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": "Find the values of $p$ and $q$ in the equation $3x^2 - px + q = 0$, if the sum of the roots is 10 and the product of the roots is 15.",
"role": "user"
}
] | math | {
"ground_truth": "p + q = 75",
"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": "Some people know each other in a group of people, where \"knowing\" is a symmetric relation. For a person, we say that it is $social$ if it knows at least $20$ other persons ... | math | {
"ground_truth": "40",
"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 math test starts at 12:35 PM and lasts for $4 \\frac{5}{6}$ hours. At what time does the test end?",
"role": "user"
}
] | math | {
"ground_truth": "17 \\text{ hours } 25 \\text{ minutes}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A box contains 3 white balls, 3 black balls, and 3 red balls. I draw them out of the box, one at a time. What is the probability that no two balls of the same color are drawn con... | math | {
"ground_truth": "\\frac{48}{105}",
"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 $T$ be the set of lattice points in the coordinate plane, both of whose coordinates are integers between $1$ and $50,$ inclusive. Exactly $750$ points in $T$ lie on or below ... | math | {
"ground_truth": "76",
"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 merchant buys goods at 30% off the list price. He desires to mark the goods so that he can give a discount of 20% on the marked price and still clear a profit of 20% on the sel... | math | {
"ground_truth": "109.375\\%",
"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 $x=\\sqrt{5}-1$, find the value of $x^{2}+2x-4$.",
"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": "Four bags of jelly beans contain 24, 32, 35, and 40 beans. The ratios of yellow beans to all beans in each of these bags are $40\\%$, $30\\%$, $25\\%$, and $15\\%$, respectively.... | math | {
"ground_truth": "C) 26%",
"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": "Consider all ordered pairs $(m, n)$ of positive integers satisfying $59 m - 68 n = mn$ . Find the sum of all the possible values of $n$ in these ordered pairs.",
"role":... | math | {
"ground_truth": "237",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $c$ be a real number. If the inequality $$ f(c)\\cdot f(-c)\\ge f(a) $$ holds for all $f(x)=x^2-2ax+b$ where $a$ and $b$ are arbitrary real numbers, find all possib... | math | {
"ground_truth": "c = \\pm \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $| \\overrightarrow{a} - \\overrightarrow{b} | = \\sqrt{41 - 20 \\sqrt{3}}$, $|\\overrightarrow{a}| = 4$, $|\\overrightarrow{b}| = 5$, determine the dot product of $\\... | math | {
"ground_truth": "10 \\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": "How many of the first 2023 numbers in the sequence $99, 999, 9999, 99999, \\dots$ are divisible by $103$?",
"role": "user"
}
] | math | {
"ground_truth": "404",
"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 triangle with vertices $A=(2,2)$, $B=(5,5)$, and $C=(3,6)$ is plotted on an $8\\times7$ grid. Find the fraction of the grid covered by the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{112}",
"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 school wants to select 6 students from 10 to participate in a study seminar, with the restriction that two specific students, A and B, cannot attend at the same time. Calcula... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a bag, there are 8 green balls, 6 red balls, and 4 blue balls. A ball is taken from the bag, its color recorded, then placed back in the bag. A second ball is taken and its co... | math | {
"ground_truth": "\\dfrac{29}{81}",
"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": "Josh is older than Fred. Josh notices that if he switches the two digits of his age (an integer), he gets Fred’s age. Moreover, the difference between the squares of their ages i... | math | {
"ground_truth": "65 \\text{ and } 56",
"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 an arithmetic sequence $\\{a_n\\}$ satisfies $a_2 + a_4 = 4$ and $a_3 + a_5 = 10$, determine the sum of its first 10 terms, $S_{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "65",
