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": "The following $100$ numbers are written on the board: $$ 2^1 - 1, 2^2 - 1, 2^3 - 1, \\dots, 2^{100} - 1. $$ Alice chooses two numbers $a,b,$ erases them and writes the num... | math | {
"ground_truth": "100",
"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 each digit of a 5-digit positive integer is an even number, calculate how many such integers are divisible by 4.",
"role": "user"
}
] | math | {
"ground_truth": "1875",
"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 largest real number $k$ , such that for any positive real numbers $a,b$ , $$ (a+b)(ab+1)(b+1)\\geq kab^2 $$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{27}{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": "15. Let $a_{n}$ denote the number of ternary strings of length $n$ so that there does not exist a $k<n$ such that the first $k$ digits of the string equals the last $k$ ... | math | {
"ground_truth": "2022",
"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 smallest positive solution to\n\\[\\tan 3x + \\tan 4x = \\sec 4x\\] in radians.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{17}",
"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 $a$ be a positive integer. Determine all $a$ such that the equation $$ \\biggl( 1+\\frac{1}{x} \\biggr) \\cdot \\biggl( 1+\\frac{1}{x+1} \\biggr) \\cdots \\biggl( 1+\\f... | math | {
"ground_truth": "x_1 = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ to be a positive integer. A family $\\wp$ of intervals $[i, j]$ with $0 \\le i < j \\le n$ and $i$ , $j$ integers is considered *happy* if, for any $I_1 = [i_... | math | {
"ground_truth": "C_n = \\frac{1}{n+1} \\binom{2n}{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": "When each of $702$, $787$, and $855$ is divided by the positive integer $m$, the remainder is always the positive integer $r$. When each of $412$, $722$, and $815$ is divided by ... | math | {
"ground_truth": "62",
"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": "Compute $\\cos 30^\\circ$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{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": "What is the units digit of the sum $1! + 2! + 3! + 4! + 5! + 6! + 7! + \\cdots + 500! + (2! \\cdot 4! + 3! \\cdot 7!)$?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest positive integer \\( m \\) such that each cell in an \\( m \\)-row \\( 8 \\)-column grid can be filled with one of the letters \\( C, G, M, \\) or \\( O \\) whil... | 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": "Given that a big L is formed as shown, calculate its area.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a circle with center $O$, diameters $\\overline{AB}$ and $\\overline{CD}$ are perpendicular to each other. A chord $\\overline{DF}$ intersects $\\overline{CD}$ at $E$. If $DE ... | math | {
"ground_truth": "32 \\pi",
"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": "Among $100$ points in the plane, no three collinear, exactly $4026$ pairs are connected by line segments. Each point is then randomly assigned an integer from $1$ to $100$... | math | {
"ground_truth": "1037",
"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": "Write the expression $\\frac{5 - 4c}{9} - 3$ as a single fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-22 - 4c}{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": "Which digit will appear in the 725th place after the decimal point in the decimal representation of $\\frac{7}{29}$?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with $AB = 3$ , $BC = 4$ , and $AC =5$ . If $D$ is the projection from $B$ onto $AC$ , $E$ is the projection from $D$ onto $BC$ , and $F$ ... | math | {
"ground_truth": "0",
"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 three internal angles of $\\triangle ABC$ satisfy $A$:$B$:$C=1$:$2$:$3$, and the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, wit... | math | {
"ground_truth": "\\sqrt{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 family of four octopuses went to a shoe store (each octopus has 8 legs). Father-octopus already had half of his legs shod, mother-octopus had only 3 legs shod, and their two so... | math | {
"ground_truth": "13",
"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": "It is known that the graph of the function $y= \\frac {1}{x}$ has its center of symmetry at $(0,0)$, the graph of the function $y= \\frac {1}{x}+ \\frac {1}{x+1}$ has its center ... | math | {
"ground_truth": "(-1009,2019)",
"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 rectangular garden measures 30 meters in length. One day, John decides to increase both the length and the width of his garden. He extends the length by 10 meters, and the widt... | math | {
"ground_truth": "C) 800 square meters",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=f(x)$ whose domain is $[-1,1]$, and $f(x)$ is an increasing function on $[-1,1]$, then the solution set of the inequality $f(x+ \\frac{1}{2}) \\leqslant f( ... | math | {
