 109, 103, and 105 for his first five 100-meter sprints. After his sixth sprint, he reduced his median time to 104 seconds. What was ... | math | {
"ground_truth": "103",
"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 $p$: For real number $x$, $x^{2}-10x+16\\leqslant 0$; $q$: For real number $x$, $x^{2}-4mx+3m^{2}\\leqslant 0$ (where $m \\gt 0$).<br/>$(1)$ If $m=1$ and at least one of $p... | math | {
"ground_truth": "[2, \\frac{8}{3}]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of the smallest and largest possible values for $x$ which satisfy the following equation. $$ 9^{x+1} + 2187 = 3^{6x-x^2}. $$",
"role": "user"
}
] | 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": "Given the function f(x) = ka^x - a^-x (a > 0 and a ≠ 1) defined on the domain R as an odd function.\n1. If f(1) > 0, find the solution set of the inequality f(x^2 + 2x) + f(x - 4... | math | {
"ground_truth": "g(x) = -2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point-like mass moves horizontally between two walls on a frictionless surface with initial kinetic energy E . With every collision with the walls, the mass loses 1/2 of its k... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Katelyn is building an integer (in base $10$ ). She begins with $9$ . Each step, she appends a randomly chosen digit from $0$ to $9$ inclusive to the right end of her curre... | math | {
"ground_truth": "31",
"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": "Show a way to construct an equiangular hexagon with side lengths 1, 2, 3, 4, 5, and 6 (not necessarily in that order).",
"role": "user"
}
] | math | {
"ground_truth": "1, 6, 2, 4, 3, 5 \\text{ (in that order)}",
"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 vertex of a parabola is at the origin, its axis of symmetry is a coordinate axis, and its focus lies on the line $x-y+2=0$. What is the equation of this parabola?",
"role... | math | {
"ground_truth": "x^2 = 8y",
"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": "Compute the number of nonempty subsets $S$ of $\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\}$ such that $\\frac{\\max \\,\\, S + \\min \\,\\,S}{2}$ is an element of $S$ .",
"rol... | math | {
"ground_truth": "234",
"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 space, we start with a set of 7 vertices of a cube. At each step, we are allowed to replace a point with its symmetric image with respect to one of the other points. Can we re... | math | {
"ground_truth": "\\text{We cannot reach the 8th vertex } (1,1,1) \\text{ using the described symmetry operations.}",
"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 $BCDE$ be a trapezoid with $BE\\parallel CD$ , $BE = 20$ , $BC = 2\\sqrt{34}$ , $CD = 8$ , $DE = 2\\sqrt{10}$ . Draw a line through $E$ parallel to $BD$ and a line... | math | {
"ground_truth": "203",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The perimeter of a rectangle is 36 meters, and it is known that the length is three times the width. The area of this rectangle is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "60.75",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the degree of the resulting polynomial when the expression $(3x^5 + 2x^3 - x - 15)(2x^{12} - 8x^8 + 7x^5 + 25) - (x^3 + 3)^6$ is expanded?",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that two calculators are sold at the same price of 80 yuan each, one making a profit of 60% and the other incurring a loss of 20%, calculate the net profit or loss in yuan.... | 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": "Evaluate the expression $500(500^{500}) \\cdot 500$.",
"role": "user"
}
] | math | {
"ground_truth": "500^{502}",
"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 function f(x) = alnx - x^2 + (2a - 1)x, where a ∈ R.\n(I) Find the monotonic intervals of the function f(x) when a = 1;\n(II) Find the extreme values of the function f(... | math | {
"ground_truth": "(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": "Compute the sum of all real numbers x which satisfy the following equation $$ \\frac {8^x - 19 \\cdot 4^x}{16 - 25 \\cdot 2^x}= 2 $$",
