data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In trapezoid $ABCD$, sides $AB$ and $CD$ are parallel with $AB = 10$ units and $CD = 14$ units. The angle between side $AD$ and base $AB$ is $45^\\circ$, and the angle between si... | math | {
"ground_truth": "24 + 2\\sqrt{2} + \\frac{4\\sqrt{3}}{3}\\text{ units}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all values of $a$ such that there are positive integers $a$ and $b$ satisfying $(a - b)\\sqrt{ab} = 2016$ .",
"role": "user"
}
] | math | {
"ground_truth": "209",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $3/7$ of the students are wearing glasses and $4/9$ of the students are wearing blue shirts, find the minimum number of students in the classroom wearing both glasses ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive sequences $\\{a_n\\},\\{b_n\\}$ satisfy: $a_1=b_1=1,b_n=a_nb_{n-1}-\\frac{1}{4}(n\\geq 2)$ .\nFind the minimum value of $4\\sqrt{b_1b_2\\cdots b_m}+\\sum_{k=1}^m\\fra... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain line reflection transforms $\\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}$ to $\\begin{pmatrix} 1 \\\\ -6 \\end{pmatrix}.$ Which vector does the same reflection operation tr... | math | {
"ground_truth": "\\begin{pmatrix} -3 \\\\ 7 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the plane vector $\\overrightarrow{AB}=(-1,2)$, determine the unit vector in the same direction as $\\overrightarrow{AB}$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\frac{\\sqrt{5}}{5}, \\frac{2\\sqrt{5}}{5})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a math class exercise, the teacher modifies the game,\n\n\"Think of a number, multiply it by 3, add 2 to it, and then double the result. Give the answer to your partner. Partn... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following system of equations, in which $a$ is a given number satisfying $|a| > 1$ :\r\n\r $\\begin{matrix} x_{1}^2 = ax_2 + 1 x_{2}^2 = ax_3 + 1 \\ldots x_{999}^... | math | {
"ground_truth": "x_i = \\frac{a + \\sqrt{a^2 + 4}}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an even function $f(x)$ that is monotonically increasing on $[0,+\\infty)$, and $f(-2)=1$, determine the range of $x$ for which $f(x-2) \\leqslant 1$.",
"role": "user"
... | math | {
"ground_truth": "[0,4]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the positive numbers $x$ and $y$ satisfy the equation $x + 3y = 5xy$, find the minimum value of $3x + 4y$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John is thinking of another number. He now gives the following clues: \"My number has 64 as a factor. My number is a multiple of 45. My number is between 1000 and 3000.\" What is... | math | {
"ground_truth": "2880",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola \\( y = (n^2 + n) x^2 - (2n + 1) x + 1 \\), find the value of \\( \\sum_{i=1}^{1992} |A_i B_i| \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1992}{1993}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the expansion of ${({{x^2}-\\frac{1}{x}+1})^4}$, the constant term is ______.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the program: \nINPUT x \nIF 9<x AND x<100 THEN \na=x＼10 \nb=x MOD 10 \nx=10*b+a \nPRINT x \nEND IF \nEND \n(Note: \"＼\" represents the integer part of the quotient... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a cube with sides of length 6 feet. If a cylindrical section with a radius of 3 feet is removed from the solid vertically, determine the total remaining volume of the cu... | math | {
"ground_truth": "216 - 54\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression $\\sqrt[4]{M\\sqrt[4]{M\\sqrt[4]{M}}}$ for $M > 1$.\nA) $M^{\\frac{1}{16}}$\nB) $M^{\\frac{21}{64}}$\nC) $M^{\\frac{1}{4}}$\nD) $M^{\\frac{5}{64}}$",
... | math | {
"ground_truth": "M^{\\frac{21}{64}}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Samantha has two pennies, one nickel, three dimes, and two quarters in her purse. Find the percentage of one dollar that is in her purse.",
"role": "user"
}
] | math | {
"ground_truth": "87\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all nonempty finite sets \\(X\\) of real numbers with the following property:\n\\[ x + |x| \\in X \\quad \\text{ for all } x \\in X. \\]",
"role": "user"
}
] | math | {
"ground_truth": "\\{0, x_1, x_2, \\ldots, x_m\\} \\text{ where } x_1, x_2, \\ldots, x_m \\leq 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the vertex angle of the axial section of a cone if the central angle in the development of its lateral surface is $\\alpha$ radians.",
"role": "user"
}
] | math | {
"ground_truth": "2 \\cdot \\arcsin \\left(\\frac{\\alpha}{2\\pi}\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of the cross-section of a sphere with a radius of 3 by a plane that is at a distance of 2 from its center.",
