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": "Find the number of ordered pairs of integers $(a, b)$ with $1 \\leq a \\leq 50$ and $b \\geq 0$ such that the polynomial $x^2 - ax + b$ can be factored into the product of two (n... | math | {
"ground_truth": "377",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = \\begin{cases} x^2+4x, & x\\geqslant 0 \\\\ 4x-x^2, & x < 0 \\end{cases}$, find the range of values for the real number $a$ if $f(2-2a) > f(a)$.",
... | math | {
"ground_truth": "(-\\infty, \\frac {2}{3})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A magician and his assistant perform in front of an audience of many people.\nOn the stage there is an $8$ × $8$ board, the magician blindfolds himself, and then the assistant ... | math | {
"ground_truth": "a_{S+1} = T - S \\cdot a_S \\mod 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": "Given that Jill's grandmother takes one half of a pill every other day, and one supply of medicine contains 60 pills, calculate the approximate number of months that the supply o... | 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": "If $\\left|\\frac{18}{x} - 4\\right| = 3$, find the product of all possible values of $x$. Express your answer as an improper fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{324}{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": "What is the area of a sector with a central angle of 120 degrees in a circle whose diameter is 6 meters? Express your answer in terms of \\(\\pi\\).",
"role": "user"
}
] | math | {
"ground_truth": "3\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equations:<br/>$(1)2\\left(x-1\\right)=2-5\\left(x+2\\right)$;<br/>$(2)\\frac{5x+1}{2}-\\frac{6x+2}{4}=1$.",
"role": "user"
}
] | math | {
"ground_truth": "x = 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": "Find the number of real values of \\( a \\) such that for each \\( a \\), the cubic equation \\( x^{3} = ax + a + 1 \\) has an even root \\( x \\) with \\( |x| < 1000 \\).",
... | math | {
"ground_truth": "999",
"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 ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$ with eccentricity $e = \\frac{1}{2}$, and the distance from the right focus to the right vertex is $1... | math | {
"ground_truth": "-\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The coordinates of the vertices of an isosceles trapezoid $ABCD$ are all integers, with $A=(30,120)$ and $D=(32,129)$. The trapezoid has no horizontal or vertical sides, and the ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the graph of the function $f(x) = \\log_{a}(4x-3) + 1$ ($a > 0$ and $a \\neq 1$) has a fixed point $A(m,n)$, find the minimum value of $\\frac{1}{x+1} + \\frac{1}{y}$, wher... | 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": "Given propositions $p$ and $q$: Proposition $p$ states that the equation $4x^{2}-4(m-2)x+1=0$ has two unequal negative roots; Proposition $q$ states that the equation $x^{2}+3mx+... | math | {
"ground_truth": "\\frac{2}{3} \\leq m < 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": "Twenty-one rectangles of size $3\\times 1$ are placed on an $8\\times 8$ chessboard, leaving only one free unit square. What position can the free square lie at?",
"role"... | math | {
"ground_truth": "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": "Suppose $x$ and $y$ are both positive real numbers, and $x + 2y + 2xy = 8$, find the minimum value of $x + 2y$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bamboo plant grows at a rate of 105 cm per day. On May 1st at noon it was 2 m tall. Calculate the height of the bamboo plant on May 8th at noon.",
"role": "user"
}
] | math | {
"ground_truth": "9.35",
"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 $a=1+10^{-4}$ . Consider some $2023\\times 2023$ matrix with each entry a real in $[1,a]$ . Let $x_i$ be the sum of the elements of the $i$ -th row and $y_i$ be the ... | math | {
"ground_truth": "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": "We are given a tetrahedron with two edges of length $a$ and the remaining four edges of length $b$ where $a$ and $b$ are positive real numbers. What is the range of possi... | math | {