"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": "Katie's clock, which was set correctly at 8:00 AM, is showing 8:37 AM when the actual time is 9:00 AM. Assuming the clock loses time at a constant rate, determine the actual time... | math | {
"ground_truth": "10:36 PM",
"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 p is a positive integer, determine the conditions under which $\\frac{5p + 15}{3p - 9}$ can be a positive integer.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{at least }4\\text{ and no more than }19",
"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": "For each integer $n \\geq 5$, let $a_n$ denote the base-$n$ number $0.\\overline{143}_n$. Calculate the product $a_5a_6 \\dotsm a_{50}$ and express it as $\\frac{p}{q!}$, where $... | math | {
"ground_truth": "p = 143^{46}",
"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 $a,b,x,y$ are real numbers then find all solutions of $a,b$ such that $\\left \\lfloor ax+by \\right \\rfloor + \\left \\lfloor bx+ay \\right \\rfloor = (a+b) \\left \\l... | math | {
"ground_truth": "a = b = 0",
"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 notebook lists all the irreducible fractions with numerator 15 that are greater than $\\frac{1}{16}$ and less than $\\frac{1}{15}$. How many such fractions are listed in the ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ such that $n^2+4$ has at least four distinct prime factors.\n\n*Proposed by Michael Tang*",
"role": "user"
}
] | math | {
"ground_truth": "179",
"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 rectangle measuring \\(3 \\times 5\\) is divided into 15 unit squares of \\(1 \\times 1\\). Define a path as a movement along the sides of the unit squares, where no side is tr... | math | {
"ground_truth": "30",
"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": "Round $78.\\overline{367}$ to the nearest tenth.",
"role": "user"
}
] | math | {
"ground_truth": "78.4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( S = \\{1, 2, 3, \\ldots, 64, 65\\} \\). Determine the number of ordered triples \\((x, y, z)\\) such that \\( x, y, z \\in S \\), \\( x < z \\), and \\( y < z \\).",
... | math | {
"ground_truth": "89440",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For given natural numbers \\( k_{0} < k_{1} < k_{2} \\), determine the minimum number of roots in the interval \\([0, 2\\pi)\\) that the equation\n\n\\[ \n\\sin k_{0} x + A_{1} \... | math | {
"ground_truth": "2k_0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a similar setup, Mrs. Huang places integers from 1 to 289 into a 17 by 17 grid. She places the number 1 in the middle square (ninth row and ninth column) and continues placing... | math | {
"ground_truth": "C) 526",
"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 hyperbola $\\frac {x^{2}}{a^{2}}- \\frac {y^{2}}{b^{2}}=1(a＞0，b＞0)$, $A_1$, $A_2$ are the left and right vertices of the hyperbola, respectively. $M(x_0, y_0)$ is a poi... | math | {
"ground_truth": "\\frac {x^{2}}{9} - \\frac {y^{2}}{16} = 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": "On a rectangular sheet of paper, a picture in the shape of a \"cross\" is drawn using two rectangles $ABCD$ and $EFGH$, whose sides are parallel to the edges of the sheet. It is ... | math | {
"ground_truth": "52.5",
"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": "Aurick throws $2$ fair $6$ -sided dice labeled with the integers from $1$ through $6$ . What is the probability that the sum of the rolls is a multiple of $3$ ?",
"rol... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $12 \\cdot \\left(\\frac{1}{3} + \\frac{1}{4} - \\frac{1}{12}\\right)^{-1}$.\nA) 12\nB) 18\nC) 24\nD) 30\nE) 36",
"role": "user"
}
] | math | {
"ground_truth": "C) 24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Point $A$ on the number line represents the number $-3$. If point $A$ is moved $7$ units to the right on the number line to point $B$, then the number represented by point $B$ af... | 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": "Given that there are 40 rods with lengths ranging from 1 cm to 40 cm, Joy initially selects rods of lengths 10 cm, 20 cm, and 30 cm. Then determine the number of remaining rods a... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that 60 students from schools $A$, $B$, and $C$ participate in an interview, with 10 students from school $A$, 20 students from school $B$, and 30 students from school $C$.... | math | {
