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": "Consider the infinite series $1 - \\frac{1}{3} - \\frac{1}{9} + \\frac{1}{27} - \\frac{1}{81} - \\frac{1}{243} + \\frac{1}{729} - \\frac{1}{2187} - \\cdots$. Evaluate the sum of ... | math | {
"ground_truth": "\\frac{15}{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": "Positive integers $1,2,...,n$ are written on а blackboard ( $n >2$ ). Every minute two numbers are erased and the least prime divisor of their sum is written. In the end only... | math | {
"ground_truth": "n = 18",
"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": "Isosceles triangle $ABC$, where $AB = AC$, has been folded so that vertex $A$ now rests at $A'$ on $\\overline{BC}$, such that $BA' = 3$ and $A'C = 5$. The original length of eac... | math | {
"ground_truth": "\\frac{\\sqrt{7393}}{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": "Define a fraction $\\frac{a}{b}$ as special if $a + b = 20$ where $a$ and $b$ are positive integers. How many distinct integers can be written either as the sum or as the product... | math | {
"ground_truth": "B) 12",
"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, 2, 3, 4, 5, and 6 need to be combined using mathematical operations to result in 3.",
"role": "user"
}
] | math | {
"ground_truth": "1 + 2 - 3 + 4 + 5 - 6 = 3; \\quad 1 + 2 + 3 - 4 - 5 + 6 = 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": "Consider two circles of radius one, and let $O$ and $O'$ denote their centers. Point $M$ is selected on either circle. If $OO' = 2014$ , what is the largest possible are... | math | {
"ground_truth": "1007",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(\\frac{5+6+7}{3} = \\frac{2020+2021+2022}{N}\\), calculate the value of \\(N\\).",
"role": "user"
}
] | math | {
"ground_truth": "1010.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle has a center O and radius 5 units. Two tangents are drawn such that one is 3 units above the circle and one is 7 units below it. Find the number of points that are equid... | 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": "Given triangle $ABC$ with $\\angle BAC = 60^o$, $AB = 3a$, and $AC = 4a$ ($a > 0$), determine the length of $BI$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a\\sqrt{19}}{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": "Triangle $PAB$ is formed by three tangents to circle $O$ with $\\angle APB = 50^\\circ$. Calculate $\\angle AOB$.",
"role": "user"
}
] | math | {
"ground_truth": "65^\\circ",
"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 ATM password at Gloria's Bank comprises five digits from $0$ to $9$, and repeated digits are allowed, but no password may begin with the sequence $9,1,1,1$, how many val... | math | {
"ground_truth": "99990",
"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": "Three male reporters and two female reporters are assigned to four tasks, with the restriction that the two female reporters do not participate in the \"carrying equipment\" task... | math | {
"ground_truth": "126",
"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) Find the number of all resulting shapes.\n\nb) Find the number of bounded shapes, i.e., polygons.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{n^2 - 3n + 2}{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 $\\dbinom{20}{19} + \\dbinom{20}{1}$.",
"role": "user"
}
] | math | {
"ground_truth": "40",
"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 numbers \\( a \\) and \\( b \\) for which the equality \\( |a x + b y| + |b x + a y| = |x| + |y| \\) holds for all values of the variables \\( x \\) and \\( y \\).",
... | math | {
"ground_truth": "a = \\pm 1, b = 0 \\text{ or } a = 0, b = \\pm 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": "What is the reciprocal of $\\frac{3}{4} + \\frac{4}{5}$?\nA) $\\frac{31}{20}$\nB) $\\frac{20}{31}$\nC) $\\frac{19}{20}$\nD) $\\frac{20}{19}$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{20}{31}",
"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": "Ethan Song and Bryan Guo are playing an unfair game of rock-paper-scissors. In any game, Ethan has a 2/5 chance to win, 2/5 chance to tie, and 1/5 chance to lose. How many games ... | 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": "Assume that $h$ and $k$ are functions for which $k^{-1}(h(z)) = 7z - 4$. Find $h^{-1}(k(12))$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{16}{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": "Forty-five decreased by three times the square of a number is 12. What is the number?",
"role": "user"
}
] | math | {
"ground_truth": "-\\sqrt{11}",
"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 price of an article is cut $10 \\%$. Calculate the percentage by which the new price must be increased to restore it to its former value.",
"role": "user"
}
] | math | {
"ground_truth": "11\\frac{1}{9}\\%",
"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": "A square has an area of 64. A rectangle has the same width as the square. The length of the rectangle is three times its width. What is the area of the rectangle?",