"ground_truth": "\\left(0, \\frac{\\sqrt{6} + \\sqrt{2}}{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": "Determine the non-zero, real value of $y$ satisfying $(3y)^5 = (9y)^4$.",
"role": "user"
}
] | 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": "Consider the following functions:\n$$\n\\begin{array}{ccc}\nf(x) & = & 4x^2 - 3x + 5 \\\\\ng(x) & = & x^2 - mx - 8\n\\end{array}\n$$\nIf \\( f(5) - g(5) = 15 \\), find the value ... | math | {
"ground_truth": "-15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We will call a natural number \\( n \\) squareable if the numbers from 1 to \\( n \\) can be arranged in such a way that each member of the sequence, when added to its position n... | math | {
"ground_truth": "9, 15",
"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 price of a smartphone is $\\textdollar{800}$. A store offers a single discount of 25%. Another store offers two successive discounts of 20% and 10%. Calculate the difference ... | math | {
"ground_truth": "\\textdollar{24}",
"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 line $y = 5$ intersects the graph of $y = 3x^2 + 2x - 2$ at points $C$ and $D$. Find the distance between $C$ and $D$, expressed in the form $\\frac{\\sqrt{p}}{q}$, where $p$... | math | {
"ground_truth": "19",
"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": "We call a sequence of integers a *Fibonacci-type sequence* if it is infinite in both ways and $a_{n}=a_{n-1}+a_{n-2}$ for any $n\\in\\mathbb{Z}$ . How many *Fibonacci-type seq... | math | {
"ground_truth": "\\left(\\frac{N}{2}\\right) \\left(\\frac{N}{2} + 1\\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": "Let the initial price of the product be represented by $P$. The price of the product increased by 10% in January, decreased by 15% in February, increased by 20% in March, decreas... | math | {
"ground_truth": "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": "Find the volume of a cone if the base contains a chord of length \\( a \\) that subtends an arc of \\( \\alpha^{\\circ} \\), and the height of the cone makes an angle \\( \\beta ... | math | {
"ground_truth": "\\frac{\\pi a^3 \\cot \\beta}{24 \\sin^3 \\left( \\frac{\\alpha}{2} \\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": "How many rectangles with sides parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line $y = 2x$, the line $y... | math | {
"ground_truth": "D) 51",
"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": "Archipelago consists of $ n$ islands : $ I_1,I_2,...,I_n$ and $ a_1,a_2,...,a_n$ - number of the roads on each island. $ a_1 \\equal{} 55$ , $ a_k \\equal{} a_{k \\minus... | math | {
"ground_truth": "55n + \\binom{n+1}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all solutions to the inequality \\[\\frac{x^2+1}{(x-3)(x+2)} \\ge 0.\\] (Give your answer in interval notation.)",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, -2] \\cup (3, \\infty)",
"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": "Simplify:<br/>$(1)\\frac{1}{2}\\sqrt{\\frac{4}{7}}$;<br/>$(2)\\sqrt{{{20}^2}-{{15}^2}}$;<br/>$(3)\\sqrt{\\frac{{32×9}}{{25}}}$;<br/>$(4)\\sqrt{22.5}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3\\sqrt{10}}{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": "In the sequence of 51 consecutive odd numbers \\(1, 3, 5, \\cdots, 101\\), select \\(k\\) numbers such that their sum is 2013. What is the maximum value of \\(k\\)?",
"role":... | math | {
"ground_truth": "43",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, $AB = BC$ and $\\overline{BD}$ is an altitude. Point $E$ is on the extension of $\\overline{AC}$ such that $BE = 8$. The values of $\\sin \\angle CBE$, $\\sin ... | math | {
"ground_truth": "\\frac{1}{2}ab = \\frac{1}{2} \\times 4\\sqrt{2} \\times 2\\sqrt{2} = 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 an arithmetic sequence $\\{a_{n}\\}$ with the sum of the first $n$ terms as $S_{n}$, $a_{4}-a_{2}=6$, and $a_{1}$, $a_{3}$, $a_{8}$ form a geometric sequence, find $\\frac{... | math | {
"ground_truth": "\\frac{35}{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 that \\(x > 0, y > 0\\), and satisfying the following system of equations:\n\\[\n\\begin{cases}\n\\cos ^{2}(\\pi x) + 2 \\sin (\\pi y) = 1 \\\\\n\\sin (\\pi x) + \\sin (\\p... | math | {