"ground_truth": "\\frac{7}{12}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fleet has 7 vehicles, and 4 need to be dispatched in a certain order to execute tasks. The requirements are that vehicles A and B must participate and vehicle A must go before ... | math | {
"ground_truth": "120",
"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": "$1-2-3+4+5-6-7+8+9-10-11+12+13 \\cdots + 1989+1990-1991-1992+1993=$",
"role": "user"
}
] | math | {
"ground_truth": "1990",
"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 $f(x)=ax^{2}+bx-2\\ln x$ ($a > 0$, $b\\in\\mathbb{R}$), if for any $x > 0$, $f(x)\\geqslant f(2)$ holds, find the inequality involving $a$ and $b$.",
"role... | math | {
"ground_truth": "\\ln a < -b-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\Delta ABC$, line segment $\\overline{DE}$ intersects $\\overline{AB}$ at point $F$ such that $\\overline{DF}$ is perpendicular to $\\overline{AB}$, $CD = 5$ cm, $DA = 8$ cm... | math | {
"ground_truth": "CB = 4\\sqrt{5} \\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": "Given the function $y=f(x)$ ($a\\leqslant x\\leqslant b$), find the number of elements in the set $\\{(x,y)|y=f(x), a\\leqslant x\\leqslant b\\} \\cap \\{(x,y)|x=0\\}$.",
"ro... | math | {
"ground_truth": "When $0\\in[a,b]$, according to the definition of the function, for any $x=0$, there is a unique $y$ corresponding to it. Therefore, $x=0$ intersects with the function $y=f(x)$ at only one point. In other words, the set $\\{(x,y)|y=f(x), a\\leqslant x\\leqslant b\\} \\cap \\{(x,y)|x=0\\}$ contains ... | {
"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": "When \\(2x^2\\) is added to a quadratic polynomial \\(f(x)\\), its maximum value increases by 10, and when \\(5x^2\\) is subtracted from it, its maximum value decreases by \\(\\f... | math | {
"ground_truth": "\\frac{45}{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": "Simplify the expression $x^{-2} - x + 1$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x^2 - x^3 + 1}{x^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": "Evaluate the expression $2^{-(3k+1)}-3 \\cdot 2^{-(3k-1)}+4 \\cdot 2^{-3k}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3}{2} \\cdot 2^{-3k}",
"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 $\\frac{8^x}{4^{x+y}} = 64$ and $\\frac{16^{x+y}}{4^{4y}} = 256$, find the product $xy$.\nA) 7\nB) 4\nC) 12\nD) 8\nE) -2",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Is there a positive integer $m$ such that the equation \\[ {1\\over a}+{1\\over b}+{1\\over c}+{1\\over abc}={m\\over a+b+c} \\] has infinitely many solutions in positive inte... | math | {
"ground_truth": "m = 18",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(\\alpha\\) and \\(\\beta\\) be a pair of conjugate complex numbers. Given that \\(|\\alpha - \\beta| = 2 \\sqrt{3}\\), and \\(\\frac{\\alpha}{\\beta^{2}}\\) is a real numb... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\triangle{DEF}$ is an equilateral triangle of side length $t$, and inside the triangle exists a unique point $Q$ such that $DQ=2$, $EQ=2\\sqrt{2}$, and $FQ=3$. Calculate ... | math | {
"ground_truth": "\\sqrt{19}",
"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 $w$, $x$, $y$, and $z$ be whole numbers. If \\(2^w \\cdot 3^x \\cdot 5^y \\cdot 7^z = 1260\\), then what does \\(3w + 4x + 2y + 2z\\) equal?\nA) 16\nB) 18\nC) 20\nD) 22",
... | math | {
"ground_truth": "18",
"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": "Andrew's grandfather is sixteen times older than Andrew. When Andrew was born, his grandfather was 60 years old. How old is Andrew now?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Matches are arranged to form the number 1405. What is the largest four-digit number that can be obtained by moving no more than two matches?",
"role": "user"
}
] | math | {
"ground_truth": "7705",