"role": "... | math | {
"ground_truth": "192",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A burger at Gourmet Delight weighs 200 grams, composed of 40 grams of filler and 30 grams of cheese. What percent of the burger is neither filler nor cheese?",
"role": "user"... | math | {
"ground_truth": "65\\%",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In quadrilateral $ABCD$, point $E$ is an interior point from which lines are drawn to vertices $A$, $B$, $C$, and $D$. If $p, q, r, s, t$ are the measures of angles around point ... | math | {
"ground_truth": "\\textbf{(A)}\\ 360 - q - r - s - t",
"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 there exist \\( n \\) integers \\( a_1, a_2, \\cdots, a_n \\) satisfying the following equations\n$$\na_1 + a_2 + \\cdots + a_n = a_1 a_2 \\cdots a_n = 1990,\n$$\nfind the sma... | math | {
"ground_truth": "5",
"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": "Five fair six-sided dice are rolled. Find the probability that at least four of the five dice show the same value.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{54}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many distinct sequences of six letters can be made from the letters in EQUALITY if each sequence must begin with Y and end with T, and no letter can appear in a sequence more... | math | {
"ground_truth": "360",
"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": "Triangle $PQR$ is scalene with angle $Q$ being twice the measure of angle $P$ and angle $R$ being three times the measure of angle $P$. What is the number of degrees in the measu... | math | {
"ground_truth": "60^\\circ",
"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 the value of $k$ if\n\\[(\\sin \\alpha + \\csc \\alpha)^2 + (\\cos \\alpha + \\sec \\alpha)^2 = k + 3\\tan^2 \\alpha + 3\\cot^2 \\alpha.\\]",
"role": "user"
}
] | math | {
"ground_truth": "5",
"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 $y=x^3-3x^2-9x$ ($-2<x<4$) has a maximum value and a minimum value.",
"role": "user"
}
] | math | {
"ground_truth": "5; -27",
"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 function \\( f(n) \\) is defined on the positive integers and takes non-negative integer values. \\( f(2) = 0 \\), \\( f(3) > 0 \\), \\( f(9999) = 3333 \\) and for all \\( m,... | math | {
"ground_truth": "f(1982) = 660",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 4 people in the family. If Masha's scholarship is doubled, the total family income will increase by 5%. If the mother's salary is doubled instead, the total family inco... | math | {
"ground_truth": "55\\%",
"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 remainder when \\(x^4 + x^3 + 1\\) is divided by \\(x - 2\\).",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an oblique parallelepiped, the projection of the lateral edge on the base plane is 5 dm, and the height is 12 dm. A section perpendicular to the lateral edge is a rhombus with... | math | {
"ground_truth": "260 \\, \\text{dm}^2; \\, 312 \\, \\text{dm}^3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the polynomial $p(x)$ of the lowest degree with integer coefficients such that its leading coefficient is 1, and $p(0) = 0$, $p(1) = 1$, and $p(-1) = 3$.",
"role": "user... | math | {
"ground_truth": "p(x) = x^3 + 2x^2 - 2x",
"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 curve that passes through the point \\((2, 3)\\) and has the property that the segment of any of its tangents, intercepted between the coordinate axes, is bisected at th... | math | {
"ground_truth": "xy = 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": "Given the function $f(x)=a\\sin x - \\sqrt{3}\\cos x$, one of its graphs has an axis of symmetry at $x=-\\frac{\\pi}{6}$, and $f(x_1) - f(x_2) = -4$, calculate the minimum value ... | math | {
"ground_truth": "\\frac{2\\pi}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that set $A$ is $\\{x|x^{2}+5x-6 \\lt 0\\}$, and set $B$ is $\\{x|m-2 \\lt x \\lt 2m+1\\}$. \n$(1)$ When $m=1$, find $A\\cap (\\complement _{R}B)$. \n$(2)$ If $A\\cup B=A... | math | {
"ground_truth": "(-\\infty, 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": "Given that Norb's age is a prime number and at least 60% of the guesses (7 out of 11) are too low, two of the guesses are off by 1, find Norb's age.",
"role": "user"
}
] | math | {
"ground_truth": "59",
"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 number of four-digit numbers without repeated digits that can be formed using the digits 1, 2, 3, and 4, where exactly one even digit is sandwiched between two odd digit... | math | {
"ground_truth": "8",
"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 any positive integer $n$ , we have the set $P_n = \\{ n^k \\mid k=0,1,2, \\ldots \\}$ . For positive integers $a,b,c$ , we define the group of $(a,b,c)$ as lucky if ther... | math | {
"ground_truth": "18",
"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 solution interval for the equation $3^x + x = 3$ is to be found.",