"ground_truth": "(4, 2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the inequality $2|x-3|+|x-4| < 2a$.\n(I) If $a=1$, find the solution set;\n(II) If the solution set of the inequality is not empty, find the range of $a$.",
"role": "us... | math | {
"ground_truth": "(\\frac {1}{2},+\\infty)",
"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": "Determine the value of \\(c\\) such that the vertex of the parabola described by the equation \\(y = x^2 - 12x + c\\) lies on the \\(x\\)-axis.\nA) 12\nB) 24\nC) 36\nD) 48\nE) 72... | math | {
"ground_truth": "C) 36",
"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 $p$: $-4 < x-a < 4$, and $q$: $(x-1)(2-x) > 0$. If $\\neg p$ is a sufficient condition for $\\neg q$, then the range of the real number $a$ is __________.",
"role": "us... | math | {
"ground_truth": "[-2, 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 solutions to the equation $(z-3)^6 = 64$ are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled $D, E,$ and $F$. What is the... | math | {
"ground_truth": "\\sqrt{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": "Given a mathematics contest with twelve problems, a student gains 4 points for a correct answer and loses 1 point for an incorrect answer. If Jason answered every problem and his... | math | {
"ground_truth": "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": "Orvin went to the store with enough money to buy 40 balloons at full price. He discovered a revised store promotion: after buying 4 balloons at full price, the next balloon could... | math | {
"ground_truth": "44",
"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": "Let $S$ be the set of [ordered pairs](https://artofproblemsolving.com/wiki/index.php/Ordered_pair) $(x, y)$ such that $0 < x \\le 1, 0<y\\le 1,$ and $\\left[\\log_2{\\left(\\frac... | math | {
"ground_truth": "14",
"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 sequence \\(\\left\\{\\alpha_{n}\\right\\}\\) is an arithmetic sequence with a common difference \\(\\beta\\). The sequence \\(\\left\\{\\sin \\alpha_{n}\\right\\}\\) is a ge... | math | {
"ground_truth": "1 \\text{ or } -1",
"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 \\in \\mathbb{R}\\\\), and vectors \\\\(\\vec{a} = (m+2, 1)\\\\), \\\\(\\vec{b} = (1, -2m)\\\\), and \\\\(\\vec{a} \\perp \\vec{b}\\\\). Find the magnitude of \\\\(\\v... | math | {
"ground_truth": "\\sqrt{34}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $\\sqrt{(5-3\\sqrt{2})^2} - \\sqrt{(5+3\\sqrt{2})^2}$?",
"role": "user"
}
] | math | {
"ground_truth": "-6\\sqrt{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": "Apply the following two transformations to the complex number $-1 + 7i$:\n1. A $60^\\circ$ rotation around the origin in the counter-clockwise direction.\n2. A dilation, centered... | math | {
"ground_truth": "-22 - (\\sqrt{3} - 7)i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)$ such that $f(xy) = f(x)f(y)$ for any real numbers $x$ and $y$, and $f(-1) = 1$, $f(27) = 9$. When $0 \\leq x < 1$, it holds that $0 \\leq f(x) < 1$.\n1.... | math | {
"ground_truth": "0 \\leq a \\leq 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 the function $y=2x+2x^{-1} (x > 0)$, determine the range of the function.",
"role": "user"
}
] | math | {
"ground_truth": "[4,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many integers $n$ with $1 \\le n \\le 2023$ is the product\n\\[\n \\prod_{k=0}^{n-1} \\left( \\left( 1 + e^{2 \\pi i k / n} \\right)^n + 1 \\right) \n\\]equal to zero, w... | math | {
"ground_truth": "202",
"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 largest positive $p$ ( $p>1$ ) such, that $\\forall a,b,c\\in[\\frac1p,p]$ the following inequality takes place\r\n\\[9(ab+bc+ca)(a^2+b^2+c^2)\\geq(a+b+c)^4\\]",
... | math | {
"ground_truth": "\\sqrt{4 + 3\\sqrt{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": "The standard enthalpy of formation (ΔH_f°) of a substance is equal to the heat effect of the formation reaction of 1 mole of the substance from simple substances in their standar... | math | {
"ground_truth": "\\text{Q}_{\\text{обр}} \\left( \\mathrm{C}_6 \\mathrm{H}_6 \\right) = -82.9 \\text{ кДж/моль}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x \\neq 0 \\), \\( \\frac{x}{3} = y^2 \\) and \\( \\frac{x}{5} = 5y + 2 \\), find the value of \\( x \\).\nA) \\( \\frac{125 + 5\\sqrt{745}}{6} \\)\nB) \\( \\frac{685 + 25... | math | {