"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 \\( A \\subset \\mathbf{N}^{\\cdot} \\), for any \\( x, y \\in A \\), it satisfies \\( |x-y| \\geqslant \\frac{xy}{25} \\), where \\( x \\neq y \\). How many elements are i... | math | {
"ground_truth": "12",
"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": "(1) Given that $f(\\sqrt{x} + 1) = x + 2\\sqrt{x}$, find the analytical expression of $f(x)$;\n(2) Given that $f(x)$ is a first-degree function and satisfies $3f(x+1) - 2f(x-1) =... | math | {
"ground_truth": "f(x) = 2x + 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": "Two circles with radii 1 meet in points $X, Y$ , and the distance between these points also is equal to $1$ . Point $C$ lies on the first circle, and lines $CA, CB$ are tan... | math | {
"ground_truth": "150^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Farmer Euclid has a rectangular field measuring 6 units by 4 units, and in one corner he leaves an unplanted circular region of radius 1 unit, calculate the fraction o... | math | {
"ground_truth": "\\frac{24 - \\pi}{24}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a circle with a radius of 8 inches, there are two equal parallel chords that are 8 inches apart, find the area of the circle between these two parallel chords.",
"role": "... | math | {
"ground_truth": "32 \\sqrt{3}+21 \\frac{1}{3} \\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer \\( A \\) divided by \\( 3! \\) gives a result where the number of factors is \\(\\frac{1}{3}\\) of the original number of factors. What is the smallest such \... | math | {
"ground_truth": "12",
"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": "This problem involves four different natural numbers written by a teacher. For each pair of these numbers, Peter found their greatest common divisor. He obtained six numbers: 1, ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $(-125)^{4/3}$.",
"role": "user"
}
] | math | {
"ground_truth": "625",
"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 series of three-digit numbers is structured such that the last two digits (tens and units) of each number become the first two digits (hundreds and tens) of the subsequent numb... | math | {
"ground_truth": "- (E) 37",
"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 polynomials $A$ and $B$, and $2A+B=7ab+6a-2b-11$, $2B-A=4ab-3a-4b+18$. \n$(1)$ Reading material: We can always find polynomials $A$ and $B$ by adding parentheses, such as:... | math | {
"ground_truth": "b = 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": "Given \\\\(x > 0, y > 0\\\\), and \\\\(2x+8y-xy=0\\\\), find the minimum value of \\\\(x+y\\\\).",
"role": "user"
}
] | math | {
"ground_truth": "18",
"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 \"Two Mice Through the Wall\" problem from the \"Nine Chapters on the Mathematical Art\" is a classic problem in Chinese mathematics: \"There is a wall of certain thickness. ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a geometric sequence $\\{a_n\\}$ satisfies $a_{n+1}+a_{n}=9\\cdot2^{n-1}$, where $n\\in\\mathbb{N}^*$. \n(I) Find the general formula for the sequence $\\{a_n\\}$. \n(II)... | math | {
"ground_truth": "(-\\infty, \\dfrac {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": "Let $S$ be a square one of whose sides has a length of $\\sqrt{2}$. A point $v=(x,y)$ is chosen uniformly at random over all pairs of real numbers $x$ and $y$ such that $0 \\le x... | math | {
"ground_truth": "\\frac{4}{625}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a square $ABCD$, a point $K$ on side $[AB]$, a point $L$ on side $[BC]$, $|AK|=3$, $|KB|=2$, and the distance of $K$ to the line $DL$ is $3$, calculate the ratio of $|BL|$ ... | math | {
"ground_truth": "\\frac{8}{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": "In triangle $ABC$, side $AC$ is twice the length of side $AB$. Let $D$ be on $\\overline{AB}$ such that $AD$ is half of $AB$, and let $E$ be on $\\overline{BC}$, such that $\\ang... | math | {
"ground_truth": "C) 90^\\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": "If $2^{2x}+4=12(2^{x})$, then the value of $(x^2+1)$ is:\n**A)** $(\\log_2(10))^2 + 1$\n**B)** $(\\log_2(6 + 4\\sqrt{2}))^2 + 1$\n**C)** $(\\log_2(8))^2 + 1$\n**D)** $0$",
"r... | math | {
