data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A coloring of all plane points with coordinates belonging to the set $S=\\{0,1,\\ldots,99\\}$ into red and white colors is said to be *critical* if for each $i,j\\in S$ at le... | math | {
"ground_truth": "5000",
"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 power bureau needs to inspect the power lines in the urban area. The inspection team travels by car from point $A$ to inspect the power lines on the east-west road and ... | math | {
"ground_truth": "\\text{22.5 liters}",
"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 country with 15 cities, some of them are connected by air routes belonging to three airlines. It is known that even if any one of the airlines stops flying, it will still be... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $m$ be an even integer with exactly 13 positive divisors, where $m$ is in the form of $2^ap^b$ for a single prime $p$ other than 2. Find the number of positive divisors of $2... | math | {
"ground_truth": "300",
"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": "Replace the letters A, B, C, D, E with digits (different letters correspond to different digits) so that the difference of the three-digit numbers ABC - DEF takes the smallest po... | math | {
"ground_truth": "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": "Given that $7x^{m}y^{3}$ and $-\\frac{1}{2}x^{2}y^{n}$ are like terms, then $\\left(-n\\right)^{m}=$____.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A lemming sits at a corner of a rectangle with side lengths 12 meters and 16 meters. The lemming runs 9.6 meters along a diagonal toward the opposite corner. It stops, makes a $9... | math | {
"ground_truth": "7",
"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": "Ed and Sue bike at equal and constant rates. Similarly, they jog at equal and constant rates, and they swim at equal and constant rates. Ed covers $ 74$ kilometers after biki... | math | {
"ground_truth": "314",
"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": "p1. Find all real numbers that satisfy the equation $$ (1 + x^2 + x^4 + .... + x^{2014})(x^{2016} + 1) = 2016x^{2015} $$ p2. Let $A$ be an integer and $A = 2 + 20 + 201 + 2... | math | {
"ground_truth": "200.5",
"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": "Suppose two distinct even integers are chosen from between 6 and 18, inclusive. What is the probability that their product is a multiple of 4?",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{5}{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": "Find the number of integer points that satisfy the system of inequalities:\n\\[\n\\begin{cases}\ny \\leqslant 3x \\\\\ny \\geqslant \\frac{1}{3}x \\\\\nx + y \\leqslant 100\n\\en... | math | {
"ground_truth": "2551",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be a set. We say $S$ is $D^\\ast$ *-finite* if there exists a function $f : S \\to S$ such that for every nonempty proper subset $Y \\subsetneq S$ , there exists ... | math | {
"ground_truth": "120",
"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": "Point $P_1$ is located $600$ miles West of point $P_2$ . At $7:00\\text{AM}$ a car departs from $P_1$ and drives East at a speed of $50$ mph. At $8:00\\text{AM}$ anot... | math | {
"ground_truth": "60",
"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": "Calculate $\\sqrt{\\frac{9}{49}+\\frac{16}{9}}$ and express it as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{865}}{21}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the product of $\\sqrt[4]{16}$ and $\\sqrt[6]{64}$.\nA) 2\nB) 4\nC) 8\nD) 16\nE) 32",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On hypotenuse $AB$ of a right triangle $ABC$ a second right triangle $ABD$ is constructed with hypotenuse $AB$. If $\\overline{BC}=1$, $\\overline{AC}=b$, and $\\overline{AD}=2$,... | math | {
"ground_truth": "\\sqrt{b^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": "What weights can three weights have so that with their help, any whole number of kilograms from 1 to 10 can be weighed on a balance scale (weights can be placed on both pans)? Pr... | math | {