"ground_truth": "\\left\\{x\\left|- \\frac{3}{2}\\leqslant x\\leqslant -1\\right.\\right\\}",
"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 perimeter of an equilateral triangle exceeds the perimeter of a square by 1575 cm. The length of each side of the triangle exceeds the length of each side of the square by d ... | math | {
"ground_truth": "525",
"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 coefficient of $x^2$ when $-3x^4 - 2x^3 - 4x^2 - 8x + 2$ is multiplied by $2x^3 - 5x^2 + 3x - 1$ and the like terms are combined?",
"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": "The codes in the library catalog consist of six digits and do not begin with the digit 0. A reader is searching for the code of the book they need in the catalog. What is the pro... | math | {
"ground_truth": "0.13608",
"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 first $20$ numbers of an arrangement are shown below. What would be the value of the $60^\\text{th}$ number if the arrangement were continued?\n\n$\\bullet$ Row 1: $2,$ $2$\n... | math | {
"ground_truth": "16",
"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) = |x-1|$, the solution set of the inequality $f(x+5) \\leq 3m$ ($m>0$) is $[-7, -1]$.\n\n(1) Find the value of $m$; \n(2) Given $a>0$, $b>0$, and $2a^2+... | 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": "Find all integer triples \\((a, b, c)\\) \\((a \\neq 0)\\), such that the quadratic function \\(f(x) = ax^2 + bx + c\\) has the following property: For any integer \\(n\\), there... | math | {
"ground_truth": "(1, b, c), \\left(k^2, 2kl, l^2\\right) \\text{ where } k \\in \\mathbb{Z}_{+}, k | (l^2 - l) \\text{ or } k | (l^2 + l)",
"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 there are $121$ grid points in a square, including the points at the edges, and point $P$ is in the center of the square, determine the probability that the line $PQ$ ... | math | {
"ground_truth": "\\frac{1}{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": "A circle with center \\(P\\) and radius 4 inches is tangent at point \\(D\\) to a circle with center \\(Q\\), as illustrated. If point \\(Q\\) is on the smaller circle, determine... | math | {
"ground_truth": "48\\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": "Find the coordinates of vector $\\overline{A B}$, if $A(1, -3, 4)$ and $B(-3, 2, 1)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{-4, 5, -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": "Determine the value of $\\cos \\left( -\\frac{\\pi}{6} \\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\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": "Find all triples $(x,y,z)$ of positive rationals such that $x + y + z$ , $\\dfrac{1}{x} + \\dfrac{1}{y} + \\dfrac{1}{z}$ and $xyz$ are all integers.",
"role": "user"
... | math | {
"ground_truth": "\\{ \\{1, 1, 1\\}, \\{1, 2, 2\\}, \\{2, 3, 6\\}, \\{2, 4, 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": "A subset of the positive integers $S$ is said to be a \\emph{configuration} if 200 $\\notin S$ and for all nonnegative integers $x$ , $x \\in S$ if and only if both 2 $x\\... | math | {
"ground_truth": "1359",
"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 last two digits of the decimal representation of the square of a natural number are the same and are not zero. What are these digits? Find all solutions.",
"role": "user"... | math | {
"ground_truth": "44",
"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 $RICE$ be a quadrilateral with an inscribed circle $O$ such that every side of $RICE$ is tangent to $O$ . Given taht $RI=3$ , $CE=8$ , and $ER=7$ , compute $IC$ ."... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=4\\sin(x)\\cos\\left(x+\\frac{\\pi}{3}\\right)+\\sqrt{3}$. By changing all the abscissas of the points on the graph of function $f(x)$ to $\\frac{2}{3}$ ... | math | {
"ground_truth": "[\\frac{1}{2}, 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": "Consider a set of $1001$ points in the plane, no three collinear. Compute the minimum number of segments that must be drawn so that among any four points, we can find a triangl... | math | {
"ground_truth": "500500",
"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": "Peter said to Paul: \"Write a two-digit natural number that has the property that when you subtract the same two-digit number written in reverse, you get a difference of 63.\"\n\... | math | {
"ground_truth": "81 \\text{ or } 92",
"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": "Three cones with apex at point $A$ touch each other externally, with the first two cones being identical and the third cone having an apex angle of $2 \\arcsin \\frac{1}{4}$. Eac... | math | {