"role": "user"
}
] | math | {
"ground_truth": "5 \\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $2+i$ ($i$ is the imaginary unit) is a root of the equation $x^2+mx+n=0$ with real coefficients, then the focal length of the conic section $\\frac {x^{2}}{m}$$+ \\frac {y^{2}... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For every $5^\\circ$ rise in temperature, the volume of a certain gas expands by $5$ cubic centimeters. If the volume of the gas is $40$ cubic centimeters when the temperature is... | math | {
"ground_truth": "C) 20 cm³",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the odd function $f(x)$ defined on $\\mathbb{R}$ is monotonically increasing on $(0,+\\infty)$, and $f(-1)=2$, determine the solution set of the inequality $f(x-1)+2\\... | math | {
"ground_truth": "(1,2]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The square root of the real number $\\sqrt{9}$ is what?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the average number of pairs of consecutive integers in a randomly selected subset of $5$ distinct integers chosen from the set $\\{ 1, 2, 3, …, 30\\}$?",
"role": "use... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $X_1, X_2, \\ldots$ are real numbers between 0 and 1 that are chosen independently and uniformly at random. Let $S=\\sum_{i=1}^kX_i/2^i,$ where $k$ is the lea... | math | {
"ground_truth": "2\\sqrt{e} - 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an acute angle $\\theta$ in a right triangle, determine the smallest possible positive value of $\\frac{\\sin \\theta + \\cos \\theta}{\\sin \\theta - \\cos \\theta} + \\fr... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When Ringo places his marbles into bags with 8 marbles per bag, he has 5 marbles left over, and when Paul does the same, he has 7 marbles left over. George has 2 fewer marbles th... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right triangle has a perimeter of $k$ and an incircle radius of $\\varrho$. What are the lengths of the sides? (Numerical example: $k=40 \\mathrm{~cm}, \\varrho=3 \\mathrm{~cm}... | math | {
"ground_truth": "a = 15 \\, \\mathrm{cm}, \\, b = 8 \\, \\mathrm{cm}, \\, c = 17 \\, \\mathrm{cm}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equality $(x+m)^2-(x+n)^2=(m-n)^2$, where $m$ and $n$ are unequal non-zero constants, find the expression for $x$ in terms of $m$ and $n$ and determine the number of no... | math | {
"ground_truth": "a = 0, b \\text{ has a unique non-zero value}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rectangle $ABCD$ is inscribed in triangle $EFG$ such that side $AD$ of the rectangle is along side $EG$ of the triangle, and side $AB$ is now one-third the length of side $AD$. T... | math | {
"ground_truth": "\\frac{10800}{289}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The bases \\(AB\\) and \\(CD\\) of the trapezoid \\(ABCD\\) are 41 and 24 respectively, and its diagonals are mutually perpendicular. Find the dot product of the vectors \\(\\ove... | math | {
"ground_truth": "984",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the $y$-intercept and the slope of the line given by the equation \\( 3x - 4y = 12 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many of the following types of quadrilaterals is there a point within the plane of the quadrilateral from which all corners are equidistant?\n\n1. A square\n2. A rectangl... | math | {
"ground_truth": "\\text{(C) } 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the minimum value of the expression \\(x^2 + y^2 - 4x + 6y + 20\\) for real \\(x\\) and \\(y\\)?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four integers, added three at a time, give the sums $160, 185, 205,$ and $230$. Find the largest of these four integers.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A line segment starts at $(3, -2)$ and has a length of 15 units. It ends at the point $(x, 10)$ where $x$ is a real number. Determine the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "12 \\text{ and } -6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be an isosceles trapezoid with bases $AB = 92$ and $CD = 19$. Suppose $AD = BC = x$ and a circle with center on $\\overline{AB}$ is tangent to segments $\\overline{AD}... | math | {
"ground_truth": "1679",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ and $y$ be real numbers with $x>y$ such that $x^2y^2+x^2+y^2+2xy=40$ and $xy+x+y=8$ . Find the value of $x$ .",
"role": "user"
}
] | math | {
"ground_truth": "3 + \\sqrt{7}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of even digits in the base-7 representation of $528_{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the convex pentagon $ABCDE$, $\\angle A = \\angle B = 120^{\\circ}$, $EA = AB = BC = 2$, and $CD = DE = 4$. Calculate the area of $ABCDE$.",