"ground_truth": "The weights 3 kg, 4 kg, and 9 kg can be used to measure any whole number of kilograms from 1 to 10 kg.",
"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 points $a$ and $b$ in the plane, let $a\\oplus b$ be the unique point $c$ such that $abc$ is an equilateral triangle with $a,b,c$ in the clockwise orientation.\... | math | {
"ground_truth": "\\left( \\frac{1 - \\sqrt{2}}{2}, \\frac{(1 - \\sqrt{2}) \\sqrt{3}}{2} \\right)",
"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 board, the product \\(a_{1} a_{2} \\ldots a_{100}\\) is written, where \\(a_{1}, \\ldots, a_{100}\\) are natural numbers. Consider 99 expressions, each obtained by replacing... | math | {
"ground_truth": "33",
"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": "Selecting 3 people from 3 boys and \\( n \\) girls to participate in a competition, given that the probability of having at least one girl among the 3 people is \\( \\frac{34}{35... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n \\geq 4$ be an integer. Find all positive real solutions to the following system of $2n$ equations:\\begin{align*} a_{1} &=\\frac{1}{a_{2 n}}+\\frac{1}{a_{2}}, & a_{2}&=a_... | math | {
"ground_truth": "a_{2k+1} = 1, \\quad a_{2k+2} = 2 \\quad \\text{for all } k \\text{ such that } 0 \\leq k < n",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The probability that the sum of the numbers rolled is even.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{9}",
"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 an arithmetic sequence $\\{a_{n}\\}$ with a non-zero common difference, it satisfies: $a_{3}+a_{8}=20$, and $a_{5}$ is the geometric mean of $a_{2}$ and $a_{14}$. Let $\\{b... | math | {
"ground_truth": "\\frac{1}{2}\\left(1-\\frac{1}{2n+1}\\right)=\\frac{n}{2n+1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a triangular corner with side lengths $DB=EB=1$ is cut from equilateral triangle ABC of side length $3$, calculate the perimeter of the remaining quadrilateral.",
... | math | {
"ground_truth": "8",
"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": "In the arithmetic sequence $\\{a_n\\}$: \n(1) It is known that $a_5 = -1$, $a_8 = 2$, find $a_1$ and $d$; \n(2) It is known that $a_1 + a_6 = 12$, $a_4 = 7$, find $a_9$.",
... | math | {
"ground_truth": "a_9 = 17",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$A B C$ is an equilateral triangle with center $O$. Let $f$ be a line passing through $O$ and intersecting the sides of the triangle at points $A_{1}, B_{1}, C_{1}$. What is the ... | math | {
"ground_truth": "\\text{When the product is minimal: } 30^\\circ, 30^\\circ, 90^\\circ\\\\\n\\text{When the product is twice the minimum: } 10^\\circ, 70^\\circ, 50^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Does there exist a second-degree polynomial $p(x, y)$ in two variables such that every non-negative integer $ n $ equals $p(k,m)$ for one and only one ordered pair $(k,m)$... | math | {
"ground_truth": "p(x, y) = \\frac{(x+y)^2 + 3x + y}{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 the ratio of boys to girls in Mr. Brown's math class is $2:3$, and there are $30$ students in the class, calculate the difference between the number of girls and the number... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate: $-\\left(18\\div 3\\cdot 8-70+5\\cdot 7\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "-13",
"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 three integers have a sum of $18$. When four more integers are added to the first three, the sum is $49$. Finally, when another three integers are added to the sum of the p... | math | {
"ground_truth": "7",
"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 7623 is divided by 11?",
"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": "Given propositions $p$ and $q$:\n- Proposition $p$: The equation $\\frac{x^2}{2m} - \\frac{y^2}{m-1} = 1$ represents an ellipse with foci on the $y$-axis.\n- Proposition $q$: The... | math | {