"ground_truth": "\\text{(B)}\\ \\frac{685 + 25\\sqrt{745}}{6}",
"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 $S\\_n$ is the sum of the first $n$ terms of the sequence ${a\\_n}$, and $a\\_1=-1$, $\\frac{a_{n+1}}{S_{n+1}} = S\\_n$, find the sum of the first $n$ terms of the seq... | math | {
"ground_truth": "\\begin{cases} -1 & n=1 \\\\ \\frac{1}{n(n-1)} & n\\geq 2 \\end{cases}",
"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": "Star lists the whole numbers $1$ through $30$ once. Emilio copies Star's numbers, replacing each occurrence of the digit 3 with the digit 2. Star adds her numbers and Emilio adds... | math | {
"ground_truth": "\\textbf{(C)}\\ 13",
"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 function $f(x)=\\sin (2x+\\varphi)$, where $\\varphi$ is a real number. If $f(x) \\leqslant |f( \\frac {\\pi}{6})|$ holds for $(0,+\\infty)$, and $f( \\frac {\\pi}{2}) > f(\\... | math | {
"ground_truth": "[\\frac {\\pi}{6}+k\\pi, \\frac {2\\pi}{3}+k\\pi]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x = \\dfrac{2 - i\\sqrt{3}}{3} \\) where \\( i = \\sqrt{-1} \\), calculate the value of \\( \\dfrac{1}{x^2 - x} \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{-45}{28} + \\dfrac{9i\\sqrt{3}}{28}",
"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": "Does there exist a 4-digit integer which cannot be changed into a multiple of 1992 by changing 3 of its digits?",
"role": "user"
}
] | math | {
"ground_truth": "2251",
"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 \\(x=-3000\\). Calculate the value of $\\Bigg\\vert\\Big\\vert |x|-x\\Big\\vert-|x|+500\\Bigg\\vert-x$.",
"role": "user"
}
] | math | {
"ground_truth": "6500",
"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": "For each positive integer $n$ , let $s(n)$ be the sum of the squares of the digits of $n$ . For example, $s(15)=1^2+5^2=26$ . Determine all integers $n\\geq 1$ such that ... | math | {
"ground_truth": "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": "For how many values of $d$ is $3.04d0 > 3.040$?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence of 0s and 1s of length 21 that begins with a 0, ends with a 0, contains no two consecutive 0s, and contains no four consecutive 1s, find the total number of vali... | math | {
"ground_truth": "135",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive interger number $k$ is called “ $t-m$ ”-property if forall positive interger number $a$ , there exists a positive integer number $n$ such that ${{1}^{k}}+{{2}^{k}... | math | {
"ground_truth": "k = 4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(12 points) A rental company owns 100 cars. When the monthly rent for each car is set at 3000 yuan, all cars can be rented out. For every 50 yuan increase in the monthly rent per... | math | {
"ground_truth": "307050",
"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 two integers have a sum of 34, and when two more integers are added to the first two integers, the sum is 51, and finally, when two more integers are added to the sum of th... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the modulo $5$ remainder of the sum $(1 \\times 3 + 2 \\times 3 + 3 \\times 3 + \\ldots + 150 \\times 3)$?",
"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": "Jia has a fixed seat in a circular arrangement with 4 other individuals. If Yi and Ding cannot sit next to each other, determine the number of possible seating arrangements for t... | math | {
"ground_truth": "12",
"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 function \\( f(x) = \\lfloor x \\rfloor + \\lfloor 2x \\rfloor + \\left\\lfloor \\frac{5x}{3} \\right\\rfloor + \\lfloor 3x \\rfloor + \\lfloor 4x \\rfloor \\) for \\( x \\in... | math | {
"ground_truth": "734",
"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 greatest prime number that is a divisor of 16,384 is 2 because 16,384 = 2^14. What is the sum of the digits of the greatest prime number that is a divisor of 16,383?",
"r... | math | {
"ground_truth": "10",