"ground_truth": "\\textbf{(B)} (\\log_2(6 + 4\\sqrt{2}))^2 + 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$64$ teams with distinct skill levels participate in a knockout tournament. In each of the $6$ rounds, teams are paired into match-ups and compete; the winning team moves on t... | math | {
"ground_truth": "\\frac{512}{1953}",
"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 checkerboard of $12$ rows and $16$ columns has a number written in each square. In the first numbering system, numbers are written row-wise starting from the upper left corner.... | math | {
"ground_truth": "C) 364",
"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 $10\\times15$ rectangle $EFGH$ is cut into two congruent pentagons, which are repositioned to form a square. Determine the length $z$ of one side of the pentagons that aligns... | math | {
"ground_truth": "5\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function \\( f \\) is not defined for \\( x = 0 \\), but for all non-zero real numbers \\( x \\),\n\\[ f(x) \\cdot 2f \\left( \\frac{1}{x} \\right) = x^2 + 4. \\]\nFind the r... | math | {
"ground_truth": "1, -1",
"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 $C$ be the left vertex of the ellipse $\\frac{x^2}8+\\frac{y^2}4 = 1$ in the Cartesian Plane. For some real number $k$ , the line $y=kx+1$ meets the ellipse at two dis... | math | {
"ground_truth": "7.94403",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the $x$ that satisfies $\\log_{32} (x+32) = \\frac{7}{5}$.",
"role": "user"
}
] | math | {
"ground_truth": "96",
"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 $(a-i)i=b-i$, where $a, b \\in \\mathbb{R}$ and $i$ is the imaginary unit, find the value of $a^2+b^2$.",
"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": "Solve the equation $\\frac{1}{x-1}+3=\\frac{3x}{1-x}$, after eliminating the denominators, multiply both sides by $\\left(x-1\\right)$ and simplify the expression.",
"role": ... | math | {
"ground_truth": "1+3(x-1)=-3x",
"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": "Positive integers $a$, $b$, $c$, and $d$ are randomly and independently selected with replacement from the set $\\{1, 2, 3, \\dots, 2025\\}$. What is the probability that $abc + ... | math | {
"ground_truth": "\\text{B) } \\frac{260056}{8125000}",
"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": "Lea rolls 8 standard 6-sided dice simultaneously. What is the probability that the product of the numbers obtained is divisible by 8?\nA) $\\frac{3}{16}$\nB) $\\frac{247}{256}$\n... | math | {
"ground_truth": "\\textbf{(B)}\\: \\frac{247}{256}",
"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": "At the Rice Mathematics Tournament, 80% of contestants wear blue jeans, 70% wear tennis shoes, and 80% of those who wear blue jeans also wear tennis shoes. What fraction of peopl... | math | {
"ground_truth": "\\frac{32}{35}",
"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": "Suppose $f(x) = 4x - 3$ and $g(x) = 3x + 2$. If $h(x) = f(g(x))$, find the inverse of $h(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "h^{-1}(x) = \\frac{x - 5}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Acute triangle $ABC$ has altitudes $AD$ , $BE$ , and $CF$ . Point $D$ is projected onto $AB$ and $AC$ to points $D_c$ and $D_b$ respectively. Likewise, $E$ is ... | math | {
"ground_truth": "25",
"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 cylindrical sculpture with a radius of $7$ and height of $9$ is painted green. Two points, $E$ and $F$, are positioned on the rim of one of its circular bases, such that the ar... | math | {
"ground_truth": "177",
"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 a school maze game, there are various marked checkpoints. Starting from point M, students must reach point P. The paths allowed are as described: from M you can go to X or Y; ... | math | {
"ground_truth": "C) 4",
"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": "**E**ach of the integers $1,2,...,729$ is written in its base- $3$ representation without leading zeroes. The numbers are then joined together in that order to form a continuo... | math | {
"ground_truth": "148",