"ground_truth": "\\frac{1}{3} \\leq m < 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": "Given that the angle between the plane vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $\\dfrac {π}{6}$, $|\\overrightarrow{a}|= \\sqrt {3}$, $|\\overrightarrow{b}|=1$... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Pegs are placed in a board $1$ unit apart both horizontally and vertically. A rubber band is stretched over 4 pegs forming a quadrilateral. The bounding rectangle for the pegs sp... | math | {
"ground_truth": "C) 1.5",
"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": "Find the coefficient of the $x^2$ term in the expansion of $(1-x)^3(2x^2+1)^5$.",
"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": "Xiao Ming took $20$ yuan to the supermarket to buy pens and exercise books. Each pen costs $3$ yuan, and each exercise book costs $2$ yuan. If he wants to buy both items and spen... | 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": "Let $a$ and $b$ be angles such that $\\sin(a + b) = \\frac{5}{8}$ and $\\sin(a - b) = \\frac{1}{4}.$ Find $\\frac{\\tan a}{\\tan b}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive integers $ n$ such that $f_n(x,y,z) = x^{2n} + y^{2n} + z^{2n} - xy - yz - zx$ divides $g_n(x,y, z) = (x - y)^{5n} + (y -z)^{5n} + (z - x)^{5n}$ , as p... | math | {
"ground_truth": "n = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rationalize the denominator of $\\displaystyle \\frac{1}{\\sqrt[3]{8} - \\sqrt[3]{7}}$. With your answer in the form $\\displaystyle \\frac{\\sqrt[3]{A} + \\sqrt[3]{B} + \\sqrt[3... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the $10^{th}$ term of the sequence $\\{a\\_n\\}$, where $a_{n+1} - a_{n} = 2$ and $a_{1} = 1$.",
"role": "user"
}
] | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that an octahedron has 8 vertices, 12 edges, and 6 faces, calculate the sum of these numbers.",
"role": "user"
}
] | math | {
"ground_truth": "26",
"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) Let $n$ be a prime number greater than 3. Find the value of $\\left(1+2 \\cos \\frac{2 \\pi}{n}\\right)\\left(1+2 \\cos \\frac{4 \\pi}{n}\\right) \\cdots\\left(1+2 \\cos \\fr... | math | {
"ground_truth": "0 \\text{ if } n = 3k; \\left. (-1)^{n-1} \\text{ if } n = 3k+1; \\left. (-1)^{n} \\text{ if } n = 3k+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": "Compute $\\tan(405^\\circ)$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given positive real numbers \\( x \\) and \\( y \\), define the operation \\( x*y = \\frac{x \\cdot y}{x+y} \\). If \\( z = x + 2y \\), calculate the value of the operation \\( x... | math | {
"ground_truth": "\\frac{x^2 + 2xy}{2(x + y)}",
"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 number, when doubled and then increased by 13, equals 89?",
"role": "user"
}
] | math | {
"ground_truth": "38",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the lengths of the arcs of the curves given by the equations in polar coordinates.\n\n$$\n\\rho=6(1+\\sin \\varphi),-\\frac{\\pi}{2} \\leq \\varphi \\leq 0\n$$",
"r... | math | {
"ground_truth": "12(2 - \\sqrt{2})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a complex number $z$ that satisfies $\\frac{\\overline{z}}{1-i}=i$, where $i$ is the imaginary unit, find $z$.\nA) $1-i$\nB) $1+i$\nC) $-1-i$\nD) $-1+i$",
"role": "user... | math | {
"ground_truth": "A)$ $1-i",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$A$ , $B$ , $C$ , and $D$ are points on a circle, and segments $\\overline{AC}$ and $\\overline{BD}$ intersect at $P$ , such that $AP=8$ , $PC=1$ , and $BD=6$ . Find... | 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": "Given the sets \\( A = \\{ x \\mid x^{2} - x - 2 < 0 \\} \\) and \\( B = \\{ x \\mid x^{2} - a x - a^{2} < 0, a \\in \\mathbf{R} \\} \\), if \\( A \\subseteq B \\), determine the... | math | {
"ground_truth": "(-\\infty, -1 - \\sqrt{5}) \\cup \\left( \\frac{1+\\sqrt{5}}{2}, +\\infty \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x = \\frac{a}{b}$, $a \\neq b$, and $b \\neq 0$, determine the value of $\\frac{a^2 + b^2}{a^2 - b^2}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x^2 + 1}{x^2 - 1}",
"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 the function $f(x)=2\\sin{x}\\cos{x}+\\sqrt{3}(\\sin^{2}x-\\cos^{2}x)$. \n$(1)$ Find the minimum positive period and the interval of monotonic increase of the function $f(... | math | {