"role": "user"
}
] | math | {
"ground_truth": "7\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the range of values for \\( x \\) that satisfy the inequality \\( |x+1| + |x| < 2 \\).",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3}{2} < x < \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ for which the number \\[ A_n = \\prod_{k=1}^n \\binom{k^2}{k} = \\binom{1}{1} \\binom{4}{2} \\cdots \\binom{n^2}{n} \\] ends in the digit... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a similar one-way single-lane highway, cars travel at the same speed and obey a modified safety rule: the distance from the back of the car ahead to the front of the car behin... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the vibrations \\( y_{1} = \\sin x \\) and \\( y_{2} = \\sin^2 x \\), study the properties of their combined motion \\( y = y_{1} + y_{2} = \\sin x + \\sin^2 x \\) (range o... | math | {
"ground_truth": "[-\\frac{1}{4}, 2]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 10 people sitting around a round table, some of whom are knights and the rest are liars (knights always tell the truth, and liars always lie). It is known that among th... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The polynomial $x^3-kx^2+20x-15$ has $3$ roots, one of which is known to be $3$ . Compute the greatest possible sum of the other two roots.\n\n*2015 CCA Math Bonanza Lightni... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Set \\(A\\) is a 20-element subset of the set \\(M = \\{1, 2, 3, \\ldots, 2012\\}\\), and the difference between any two elements in \\(A\\) is a multiple of 12. How many such su... | math | {
"ground_truth": "8 \\binom{168}{20} + 4 \\binom{167}{20}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A castle has a number of halls and \\( n \\) doors. Every door leads into another hall or outside. Every hall has at least two doors. A knight enters the castle. In any hall, he ... | math | {
"ground_truth": "2n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the lines $l_1: y = 3x - 1$ and $l_2: 2x - my + 1 = 0$, find the value of the real number $m$ if $l_1$ is parallel to $l_2$ ($l_1//l_2$), and the value of $m$ if $l_1$ is p... | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the geometric mean of the expressions $\\frac{x + a}{x}$ and $\\frac{x - a}{x}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{1 - \\frac{a^2}{x^2}}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive divisors of $50!$ are prime?",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point \\( P \\) is located 15 inches from the center of a circle. A secant drawn from \\( P \\) intersects the circle at points \\( Q \\) and \\( R \\) such that the external s... | math | {
"ground_truth": "3\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define a $\\it{good\\ word}$ as a sequence of letters that consists only of the letters $A$, $B$, and $C$ --- some of these letters may not appear in the sequence --- and in whic... | math | {
"ground_truth": "1536",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a parabola $C$: $y^{2}=4x$ with a point $M(4,-4)$ on it. Points $A$ and $B$ are two moving points on the parabola such that $\\overrightarrow{MA} \\cdot \\overrightarrow{MB... | math | {
"ground_truth": "4 \\sqrt {5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider an isosceles right triangle $ABC$ with $AB = AC$ and a right angle at $C$. Suppose a point $P$ is randomly placed within triangle $ABC$. What is the probability that the... | math | {
"ground_truth": "\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The central square of the City of Mathematicians is an $n\\times n$ rectangular shape, each paved with $1\\times 1$ tiles. In order to illuminate the square, night lamps are ... | math | {
"ground_truth": "\\frac{(n+1)^2}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of permutations $( p_1, p_2, p_3 , p_4 , p_5 , p_6)$ of $1, 2 ,3,4,5,6$ such that for any $k, 1 \\leq k \\leq 5$ , $(p_1, \\ldots, p_k)$ does not form a pe... | math | {
"ground_truth": "461",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sam walks at the rate of $3$ feet per second on a long straight path. Benches are located every $300$ feet along the path. A street cleaner driving at $9$ feet per second in the ... | math | {
"ground_truth": "B) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are 2023 boxes in a line, with the box in the kth position containing k white marbles, determine the smallest value of n for which the probability that Isabella ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the remainder when $9^{333}$ is divided by $50$?",