"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 the function $$f(x)=x+ \\frac {4}{x}, x \\in [1, 5]$$, find the range of the function $f(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "[4, \\frac {29}{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": "Given a burger weighing 120 grams, 30 grams of which are filler, calculate the percentage of the burger that is not filler.",
"role": "user"
}
] | math | {
"ground_truth": "75\\%",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the slope of the line perpendicular to the line $4x - 5y = 10$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{5}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $p$ and $q$ be any two integers such that $p > q$ and $p$ is odd and $q$ is even. Determine the largest integer that divides all possible numbers of the form $p^2 - q^2$.",
... | 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": "For a convex pentagon with unequal sides, each side is colored with one of three colors: red, yellow, or blue. However, adjacent sides cannot be the same color. How many differen... | math | {
"ground_truth": "30",
"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": "Joey wrote a system of equations on a blackboard, where each of the equations was of the form $a + b = c$ or $a \\cdot b = c$ for some variables or integers $a, b, c$ . Then... | math | {
"ground_truth": "2037",
"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": "There are 30 people in a group. Each person in the group likes exactly \\( k \\) other people. What is the minimum \\( k \\) such that there are necessarily at least two people w... | math | {
"ground_truth": "k = 15",
"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 solution set of the inequality $(x-1)|x+2| \\geq 0$ is.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x | x \\geq 1 \\text{ or } x = -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": "At night, 100 tourists arrive at a hotel. They know that the hotel has single rooms numbered 1,2, …, n, of which k are under renovation (it is not known which ones), and the rest... | math | {
"ground_truth": "n = 100(k//2+1)+1\\text{ if } k \\text{ is odd, } 100(k//2 + 1) \\text{ if } k\\text{ is even}",
"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": "Four dice, each with faces numbered 1 through 6, are stacked such that nine of the twenty-four faces are visible. The total number of dots NOT visible in this view given the visi... | math | {
"ground_truth": "A) 49",
"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 range of the independent variable $x$ in the function $y=\\frac{1}{\\sqrt{x+2}}-\\sqrt{3-x}$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "-2 < x \\leq 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": "The set $M$ consists of all $7$ -digit positive integer numbers that contain (in decimal notation) each of the digits $1, 3, 4, 6, 7, 8$ and $9$ exactly once.\n(a) Find th... | math | {
"ground_truth": "d = 9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions $f: N_0 \\to N_0$ , (where $N_0$ is the set of all non-negative integers) such that $f(f(n))=f(n)+1$ for all $n \\in N_0$ and the minimum of the set $\... | math | {
"ground_truth": "f(n) = 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": "The first Math Kangaroo test was held in 1991, and it has been given annually. Alex turned 10 years old the year he participated in the ninth Math Kangaroo. In what year was Alex... | math | {
"ground_truth": "\\text{(C) } 1989",
"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": "In a drawer, there are 12 distinguishable socks: 5 white, 5 brown, and 2 blue. In how many ways can I choose a pair of socks such that the pair either contains two socks of the s... | math | {
"ground_truth": "45",
"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": "Two 30-60-90 triangles, each with a hypotenuse of 10 cm, are placed such that one vertex of each triangle exactly coincides while they lay flat on a surface. This configuration c... | math | {