"ground_truth": "\\text{The maximum perimeter of triangle } \\triangle ABC \\text{ is } 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": "Let $X_1, X_2, \\ldots, X_{100}$ be a sequence of mutually distinct nonempty subsets of a set $S$. Any two sets $X_i$ and $X_{i+1}$ are disjoint and their union is not the whole ... | math | {
"ground_truth": "8",
"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": "Given an odometer reading of 12321, Megan drives until she sees the next palindrome number on the odometer, 3 hours later. What was her average speed, in miles per hour, during t... | math | {
"ground_truth": "33.33",
"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": "Find the value of \\( n \\) such that the quadratic equation \\( 4x^2 + nx + 4 = 0 \\) has exactly one solution in \\( x \\).",
"role": "user"
}
] | math | {
"ground_truth": "-8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f(x)= \\frac {1}{3}ax^{3}+ \\frac {1}{2}ax^{2}-2ax+2a+1$ passes through all four quadrants. What is the range of possible values for the real number $a$?",
"rol... | math | {
"ground_truth": "- \\frac {6}{5} < a < - \\frac {3}{16}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A line passes through point $M(3,4)$ and is equidistant from points $A(-2,2)$ and $B(4,-2)$, find the equation of this line.",
"role": "user"
}
] | math | {
"ground_truth": "2x-y-2=0 \\text{ or } 2x+3y-18=0",
"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": "Megan intended to convert 3.5 kilometers to meters and then add 200 meters to the result to calculate the total distance for her training route. However, she forgot to do the con... | math | {
"ground_truth": "C) 3700 meters",
"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": "\\(10 \\div \\left(2 \\div 0.3\\right) \\div \\left(0.3 \\div 0.04\\right) \\div \\left(0.04 \\div 0.05\\right) =\\)",
"role": "user"
}
] | math | {
"ground_truth": "0.25",
"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": "Solve the equation \\(x^{2} + y^{2} = 3z^{2}\\) in integers.",
"role": "user"
}
] | math | {
"ground_truth": "x = y = z = 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 sum of all positive integers $n$ such that, given an unlimited supply of stamps of denominations $5$ , $n$ , and $n + 1$ cents, $91$ cents is the greatest postag... | math | {
"ground_truth": "71",
"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": "By the first of September, Vlad bought several ballpoint and gel pens. He noticed that if all the purchased pens were gel pens, he would have paid 4 times more than he actually d... | math | {
"ground_truth": "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": "A jar contains three red marbles, eight blue marbles, and nine yellow marbles, with no other marbles. Three marbles are randomly drawn from this jar without replacement. What is ... | math | {
"ground_truth": "\\frac{18}{95}",
"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": "What is the least common multiple (LCM) of the fractions $\\frac{1}{5x}$, $\\frac{1}{10x}$, and $\\frac{1}{15x}$?\nA) $\\frac{1}{30x}$ \nB) $\\frac{1}{15x}$ \nC) $\\frac{1}{5x}... | math | {
"ground_truth": "\\frac{1}{30x}",
"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": "Add $246_8 + 573_8 + 62_8$. Express your answer in base $8$.",
"role": "user"
}
] | math | {
"ground_truth": "1123_8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\rho$: $\\left|1- \\frac{x-1}{3}\\right| \\leq 2$, $q$: $(x-1+m)(x-1-m) \\leq 0$ ($m > 0$), if $q$ is a sufficient but not necessary condition for $p$, find the range of ... | math | {
"ground_truth": "(0, 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": "Let $H=\\log\\dfrac{2+x}{2-x}$. Define a new function $I$ by replacing each $x$ in $H$ by $\\dfrac{4x}{1+x^2}$, and simplify. What is the simplified expression for $I$?\nA) $H$\n... | math | {
"ground_truth": "2H",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose \\(\\left(1+x+x^{2}\\right)^{n} = \\sum_{k=0}^{2n} a_{k} x^{k}\\). Find \\(\\sum_{k=1}^{n} a_{2k}\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {3^{n} -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": "Evaluate $(\\sqrt[3]{8})^6$.",