"role": "user"
}
] | math | {
"ground_truth": "(0, 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": "Let a binary operation $\\star$ on ordered pairs of integers be defined by $(a,b)\\star (c,d)=(a-c,b+d)$. Calculate $(5,4)\\star (1,1)$. If $(x,y)\\star (2,3)$ results in the sam... | math | {
"ground_truth": "C) 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": "Alice and her Canadian cousin, Ben, are at a bookstore in Germany that accepts both euros and Canadian dollars. They want to buy a set of books, but neither of them has enough mo... | math | {
"ground_truth": "1.67 \\text{ euros}",
"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": "\\(8.424 \\cos x + \\sqrt{\\sin ^{2} x - 2 \\sin 2 x + 4 \\cos ^{2} x} = 0\\)",
"role": "user"
}
] | math | {
"ground_truth": "x_1 = \\arctan(-6.424) + \\pi(2k+1), \\quad x_2 = \\arctan(5.212) + \\pi(2k+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": "There are currently \\( m \\) colors (where \\( m \\geq 2 \\)). Using these colors to dye a \\( 1 \\times n \\) chessboard, where each square is dyed with one color, how many way... | math | {
"ground_truth": "(n^2 - 3n + 3)(n-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": "Solve the following equation with real numbers:\n\n$$\n\\log _{19}(x-3)+\\log _{93}(x-3)=3-\\lg \\left(x^{5}-24\\right)\n$$",
"role": "user"
}
] | 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": "Given Alicia earns 25 dollars per hour and 2% of her wages is deducted to pay local taxes, calculate the number of cents per hour of Alicia's wages used to pay local taxes.",
... | math | {
"ground_truth": "50",
"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 two integers have a sum of 26, two additional integers result in a sum of 41 when added to the first two, and two more integers added to the sum of the previous four result... | math | {
"ground_truth": "1",
"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": "Consider an extended deck of cards with 60 cards divided equally into 4 suits, each containing 15 cards. Two of the suits, hearts ($\\heartsuit$) and diamonds ($\\diamondsuit$), ... | math | {
"ground_truth": "\\frac{29}{247}",
"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 equations \\(3x + 9 = 0\\) and \\(cx + 15 = 3\\) have the same solution \\(x\\). What is the value of \\(c\\)?",
"role": "user"
}
] | math | {
"ground_truth": "c = 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": "Compute the number of ordered pairs of integers \\((x, y)\\) such that \\(25 \\leq x < y \\leq 50\\) where \\(i^x + i^y\\) equals zero (meaning \\(i^x\\) and \\(i^y\\) are purely... | math | {
"ground_truth": "11",
"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 numbers \\(x_{1}, x_{2}, x_{3}, \\ldots, x_{2018}\\). It is known that \\(x_{1}= \\frac{1}{2}\\) and \n\n$$\nx_{n}=\\frac{x_{n-1}}{2 n x_{n-1}+1} \\text { for } n=2, \\... | math | {
"ground_truth": "\\frac{2018}{2019}",
"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 the terminal side of angle α passes through point P(1, 2), determine the value of cos^2α - sin^2α.",
"role": "user"
}
] | math | {
"ground_truth": "- \\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\( i^{2} = -1 \\), express the sum \\( S=\\cos 45^{\\circ}+i \\cos 135^{\\circ}+\\cdots+i^{n} \\cos (45+90n)^{\\circ}+\\cdots+i^{40} \\cos 3645^{\\circ} \\) in simple... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}(21 - 20i)",
"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 box contains tiles numbered 1 through 100. Tiles marked with a number congruent to $3 \\pmod{7}$ are colored blue. One tile is randomly selected from the box. What is the proba... | math | {
"ground_truth": "\\frac{7}{50}",
"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": "There are real numbers \\( a \\) and \\( b \\) for which the function \\( f \\) has the properties that \\( f(x) = ax + b \\) for all real numbers \\( x \\), and \\( f(bx + a) = ... | math | {
"ground_truth": "-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": "Let the three-digit number be denoted as 100a + 10b + c, where a is the hundreds digit, b is the tens digit, and c is the units digit. Given that the hundreds digit is 3 more tha... | 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": "Two standard 6-sided dice are rolled. What is the probability that the sum rolled is either a prime number or a perfect square?",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{22}{36} = \\dfrac{11}{18}",
"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": "Chloe wants to buy a pair of sneakers that costs $ \\$45.50$. She checks her wallet and finds she has four $ \\$10$ bills, ten quarters, and some dimes and nickels. What is the m... | math | {
"ground_truth": "30",