"role": "user"
}
] | 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": "Solve the following system of equations:\n\n$$\n\\begin{aligned}\n(x+1)(3-4 y) & =(6 x+1)(3-2 y) \\\\\n(4 x-1)(z+1) & =(x+1)(z-1) \\\\\n(3-y)(z-2) & =(1-3 y)(z-6)\n\\end{aligned}... | math | {
"ground_truth": "(x, y, z) = \\left(0, 0, 0\\right), \\left( \\frac{25}{4} , \\frac{25}{7} , \\frac{10}{19}\\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": "Given that $|\\overrightarrow{a}|=1$ and $|\\overrightarrow{b}|=\\sqrt{2}$,\n(1) If $\\overrightarrow{a}$ is parallel to $\\overrightarrow{b}$, find $\\overrightarrow{a} \\cdot \... | math | {
"ground_truth": "45^{\\circ}",
"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 20% of students in a class are juniors and the remaining 80% are seniors, the average score of the class on the test was 84, and the average score of seniors was 82, d... | math | {
"ground_truth": "92",
"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 $g(x)$ be a polynomial of degree 504 with real coefficients, and let its roots be $s_1, s_2, \\dots, s_{504}$. There are exactly 252 distinct values among\n\\[\n|s_1|, |s_2|,... | math | {
"ground_truth": "126",
"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 power function $f(x) = (m+3)x^{m}$, find the value of $f(2) - f(-2)$ = \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An equilateral triangle has an area of $81\\sqrt{3}$ $\\text{cm}^2$. If each side of the triangle is increased by 3 cm, by how many square centimeters is the area increased?",
... | math | {
"ground_truth": "29.25\\sqrt{3} \\text{ cm}^2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\( A \\) is twice as old as \\( B \\) was when \\( A \\) was as old as \\( B \\) is now. When \\( B \\) is as old as \\( A \\) is now, the sum of their ages will be 130 years. H... | math | {
"ground_truth": "57 \\frac{7}{9} \\text{ and } 43 \\frac{1}{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 two groups of numerical sequences, each group consisting of 15 arithmetic progressions containing 10 terms each. The first terms of the progressions in the first group are ... | math | {
"ground_truth": "\\frac{160}{151}",
"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 $\\tan\\alpha = \\sqrt{2}$, with $\\alpha$ being an angle in the third quadrant, find the value of $\\sqrt{2}\\sin\\alpha + \\cos\\alpha$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If point $P$ is in the second quadrant and the distance to the $x$-axis and $y$-axis are $3$ and $4$ respectively, determine the coordinates of point $P$.",
"role": "user"
... | math | {
"ground_truth": "(-4, 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": "What is the smallest prime number dividing the sum \\(7^{15}+9^{7}\\)?\nA) 2 \nB) 3 \nC) 5 \nD) 7^{15}+9^{7} \nE) none of these",
"role": "user"
}
] | math | {
"ground_truth": "A) 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": "If $\\dfrac{a+2b}{b+2c}=\\dfrac{c+2d}{d+2a}$, determine the relationship among $a$, $b$, $c$, and $d$.",
"role": "user"
}
] | math | {
"ground_truth": "(C)\\ \\text{either }b=2a\\text{ or }a+b+c+d=0\\text{, or both}",
"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=-2016$. Evaluate $\\Bigg\\vert\\Big\\vert |x|-x\\Big\\vert-|x|\\Bigg\\vert-x$.",
"role": "user"
}
] | math | {
"ground_truth": "4032",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\left[x\\right]$ denote the largest integer not exceeding $x$. For example, $\\left[3.1\\right]=3$, $\\left[5\\right]=5$, $\\left[-4.2\\right]=-5$. Given $0 \\lt m \\lt 1$ ... | math | {
"ground_truth": "6 \\text{ or } 7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $m, n \\in \\mathbb{R}$, if line $l: mx + ny - 1 = 0$ intersects the x-axis at point A and the y-axis at point B, and the distance from the origin O to line $l$ is $\\sqrt{... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A man buys a house for $10,000 and rents it. He puts $12\\frac{1}{2}\\%$ of each month's rent aside for repairs and upkeep; pays $325 a year, which is equivalent to $\\frac{325}... | math | {
"ground_truth": "83.33",