"role": "user"
}
] | math | {
"ground_truth": "64",
"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 $\\overrightarrow{a}=(1,1,0)$, $\\overrightarrow{b}=(-1,0,2)$, and $k \\overrightarrow{a}+ \\overrightarrow{b}$ is perpendicular to $2 \\overrightarrow{a}- \\overright... | math | {
"ground_truth": "k = \\frac{7}{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": "The value of $\\log_{2}{158489}$ is between which two consecutive integers $a$ and $b$? Find $a+b$.",
"role": "user"
}
] | math | {
"ground_truth": "33",
"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 Mr. Euler teaches 12 students, Mrs. Fibonacci teaches 10 students, and Mr. Gauss teaches 11 students for a mathematics contest, and 3 students are taught by both Mr. E... | math | {
"ground_truth": "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 that a 3-digit number has a digit-sum of $27$, how many of these numbers are even?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Henry earns $25 per hour, and has $2.1\\%$ of his earnings deducted for state taxes. Additionally, he pays a fixed community fee of $0.50 per hour. How many cents per hour do Hen... | math | {
"ground_truth": "102.5",
"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": "Find the positive solution to\n\\[\\sqrt{x + \\sqrt{x + \\sqrt{x + \\dotsb}}} = \\sqrt{x \\sqrt{x \\sqrt{x \\dotsm}}}.\\]",
"role": "user"
}
] | 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": "Let\n$$\nF(x)=\\frac{1}{\\left(2-x-x^{5}\\right)^{2011}},\n$$\nand note that \\( F \\) may be expanded as a power series so that \\( F(x)=\\sum_{n=0}^{\\infty} a_{n} x^{n} \\). F... | math | {
"ground_truth": "\\left( \\frac{1}{6^{2011} \\cdot 2010!}, 2010 \\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": "Determine all ordered pairs $(x, y)$ of nonnegative integers that satisfy the equation $$ 3x^2 + 2 \\cdot 9^y = x(4^{y+1}-1). $$",
"role": "user"
}
] | math | {
"ground_truth": "(3, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Eight small circles, each with radius 4 units, are tangent to a large circle and each other, arranged symmetrically around the large circle. Determine the diameter of the large c... | math | {
"ground_truth": "\\text{The diameter of the large circle is approximately 11.312 units.}",
"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 equation \\(x^{2} + p x + q = 0\\) has roots \\(x_{1}\\) and \\(x_{2}\\). Write the equation whose roots will be the numbers \\(y_{1}, y_{2}\\) equal to:\na) \\(x_{1}^{3}\\),... | math | {
"ground_truth": "q x^2 + (2q - p^2)x + q = 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": "The equation of the line that passes through the point (1, 0) and is perpendicular to the line $x-2y-2=0$ is $2x+y-1=0$.",
"role": "user"
}
] | math | {
"ground_truth": "2x+y-2=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the reciprocals of the roots of $7x^2 + 4x + 9$ be $\\gamma$ and $\\delta$. Evaluate $\\gamma + \\delta$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{4}{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": "Find all real number pairs \\((a, b)\\) such that the function \\( f(x) = ax + b \\) satisfies the condition \\( f(x) f(y) + f(x+y-xy) \\leq 0 \\) for all real numbers \\( x, y \... | math | {
"ground_truth": "\\{ (a, b) \\mid -1 \\leq b \\leq 0, -(b + 1) \\leq a \\leq -b \\}",
"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 angle $\\theta = 1050^{\\circ}$, calculate the value of $\\sin \\theta$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{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": "Given vectors $\\overrightarrow{a} = (1, 1)$, $\\overrightarrow{b} = (1, -1)$, and $\\overrightarrow{c} = (-1, 2)$, express $\\overrightarrow{c}$ in terms of $ \\overrightarrow{a... | math | {
"ground_truth": "\\frac{1}{2} \\overrightarrow{a} - \\frac{3}{2} \\overrightarrow{b}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. Given are points $P_1,\\ P_2,\\ \\cdots,\\ P_{4n}$ of which any three points are not collinear. For $i=1,\\ 2,\\ \\cdots,\\ 4n$ , rotating hal... | math | {
"ground_truth": "8n^2 - 6n",