"role": "user"
}
] | math | {
"ground_truth": "29",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse with two foci $F_{1}(-1,0)$ and $F_{2}(1,0)$, and $P$ is a point on the ellipse. It is known that $2|F_{1}F_{2}| = |PF_{1}| + |PF_{2}|$. \n(1) Find the equation... | math | {
"ground_truth": "S_{\\triangle PF_{1}F_{2}}= \\frac{1}{2} \\cdot 2 \\cdot \\frac{3\\sqrt{3}}{5} = \\frac{3\\sqrt{3}}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the modulus and argument of the complex number\n\n$$\nz=-\\sin \\frac{\\pi}{8}-i \\cos \\frac{\\pi}{8}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "|z| = 1, \\quad \\operatorname{Arg} z = -\\frac{5\\pi}{8}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\sin(65^\\circ + \\alpha) = \\frac{1}{3}$, find the value of $\\cos(25^\\circ - \\alpha)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=2\\sin(\\omega x+\\frac{5\\pi}{12})+\\cos(\\omega x-\\frac{\\pi}{12})$ $(\\omega>0)$, and $f(\\pi)=3$. The graph of $f(x)$ on the interval $(0,\\frac{\\p... | math | {
"ground_truth": "26\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given three fair six-sided dice are rolled, calculate the probability that the values shown on two of the dice sum to the value shown on the remaining die.",
"role": "user"
... | math | {
"ground_truth": "\\frac{5}{24}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Lily got $85\\%$ of the problems correct on a $20$-problem test, $75\\%$ on a $50$-problem test, and $65\\%$ on a $15$-problem test. What percent of all the problems did Lily ans... | math | {
"ground_truth": "B) 76%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are several bowls on a table, each containing some grapes. Different bowls may have different numbers of grapes. If 8 more grapes are added to each of 12 bowls, the average... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the vector $\\mathbf{u}$ such that\n\\[\\operatorname{proj}_{\\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}} \\mathbf{u} = \\begin{pmatrix} \\frac{45}{13} \\\\ \\frac{30}{13} \\en... | math | {
"ground_truth": "\\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer such that $1 \\leq n \\leq 1000$ . Let $M_n$ be the number of integers in the set $X_n=\\{\\sqrt{4 n+1}, \\sqrt{4 n+2}, \\ldots, \\sqrt{4 n+10... | math | {
"ground_truth": "22",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Placing no more than one $\\text{X}$ in each small square on a $3 \\times 3$ grid, determine the greatest number of $\\text{X}$'s that can be placed without having three $\\text{... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cup is filled with a saline solution of $15\\%$ concentration. There are three iron balls of different sizes: large, medium, and small, with their volumes in the ratio 10:5:3. ... | math | {
"ground_truth": "10\\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Marko chose two prime numbers $a$ and $b$ with the same number of digits and wrote them down one after another, thus obtaining a number $c$ . When he decreased $c$ by the ... | math | {
"ground_truth": "1997",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the best approximation of $\\sqrt{3}$ by a rational number with denominator less than or equal to $15$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{26}{15}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of two numbers is 12, and their product is 32. Find the sum of their reciprocals.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) Given that point $P(-4,3)$ lies on the terminal side of angle $α$, find the value of $$\\frac{\\cos \\left( \\frac{π}{2}+α\\right)\\sin \\left(-π-α\\right)}{\\cos \\left( \\f... | math | {
"ground_truth": "- \\frac{5}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\frac{9}{19} - \\frac{3}{57} - \\frac{1}{3}$ and reduce your answer to simplest form.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{57}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $x_1, x_2, x_3$ are the roots of polynomial $P(x) = x^3 - 6x^2 + 5x + 12$, calculate the sum $|x_1| + |x_2| + |x_3|$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If a pair of sandals costs $60 at the regular price, and Maria gets a second pair at a 40% discount and a third pair at a 60% discount, determine the percentage of the total regu... | math | {
"ground_truth": "\\textbf{(C)}\\ 33",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The pressure $(P)$ of wind on a sail varies jointly as the area $(A)$ of the sail and the square of the velocity $(V)$ of the wind. When the velocity is $20$ miles per hour, the ... | math | {