"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": "Define the set operation \\( A \\otimes B = \\{ z \\mid z = xy, x \\in A, y \\in B \\} \\) given \\( A = \\{2, 0\\} \\) and \\( B = \\{0, 8\\} \\), find the sum of all elements i... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\omega$ be the unit circle in the $xy$ -plane in $3$ -dimensional space. Find all points $P$ not on the $xy$ -plane that satisfy the following condition: There exist... | math | {
"ground_truth": "x^2 + y^2 + 2z^2 = 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 \ffive-digit number $12110$ is divisible by the sum of its digits $1 + 2 + 1 + 1 + 0 = 5.$ Find the greatest \ffive-digit number which is divisible by the sum of its digi... | math | {
"ground_truth": "99972",
"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": "What is the remainder when $3^{303} + 303$ is divided by $3^{151} + 3^{75} + 1$?",
"role": "user"
}
] | math | {
"ground_truth": "294",
"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 every natural number $n$, let $\\mathbf{S}(n)$ denote the sum of the digits of $n$. Calculate $\\mathbf{S}^{5}(2018^{2018^{2018}})$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, the angles opposite to sides $a$, $b$, and $c$ are $A$, $B$, and $C$ respectively. Given that $2\\sin{\\frac{C}{2}}(\\sqrt{3}\\cos{\\frac{C}{2}} - \\sin{\\fr... | math | {
"ground_truth": "2\\sqrt{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": "Orvin went to the store with just enough money to buy 30 balloons where each balloon cost $1. However, the store had a two-tier discount on balloons: for every set of two balloon... | math | {
"ground_truth": "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": "In a new recipe, the ratio of butter:flour:sugar is 2:5:3. If the recipe requires 15 cups of flour, how many total cups of these three ingredients are needed?",
"role": "user... | math | {
"ground_truth": "30",
"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 slope of the line $6x - 4y = 16$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{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": "Vasily is going to finish his institute in a year. Only 270 out of 300 third-year students successfully pass the exams and complete their bachelor's degree. If Vasily ends up amo... | math | {
"ground_truth": "45025",
"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 $t$ is a constant, the function $y=|x^2-2x-t|$ has a maximum value of 2 on the interval $[0,3]$. Find the value of $t$.",
"role": "user"
}
] | 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": "What number must we subtract from $5-3i$ to get $-2+4i$? Here, $i^2 = -1.$",
"role": "user"
}
] | math | {
"ground_truth": "7-7i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many six-digit numbers are there in which each subsequent digit is smaller than the previous one?",
"role": "user"
}
] | math | {
"ground_truth": "210",
"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 line $y = 5x - 7$ is parameterized by the form\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} s \\\\ 2 \\end{pmatrix} + t \\begin{pmatrix} 3 \\\\ h \\end{pma... | math | {
"ground_truth": "\\left(\\frac{9}{5}, 15\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many distinct permutations of the letters in the word REDDER are there that do not contain a palindromic substring of length at least two? (A *substring* is a continuous bloc... | 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": "Let $M = 72^5 + 5\\cdot72^4 + 10\\cdot72^3 + 10\\cdot72^2 + 5\\cdot72 + 1$. Find the number of positive integers that are factors of $M$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "When $a$ is a positive real number, find the sum of the coefficients of the first four terms in the expansion of $\\left( 1 + \\frac{1}{a} \\right)^7$.",
"role": "user"
}
] | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $k$ be a positive integer. Marco and Vera play a game on an infinite grid of square cells. At the beginning, only one cell is black and the rest are white. \n\tA turn in th... | math | {
"ground_truth": "203",
"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": "Twenty students from five different classes collected a herbarium of 30 plants. Students from the same class brought the same number of plants, while students from different clas... | math | {
"ground_truth": "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": "Given in \\\\(\\triangle ABC\\\\), the three interior angles \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) form an arithmetic sequence, find the value of \\\\(\\sin B\\\\.",
"rol... | math | {
"ground_truth": "\\dfrac{\\sqrt{3}}{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 the sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$ is $S_n$, and it satisfies $a_n > 0, q > 1$, and $a_3 + a_5 = 20$, and $a_2a_6 = 64$, find the value... | math | {
"ground_truth": "63",
"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 all $a,$ where $0^\\circ < a < 360^\\circ,$ such that $\\cos a,$ $\\cos 3a,$ and $\\cos 5a$ form an arithmetic sequence, in that order. Enter the solutions, separated by com... | math | {
"ground_truth": "90^\\circ, 270^\\circ",