"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 three points in space \\\\(A(0,2,3)\\\\), \\\\(B(-2,1,6)\\\\), and \\\\(C(1,-1,5)\\\\):\n\\\\((1)\\\\) Find \\\\(\\cos < \\overrightarrow{AB}, \\overrightarrow{AC} >\\\\).\... | math | {
"ground_truth": "7\\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": "Given the equation $x^4-7x^3+14x^2-14x+4=0$, find the sum of its real roots.",
"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": "Find all real numbers $k$ for which the inequality $(1+t)^k (1-t)^{1-k} \\leq 1$ \n\nis true for every real number $t \\in (-1, 1)$ .",
"role": "user"
}
] | math | {
"ground_truth": "k = \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five years ago, there were 30 trailer homes on Maple Drive with an average age of 15 years. At that time, a group of trailer homes, which were all 3 years old, was then added to ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a \\gt b \\gt 0$, the quadratic function $f\\left(x\\right)=ax^{2}+2x+b$ has exactly one zero. Determine the minimum value of $\\frac{{a}^{2}{+b}^{2}}{a-b}$.",
"role":... | math | {
"ground_truth": "2\\sqrt{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 geometric progression \\( b_{1}, b_{2}, \\ldots \\) is such that \\( b_{25} = 2 \\tan \\alpha \\) and \\( b_{31} = 2 \\sin \\alpha \\) for some acute angle \\( \\alpha \\). Fin... | 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": "Let the sequence \\(\\left\\{a_{n}\\right\\}\\) satisfy the condition that for all positive integers \\(n\\),\n\\[ 1+\\sum_{m=1}^{n} \\mathrm{C}_{n}^{m} a_{m}=2^{\\frac{n}{2}} \\... | math | {
"ground_truth": "a_n = \\frac{\\mathrm{i}^n + (-\\mathrm{i})^n}{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": "There are $n$ people, and it is known that any two of them can make at most one phone call to each other. For any $n-2$ people among them, the total number of phone calls is equa... | math | {
"ground_truth": "5",
"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": "How many pairs of numbers \\((m, n)\\) are there such that the following statement is true?\n'A regular \\(m\\)-sided polygon has an exterior angle of size \\(n^{\\circ}\\) and a... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with $AB = 26$ , $BC = 51$ , and $CA = 73$ , and let $O$ be an arbitrary point in the interior of $\\vartriangle ABC$ . Lines $\\ell_1$ , $\\ell... | math | {
"ground_truth": "280",
"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 diagonals of a convex quadrilateral $ABCD$ intersect at a point $O$ . Find all angles of this quadrilateral if $\\measuredangle OBA=30^{\\circ},\\measuredangle OCB=45^{\\... | math | {
"ground_truth": "\\angle A = 120^\\circ, \\angle B = 45^\\circ, \\angle C = 120^\\circ, \\angle D = 75^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The base of an isosceles triangle is 20 inches. A line is drawn parallel to the base, which divides the triangle into two regions where the area of the smaller region is $\\frac{... | math | {
"ground_truth": "10",
"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": "For some positive integer $n>m$ , it turns out that it is representable as sum of $2021$ non-negative integer powers of $m$ , and that it is representable as sum of $2021$ ... | math | {
"ground_truth": "43",
"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": "What is the number of square units in the area of trapezoid EFGH with vertices E(2,2), F(2,5), G(6,2), and H(6,8)?",
"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": "A sequence of $10$ numbers starts with two given numbers. Each subsequent number in the list is the product of the two preceding numbers. Given the last three numbers in the sequ... | math | {
"ground_truth": "60466176",
"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 all positive integers $M$ such that the sequence $a_0, a_1, a_2, \\cdots$ defined by \\[ a_0 = M + \\frac{1}{2} \\qquad \\textrm{and} \\qquad a_{k+1} = a_k\\l... | math | {
"ground_truth": "M > 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular yard contains three flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, with the parallel sides meas... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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