"ground_truth": "C) 35",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right circular cone is 12 inches tall with a 1-inch radius at the opening. The interior of this cone is filled with ice cream. To add more appeal, a hemisphere of ice cream wit... | math | {
"ground_truth": "\\frac{16}{3}\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In 2022, the Ministry of Education issued the \"Compulsory Education Curriculum Plan\" and the curriculum standard (2022 edition), separating labor from the original comprehensiv... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the sum of the first 15 terms and the sum of the first 75 terms of a given arithmetic progression are 150 and 30 respectively, then the sum of the first 90 terms is:\nA) -160\... | math | {
"ground_truth": "B) -180",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all $3$ -digit numbers $\\overline{abc}$ ( $a,b \\ne 0$ ) such that $\\overline{bcd} \\times \u0002 a = \\overline{1a4d}$ for some integer $d$ from $1$ to $9$",
... | math | {
"ground_truth": "627",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all the real numbers $k$ that have the following property: For any non-zero real numbers $a$ and $b$ , it is true that at least one of the following numbers: $$ a, b... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Which positive integers $m$ are such that $k^m - 1$ is divisible by $2^m$ for all odd numbers $k \\ge 3$ ?",
"role": "user"
}
] | math | {
"ground_truth": "1, 2, 4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jeffrey jogs $3$ miles at $4$ miles per hour. Then, he walks $4$ miles at $3$ miles an hour. What was Jeffrey's average speed in miles per hour for the entire trip? Expre... | math | {
"ground_truth": "3.36",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the equation $x^{2}-mx+2=0$ has a solution in the interval $[1,2]$, then the range of the real number $m$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "[2 \\sqrt{2},3]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When a certain unfair die is rolled, an even number is 2 times as likely to appear as an odd number. The die is rolled three times. What is the probability that the sum of the nu... | math | {
"ground_truth": "\\frac{14}{27}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a function \\( f \\) that takes positive integer values and is defined on the positive integers, it satisfies the functional equation \\( f( f(m) + f(n) ) = m + n \\) for a... | math | {
"ground_truth": "1988",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a mathematics test containing 80 questions (20 arithmetic, 25 algebra, and 35 geometry), a student, Tori, answered 60% of the arithmetic, 50% of the algebra, and 70% of the ge... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(D\\) is the diameter of a sphere, then \\(\\frac{D^{3}}{2}+\\frac{1}{21} \\cdot \\frac{D^{3}}{2}\\) is the measure of the volume of the sphere. Determine for which value of... | math | {
"ground_truth": "\\frac{22}{7}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Estimate the number of primes among the first thousand primes divide some term of the sequence\n \\[2^0+1,2^1+1,2^2+1,2^3+1,\\ldots.\\]\n An estimate of $E$ earns $2^{1-... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Before the World Cup, the coach of country \\( F \\) plans to evaluate the seven players \\( A_{1}, A_{2}, \\cdots, A_{7} \\) by ensuring they all participate in three practice m... | math | {
"ground_truth": "42244",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $x$ and $y$ are positive real numbers satisfying $8x^2 + 16xy = x^3 + 3x^2y$. Determine the value of $x$ if $y = 2x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{40}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, $DE = 15 \\mbox{ cm},$ $DF = 36 \\mbox{ cm},$ and $\\angle D = 90^\\circ.$ What is the area of triangle $DEF?$ Also, determine if triangle $DEF$ is isosceles.",
... | math | {
"ground_truth": "270",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive multiples of $9$ that are less than $800$ end with the digit $7$?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(x\\), \\(y\\), \\(z\\) be real numbers such that \\(2x + 3y + z = 3\\), and \\(x \\ge -2\\), \\(y \\ge -\\frac{2}{3}\\), \\(z \\ge -4\\). Find the maximum value of\n\\[\n\... | math | {
"ground_truth": "\\sqrt{168}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x=\\cos 36^{\\circ} - \\cos 72^{\\circ}$. Simplify the expression for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given set $M=\\{x|x^2-3x-4\\leq0\\}$ and set $N=\\{x|x^2-16\\leq0\\}$, find the expression for $M\\cup N$.",
"role": "user"
}
] | math | {
"ground_truth": "[-4, 4]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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