"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 the complement of $\\angle \\alpha$ is $30^{\\circ}$, then the value of $\\cos \\alpha$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify and evaluate the function: $$f(\\theta)= \\frac {(1+sin\\theta+cos\\theta)(sin \\frac {\\theta}{2}-cos \\frac {\\theta}{2})}{ \\sqrt {2+2cos\\theta}}$$, where $\\theta \... | math | {
"ground_truth": "- \\frac {\\sqrt {5}}{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": "The value of $3x + 15$ is one third of the value of $6x + 45$. After finding $x$, subtract 5 from the result. What is the final value?",
"role": "user"
}
] | math | {
"ground_truth": "-5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\lfloor x\\rfloor$ denote the greatest integer function and $\\{x\\}=x-\\lfloor x\\rfloor$ denote the fractional part of $x$ . Let $1\\leq x_1<\\ldots<x_{100}$ be t... | math | {
"ground_truth": "1275",
"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": "Define a continuous function $f(x)$ on $\\mathbb{R}$ that satisfies $f(x) + f(-x) = x^2$, and when $x < 0$, $f'(x) < x$ always holds. Then, determine the solution set of the ineq... | math | {
"ground_truth": "(-\\infty, \\frac{1}{2}]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=ax^{3}-3x+1$, for all $x\\in[-1,1]$, the condition $f(x)\\geqslant 0$ holds true. Determine the range of values for $a$.",
"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": "The diagram shows a regular octagon with sides of length 1. The octagon is divided into regions by four diagonals. What is the difference between the area of the hatched region a... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $b$ and $c$ are constants and $4(x + 2)(x + b) = x^2 + cx + 12$, then $c$ is\nA) 5\nB) 7\nC) 10\nD) 12\nE) 14",
"role": "user"
}
] | math | {
"ground_truth": "E) 14",
"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 function $f(x)=\\cos x-ax$, if the function is monotonically decreasing in its domain, determine the range of real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[1, +\\infty\\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": "Given the hyperbola $\\frac{x^{2}}{4} - \\frac{y^{2}}{3} = 1$ with left and right foci $F\\_1$ and $F\\_2$, respectively. Let $P$ be a point on the hyperbola such that $PF\\_1 = ... | math | {
"ground_truth": "PF\\_2 = 7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the total number of different integer values the function \\[ f(x) = [x] + [2x] + [\\frac{5x}{3}] + [3x] + [4x] \\] takes for real numbers $x$ with $0 \\leq x \\leq 100$ ... | math | {
"ground_truth": "734",
"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": "Define a new operation $a \\nabla b = 3 + a^b$. What is the value of $(2 \\nabla 3) \\nabla 2$?",
"role": "user"
}
] | math | {
"ground_truth": "124",
"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": "Circle $A$ is in the interior of circle $B$. The diameter of circle $B$ is 20 cm. What is the diameter of circle $A$ for which the ratio of the shaded area to the area of circle ... | math | {
"ground_truth": "8.16 \\, \\text{cm}",
"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": "Teacher Li bought prizes for students who made progress in their studies, spending a total of $42$ yuan to buy two types of notebooks, $A$ priced at $6$ yuan each and $B$ priced ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x, y, z$ be positive real numbers such that $x + y + z = 2$. Find the maximum value of $x^4y^3z^2$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{9765625}",
"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 \\(x\\) and \\(y\\) be positive real numbers such that \\(4x + 3y < 60.\\) Find the maximum value of\n\\[xy (60 - 4x - 3y).\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2000}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square with sides of length $1$ cm is given. There are many different ways to cut the square into four rectangles.\nLet $S$ be the sum of the four rectangles’ perimeters. D... | math | {