"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 semicircle has diameter $AB$ with $AB = 100$ . Points $C$ and $D$ lie on the semicircle such that $AC = 28$ and $BD = 60$ . Find $CD$ .",
"role": "user"
}
] | math | {
"ground_truth": "60",
"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": "Abby and Brian play the following game: They first choose a positive integer $N$ . Then they write numbers on a blackboard in turn. Abby starts by writing a $1$ . Thereafter, w... | math | {
"ground_truth": "31",
"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": "Two different wheels are spun to select numbers. The first wheel is fair, with an equal probability for even and odd numbers. The second wheel, however, has different probabiliti... | math | {
"ground_truth": "\\frac{1}{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": "If the complex number $z=a^2 - a - 2 + (a^2 - 3a + 2)i$ is a purely imaginary number, then the value of the real number $a$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "a = -1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Penelope plays a game where she adds $25$ points to her score each time she wins a game and deducts $13$ points from her score each time she loses a game. Starting with a sc... | math | {
"ground_truth": "87",
"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 right square pyramid has upper and lower base edge lengths of $4cm$ and $10cm$ respectively, with a height of $4cm$. Calculate the side surface area and volume of the pyramid."... | math | {
"ground_truth": "208",
"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": "It costs 8 cents to copy 5 pages. How many pages can you copy for $30?",
"role": "user"
}
] | math | {
"ground_truth": "1875",
"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": "Jo, Blair, and Parker take turns counting from 1, increasing by one more than the last number said by the previous person. What is the $100^{\\text{th}}$ number said?",
"role... | 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": "The blue parabola shown is the graph of the equation $x = ay^2 + by + c$. Find $c$. (Assume the graph has a standard unit scale.)\n\n[asy]\nsize(150);\nreal ticklen=3;\nreal tick... | math | {
"ground_truth": "-27",
"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 two arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$, with the sum of the first $n$ terms denoted as $S_n$ and $T_n$, respectively, and the ratio $\\frac{a_n}{b_n}$ equals ... | 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": "The result of the expression $2000 \\times 2001 \\times 2002 \\times \\ldots \\times 2018 \\times 2019$ has how many consecutive zeros at the end?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A binary string is a string consisting of only 0’s and 1’s (for instance, 001010, 101, etc.). What is the probability that a randomly chosen binary string of length 10 has 2 cons... | math | {
"ground_truth": "\\frac{55}{64}",
"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 2022. If the last digit 5 is erased from the first number, and the digit 1 is appended to the right of the second number, then the sum of the modified n... | math | {
"ground_truth": "1815 \\text{ and } 207",
"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 Maria has constructed a large right triangle with legs 6 units and 8 units, and a smaller triangle with an area half that of the large triangle, calculate the sum of the pe... | math | {
"ground_truth": "24 + 6\\sqrt{3} + 2\\sqrt{15}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Vasya thought of three different digits, none of which are zero. Petya wrote down all possible two-digit numbers that use only these digits in their decimal representation. The s... | math | {
"ground_truth": "2, 3, 6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The interior angles of a convex polygon are in arithmetic progression. If the common difference is \\(8^\\circ\\) and the largest angle is \\(172^\\circ\\), find the number of si... | math | {
"ground_truth": "The correct answer is B) 10.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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