"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)= \\dfrac {1}{2\\tan x}+ \\dfrac {\\sin \\dfrac {x}{2}\\cos \\dfrac {x}{2}}{2\\cos ^{2} \\dfrac {x}{2}-1}$, find the value of $f( \\dfrac {\\pi}{8})$.",
... | math | {
"ground_truth": "f( \\dfrac {\\pi}{8}) = \\sqrt {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": "Karl had his salary reduced by 10%, then increased by 10%. If his original salary was $20,000, find his present salary.",
"role": "user"
}
] | math | {
"ground_truth": "19,800",
"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 positive integer $k$ , find the least integer $n_k$ for which there exist five sets $S_1, S_2, S_3, S_4, S_5$ with the following properties:\n\\[|S_j|=k \\text{ for ... | math | {
"ground_truth": "\\left\\lceil \\frac{5k}{2} \\right\\rceil",
"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 graph of \\( y = \\frac{6x^2 - 4}{4x^2 + 3x - 1} \\) has a horizontal asymptote at \\( y = b \\). What is \\( b \\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{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": "Yang has a standard $6$ -sided die, a standard $8$ -sided die, and a standard $10$ -sided die. He tosses these three dice simultaneously. The probability that the three number... | math | {
"ground_truth": "1180",
"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 the circle defined by the equation $(x-a)^2 + (y-b)^2 = b^2 + 1$ always bisects the circumference of the circle defined by $(x+1)^2 + (y+1)^2 = 4$, determine the relat... | math | {
"ground_truth": "a^2 + 2a + 2b + 5 = 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": "Given is a regular pentagonal prism and a square plate \\(ABCD\\), all of whose edges are equal and of unit length. The prism is placed twice successively on the (horizontally pl... | math | {
"ground_truth": "2.144 \\, \\text{volume units}",
"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 all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy\n$$\nf(x+y) \\equiv f(x) + f(y) + 2xy, \\quad \\forall x, y \\in \\mathbb{R}\n$$\nand are infinite... | math | {
"ground_truth": "f(x) = x^2 + ax",
"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 $\\displaystyle \\frac{q}{r} = 8$, $\\displaystyle \\frac{s}{r} = 5$, $\\displaystyle \\frac{s}{t} = \\frac{1}{4}$, and $\\displaystyle \\frac{u}{t} = 3$, find $\\displaystyle... | math | {
"ground_truth": "\\frac{15}{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": "Given a square of metal with a side length of 6 inches has the same density as a square with a side length of 4 inches, weighing 16 ounces, calculate the weight of the square wit... | math | {
"ground_truth": "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": "Team A and team B play a series where the first team to win four games wins the series. Each team is equally likely to win each game, there are no ties, and the outcomes of the i... | math | {
"ground_truth": "\\frac{1}{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": "If $x + y = 20$ and $x - y = 8$, what is the value of $x^2 - y^2$?",
"role": "user"
}
] | math | {
"ground_truth": "160",
"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": "There exist integers $a$, $b$, and $c$ such that\n\\[(x - a)(x - 5) + 1 = (x + b)(x + c).\\]\nEnter all possible values of $a$, separated by commas.",
"role": "user"
}
] | math | {
"ground_truth": "3, 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": "Mia is helping her mom pick up 50 toys by putting 5 toys into the toy box every minute while Mia takes out 3 toys from the box after each minute. Determine the number of minutes ... | math | {
"ground_truth": "25",
"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": "Arutyun and Amayak show another effective trick. A spectator writes down on a board a sequence of $N$ (decimal) digits. Amayak closes two adjacent digits by a black disc. Then ... | math | {
"ground_truth": "101",
"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 vertex of a parabola is at (-2, 3), and it intersects the x-axis at $(x_1, 0)$ and $(x_2, 0)$, with $|x_1 - x_2| = 6$. Find the equation of this quadratic function.",
"ro... | math | {
"ground_truth": "-\\frac{1}{3}(x + 2)^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": "Given that $x$ and $y$ are distinct nonzero real numbers such that $x+\\tfrac{4}{x} = y + \\tfrac{4}{y}$, determine the value of $xy$.",
"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": "A certain model of smartphone was originally priced at $7500$ yuan per unit. After two price reductions, the current price per unit is $4800$ yuan. If the percentage of each pric... | math | {
"ground_truth": "20\\%",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the positive real number is the solution to the fractional equation $\\frac{1}{x-2}+3=\\frac{3-k}{2-x}$ with respect to $x$, find the range of values for $k$.",
"role": "u... | math | {
"ground_truth": "k > -2 \\text{ and } k \\neq 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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