"ground_truth": "8 \\text{ cm} \\text{ or } 10 \\text{ cm}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1)\nproove for positive $a, b, c, d$ $ \\frac{a}{b+c} + \\frac{b}{c+d} + \\frac{c}{d+a} + \\frac{d}{a+b} \\ge 2$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a}{b+c} + \\frac{b}{c+d} + \\frac{c}{d+a} + \\frac{d}{a+b} \\ge 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": "Positive integers \\( a \\) and \\( b \\) satisfy \\( a \\times b = 2010 \\), with \\( a > b \\). Find the smallest possible value of \\( a - b \\).",
"role": "user"
}
] | math | {
"ground_truth": "37",
"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 determinant of the matrix $\\begin{pmatrix} 5 & -2 \\\\ 3 & 1 \\end{pmatrix}$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find the sum of the arithmetic series $10 + 10.5 + 11 + \\cdots + 30$.",
"role": "user"
}
] | math | {
"ground_truth": "820",
"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 cyclic quadrilateral is inscribed in a circle. If the external angles are formed by extending each side of the quadrilateral and inscribed in the four external arcs cut off by ... | math | {
"ground_truth": "360^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine $\\cos B$ in the following right triangle:\n\n[asy]\npair A, B, C;\nA = (0,0);\nB = (8,0);\nC = (0,6);\ndraw(A--B--C--A);\ndraw(rightanglemark(C,A,B,10));\nlabel(\"$A$\... | math | {
"ground_truth": "\\frac{4}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any real number $b$ and positive integer $m$, define\n\\[\n{b \\choose m} = \\frac{b(b-1)(b-2)\\cdots(b-(m-1))}{m(m-1)(m-2)\\cdots(2)(1)}\n\\]\nWhat is\n\\[\n{-\\frac{3}{2} \... | math | {
"ground_truth": "B) -101",
"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 $n \\in \\mathbb{N}_{\\geq 2}.$ For any real numbers $a_1,a_2,...,a_n$ denote $S_0=1$ and for $1 \\leq k \\leq n$ denote $$ S_k=\\sum_{1 \\leq i_1 < i_2 < ... <i_k \... | math | {
"ground_truth": "2^{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $|\\overrightarrow{OA}|=1$, $|\\overrightarrow{OB}|=2$, $\\angle AOB= \\frac{2\\pi}{3} $, and $\\overrightarrow{OC}=\\frac{1}{2}\\overrightarrow{OA}+\\frac{1}{4}\\over... | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many numbers between $1$ and $3000$ are integer multiples of $3$ or $4$ but not $12$?\nA) 1250\nB) 1400\nC) 1500\nD) 1600\nE) 1750",
"role": "user"
}
] | math | {
"ground_truth": "C) 1500",
"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 $PQR$, $PQ = PR$ and $\\angle QPR = 104^\\circ$. Point $S$ is in the interior of the triangle such that $\\angle PSQ = 13^\\circ$ and $\\angle PSR = 27^\\circ$. Deter... | math | {
"ground_truth": "116^\\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": "Given that the point \\\\((1,t)\\\\) is above the line \\\\(2x-y+1=0\\\\), and the inequality \\\\(x^{2}+(2t-4)x+4 > 0\\\\) always holds, the value set of \\\\(t\\\\) is \\_\\_\\... | math | {
"ground_truth": "\\{t|3 < t < 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": "Let $[r, s]$ represent the least common multiple of integers $r$ and $s$. Find the number of ordered triples of positive integers $(a, b, c)$ such that $[a, b] = 1000$, $[b, c] =... | math | {
"ground_truth": "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": "Two concentric circles have radii of 7 meters and 15 meters. An aardvark starts at a point \\( A \\) on the larger circle and runs a path that includes an arc and line segments, ... | math | {
"ground_truth": "**B)** \\( \\frac{37\\pi}{2} + 23 \\)",
"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": "Mike is organizing a debate competition and needs to prepare pairs of participants for initial debates. If he has a group of 12 participants, how many unique pairs can he form fo... | math | {
"ground_truth": "66",
"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": "Real numbers $x$ and $y$ are chosen independently and uniformly at random from the interval $(0,1)$. Calculate the probability that $\\lfloor\\log_{10}x\\rfloor=\\lfloor\\log_{10... | math | {
"ground_truth": "0.00818",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of the tangent line to the curve f(x) = 2$\\sqrt{x}$ - $\\frac{1}{x}$ at x = 1 is $\\boxed{\\text{answer}}$.",