"ground_truth": "\\dfrac{75}{8} \\text{ cm}^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": "Determine the greatest number m such that the\nsystem \u001a $x^2$ + $y^2$ = 1; | $x^3$ - $y^3$ |+|x-y|= $m^3$ has a solution.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt[3]{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": "In the coordinate plane, a set of $2000$ points $\\{(x_1, y_1), (x_2, y_2), . . . , (x_{2000}, y_{2000})\\}$ is called *good* if $0\\leq x_i \\leq 83$ , $0\\leq y_i \\leq 8... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Emily places 6 ounces of tea into a twelve-ounce cup and 6 ounces of honey into a second cup of the same size, and then adds 3 ounces of lemon juice to the second cup,... | math | {
"ground_truth": "\\frac{1}{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": "An $8 \\times 8$ chessboard is divided into $p$ rectangles. The division must follow these rules:\n1. Each rectangle contains the same number of white and black squares.\n2. If t... | math | {
"ground_truth": "\\begin{array}{ccccccc}\n1 & 2 & 3 & 4 & 5 & 7 & 10 \\\\\n1 & 2 & 3 & 4 & 5 & 8 & 9 \\\\\n1 & 2 & 3 & 4 & 6 & 7 & 9 \\\\\n1 & 2 & 3 & 5 & 6 & 7 & 8 \\\\\n\\end{array}",
"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 coefficient of $x^3y^5$ in the expansion of $(x+y)(x-y)^7$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"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 football tournament, each team meets exactly twice with every other team. There are no draws, a victory earns two points and a defeat earns no points. One team won the tourn... | math | {
"ground_truth": "12",
"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 set of numbers $\\{2, 2^2, 2^3, \\ldots, 2^{20}\\}$, together with an additional number 5, find the ratio of the largest number in the set to the sum of all other numbe... | math | {
"ground_truth": "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": "Convex quadrilateral $PQRS$ has $PQ = 15$ and $RS = 20$. Diagonals $PR$ and $QS$ intersect at $T$, $PR = 22$, and $\\triangle PTR$ and $\\triangle QTS$ have equal areas. What is ... | math | {
"ground_truth": "11",
"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": "Determine the smallest positive real number $r$ such that there exist differentiable functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ and $g: \\mathbb{R} \\rightarrow \\m... | math | {
"ground_truth": "\\frac{\\pi}{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": "A gumball machine contains $8$ red, $10$ white, and $6$ blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is __?... | math | {
"ground_truth": "C) 10",
"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": "Ms. Damon gives an exam to two classes. The mean of the scores of the students in the morning class is 82, and the afternoon class's mean score is 68. The ratio of the number of ... | math | {
"ground_truth": "B) 74",
"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 $\\log _{2} \\sqrt {2}$.",
"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": "In triangle $PQR$, $PQ = 10$. The length of median $PS$ is 7. Let $N$ be the largest possible value of $PR^2 + QR^2$, and let $n$ be the smallest possible value. Find $N - n$.",
... | 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": "For any positive integers $n$ , find all $n$ -tuples of complex numbers $(a_1,..., a_n)$ satisfying $$ (x+a_1)(x+a_2)\\cdots (x+a_n)=x^n+\\binom{n}{1}a_1 x^{n-1}+\\binom{n}... | math | {
"ground_truth": "a_1 = a_2 = \\cdots = a_n",
"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": "You have 5 different shirts and 6 different pairs of pants. However, one special shirt cannot be paired with two specific pants. How many unique outfits can you make?",
"role... | math | {
"ground_truth": "28",
"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 $\\mathbf{a}$ and $\\mathbf{b}$ be vectors, and let $\\mathbf{m}$ be the midpoint of $\\mathbf{a}$ and $\\mathbf{b}.$ Given $\\mathbf{m} = \\begin{pmatrix} 4 \\\\ 8 \\end{pma... | math | {
"ground_truth": "304",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the points $(2, -1)$ and $(-2, 7)$, find the y-intercept of the line passing through these points.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $(a_n)$ and $(b_n)$ be the sequences of real numbers such that\n\\[ (1 + 2i)^n = a_n + b_ni \\]for all integers $n\\geq 0$, where $i = \\sqrt{-1}$. What is\\[\\sum_{n=0}^\\in... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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