"role": "user"
}
] | math | {
"ground_truth": "2x - y - 1 = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an ellipse, we have the following conclusion: The midpoint of a chord with a slope of 1 on the ellipse $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1$ lies on the line $\\frac{... | math | {
"ground_truth": "\\frac{x}{a^{2}}- \\frac{y}{b^{2}}=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation \\[\\frac{x^2}{49} + \\frac{(y-3)^2}{25} = 0,\\] find the largest possible \\( y \\)-coordinate of all points on the graph of this equation.",
"role": "use... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the cartesian coordinate system $(xOy)$, the parametric equations of the curve $C$ are $\\begin{cases}x=3\\cos α \\\\\\\\ y=\\sin α\\end{cases} (α\\text{ is the parameter})$. ... | math | {
"ground_truth": "\\dfrac{18 \\sqrt{2}}{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": "Let \\( n \\) be an integer greater than 1. Within a square with side length \\( n \\), we want to place \\( n^2 \\) closed discs of unit diameter without any overlap. Is there a... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a hyperbola passes through the point $(2,3)$ and one of its asymptotes is given by the equation $y= \\sqrt {3}x$, find the standard equation of the hyperbola.",
"r... | math | {
"ground_truth": "x^{2} - \\frac{y^{2}}{3} = 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 circles with centers \\( E \\) and \\( F \\) are tangent to segment \\( BD \\) and to the semicircles with diameters \\( AB \\), \\( BC \\), and \\( AC \\). Let \\( r_1 \\), ... | math | {
"ground_truth": "l_1 = \\frac{r_1 r_2}{r_1 + r_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": "The sequence $\\{a_{n}\\}$ satisfies $a_{1}=2$, $a_{n+1}=\\lambda a_{n}+2^{n}$, where $n\\in \\mathbb{N}^{*}$ and $\\lambda$ is a constant. \n$(1)$ Does there exist a real numbe... | math | {
"ground_truth": "\\frac{n(n+3)}{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": "For a positive integer \\( n \\) less than \\( 2000 \\), the decimal equivalent of \\( \\frac{1}{n} \\) is \\( 0.\\overline{abcdefgh} \\), a repeating decimal of period \\( 8 \\)... | math | {
"ground_truth": "[801, 1200]",
"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 are the positive integers \\( n \\) such that \\( n+2009 \\) divides \\( n^{2}+2009 \\) and \\( n+2010 \\) divides \\( n^{2}+2010 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "n = 0 \\quad \\text{or} \\quad n = 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 sides of a triangle are 3, 4, and 5 cm. Determine the areas of the triangles formed by the altitude and the median drawn to the longest side.",
"role": "user"
}
] | math | {
"ground_truth": "3 \\ \\text{cm}^2 \\quad ; \\quad 0.84 \\ \\text{cm}^2 \\quad ; \\quad 2.16 \\ \\text{cm}^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": "Solve the inequality: $2\\left(x-3\\right) \\lt 8$.",
"role": "user"
}
] | math | {
"ground_truth": "x < 7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "<u>Round 9</u>**p25.** Circle $\\omega_1$ has radius $1$ and diameter $AB$ . Let circle $\\omega_2$ be a circle withm aximum radius such that it is tangent to $AB$ and i... | math | {
"ground_truth": "\\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": "Given the function $f(x)=ax^{3}+3x^{2}+2$, determine the value of $a$ if ${f}'(-1)=-12$.",
"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": "Three points $A,B,C$ are such that $B \\in ]AC[$ . On the side of $AC$ we draw the three semicircles with diameters $[AB], [BC]$ and $[AC]$ . The common interior tangent ... | math | {
"ground_truth": "\\frac{r_1 r_2}{(r_1 + r_2)^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 valid license plate in New Xanadu consists of two letters followed by three digits and then one letter again. How many valid license plates are possible?",
"role": "user"
... | math | {
"ground_truth": "17,576,000",
"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 \\( f(x) = \\sqrt{\\frac{1-x}{1+x}} \\). If \\( \\alpha \\in \\left( \\frac{\\pi}{2}, \\pi \\right) \\), then simplify \\( f(\\cos \\alpha) + f(-\\cos \\alpha) \\).",
"... | math | {
"ground_truth": "2 \\csc \\alpha",
"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": "An equilateral triangle $ABC$ is divided into $100$ congruent equilateral triangles. What is the greatest number of vertices of small triangles that can be chosen so that no ... | math | {
"ground_truth": "7",
"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 $$a= \\int_{ 0 }^{ \\pi }\\sinxdx$$, find the constant term in the expansion of $$(x+ \\frac {a}{x})^{8}$$.",
"role": "user"
}
] | math | {
"ground_truth": "1120",
"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 sum of the exponents in all divisors of the number \\( N = p^{\\alpha} q^{\\beta} \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2} (\\alpha + 1) (\\beta + 1) (\\alpha + \\beta)",
"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": "Simplify the expression $3y + 5y + 2y + 7y$.",
"role": "user"
}
] | math | {
"ground_truth": "17y",
"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 sum of $0.\\overline{6} + 0.\\overline{7}$ as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the function $f(x) = a \\cdot 2^x + 2^{-x}$ is an even function, then the value of the real number $a$ is",
"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": "Find all functions $f : \\mathbb N \\mapsto \\mathbb N$ such that the following identity $$ f^{x+1}(y)+f^{y+1}(x)=2f(x+y) $$ holds for all $x,y \\in \\mathbb N$",
"role... | math | {
"ground_truth": "f(f(n)) = f(n+1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the number $4^{16}5^{25}$ is written in the usual base $10$ form, calculate the number of digits in this number.",
"role": "user"
}
] | math | {
"ground_truth": "28",
"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": "When a polynomial $p(x)$ is divided by $x + 1,$ the remainder is 3. When $p(x)$ is divided by $x + 3,$ the remainder is -4. Find the remainder when $p(x)$ is divided by $(x + 1)(... | math | {
"ground_truth": "\\frac{7}{2}x + \\frac{13}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "One digit of the decimal representation of $\\frac{2}{7}$ is randomly selected. What is the probability that the digit is a 1? Express your answer as a common fraction.",
"ro... | math | {
"ground_truth": "\\frac{1}{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 the function $f(x) = x^3 + ax^2 + 3x + 1$ is not monotonic on $\\mathbb{R}$, then the range of the real number $a$ is.",
"role": "user"
}
] | math | {
"ground_truth": "a > 3 \\text{ or } a < -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": "Determine the coefficient of \\( x^{2} \\) after expanding and combining like terms in the expression\n\n$$\n\\underbrace{\\left(\\ldots\\left(\\left((x-2)^{2}-2\\right)^{n}-2\\r... | math | {
"ground_truth": "\\frac{4^{2k-1} - 4^{k-1}}{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 vectors $\\overrightarrow {a}, \\overrightarrow {b}$, satisfy $\\overrightarrow {a}+2 \\overrightarrow {b}=(1，-3), 2 \\overrightarrow {a}- \\overrightarrow {b}=(1，9)$, find... | math | {
"ground_truth": "-\\frac {222}{25}",
"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": "Evaluate $i^{25} + i^{125}$.",
"role": "user"
}
] | math | {
"ground_truth": "2i",
"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 four vertices of a regular tetrahedron $ABCD$ lie on a sphere with radius $R$. Calculate the length of $AB$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2 \\sqrt{6}}{3} R",
"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 woman weaves 5 yards on the first day, and a total of 390 yards in a month. If she weaves a fixed amount more cloth each day than she did the previous day, starting from the ... | math | {
"ground_truth": "\\frac{16}{29}",
"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 the sum of the first 5 terms of an arithmetic sequence is 10, and the sum of the first 10 terms is 50, then the sum of the first 15 terms equals _______.",
"role": "user"
... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
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