"ground_truth": "\\frac{\\pi}{6} + \\arcsin \\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let transformation \\( T \\) have the following properties:\n(i) \\( T(a \\mathbf{v} + b \\mathbf{w}) = a T(\\mathbf{v}) + b T(\\mathbf{w}) \\) for all vectors \\( \\mathbf{v} \\... | math | {
"ground_truth": "\\begin{pmatrix} 4 \\\\ 11 \\\\ 11 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x\\geq 5, y\\geq 6, z\\geq 7$ such that $x^2+y^2+z^2\\geq 125$ . Find the minimum value of $x+y+z$ .",
"role": "user"
}
] | math | {
"ground_truth": "19",
"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 \\(\\tan \\theta = 3,\\) find \\(\\tan 4\\theta.\\)",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{24}{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": "Given that $P$ philosophy books, $A$ algebra books, and $G$ geometry books, where the thickness of an algebra book is half the thickness of a philosophy book and the thickness of... | math | {
"ground_truth": "2G + \\frac{A}{2} + P",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the arithmetic mean of $a$ and $b$ is triple their geometric mean, where $a>b>0$, then find a possible value for the ratio $\\frac{a}{b}$.",
"role": "user"
}
] | math | {
"ground_truth": "34",
"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 positive integers $m$ and $n$ , we say that $m\\mid\\mid n$ if $m\\mid n$ and $\\gcd(m,\\, n/m)=1$ . Compute the smallest integer greater than \\[\\sum_{d\\mid ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the radius $R$ of a cylindrical box is $8$ inches, the height $H$ is $3$ inches, and the condition that the volume $V = \\pi R^2H$ is to be increased by the same fixed posi... | math | {
"ground_truth": "\\frac{16}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An observation station is located at point $C$, which is to the south and west by $20^{\\circ}$ from city $A$. A road that heads south-east by $40^{\\circ}$ starts from city $A$.... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At the beginning of the semester, James set a goal to earn a grade of 'A' on at least 75% of his 60 quizzes. He has earned 'A' grades on 30 of his first 40 quizzes. To achieve hi... | math | {
"ground_truth": "\\textbf{(D) }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": "Given Hammie and his quadruplet sisters weigh 106, 5, 5, 6, and 8 pounds respectively, calculate the difference between the mean weight and the median weight of these five childr... | math | {
"ground_truth": "20",
"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 range of values for the distance between points P and Q is given the edge length of the regular tetrahedron ABCD is 1.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[ \\frac{\\sqrt{2}}{2}, 1 \\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": "About the two-digit number \\( x \\), 6 assertions have been made:\n\na) \\( x \\) is divisible by 3; b) \\( x \\) is divisible by 5;\n\nc) \\( x \\) is divisible by 9; d) \\( x ... | math | {
"ground_truth": "15, 30, 60",
"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 $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c},$ and $\\mathbf{d}$ are unit vectors in space, then find the largest possible value of\n\\[\n\\|\\mathbf{a} - \\mathbf{b}\\|^2 + \\|... | math | {
"ground_truth": "16",
"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 equalities \\(\\frac{y+1}{x-z+1}=\\frac{x+y+2}{z+2}=\\frac{x+1}{y+1}\\), find the value of \\(\\frac{x+1}{y+1}\\).",
"role": "user"
}
] | 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": "In trapezoid \\(ABCD\\), \\(AB \\parallel DC\\), \\(\\angle ABC = 90^\\circ\\), and \\(E\\) is the midpoint of leg \\(AD\\). If \\(EC = \\sqrt{13}\\) and \\(AB + BC + CD = 2\\sqr... | math | {
"ground_truth": "45^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The degree measure of the sum of the interior angles of a convex polygon with $n$ sides is 2340. What is the degree measure of the sum of the interior angles of a convex polygon ... | math | {
"ground_truth": "3060^\\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": "We write the equation on the board:\n\n$$\n(x-1)(x-2) \\ldots (x-2016) = (x-1)(x-2) \\ldots (x-2016) .\n$$\n\nWe want to erase some of the 4032 factors in such a way that the equ... | math | {
"ground_truth": "2016",
"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 sum of two numbers is 12, and their product is 36. What is the sum of their reciprocals?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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 $A=(a_{ij})$ be the $n\\times n$ matrix, where $a_{ij}$ is the remainder of the division of $i^j+j^i$ by $3$ for $i,j=1,2,\\ldots,n$ . Find the greatest $n$ for ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Anya, Vanya, Danya, and Tanya collected apples. Each of them collected a whole number percentage from the total number of apples, and all these numbers are distinct and more than... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many bases between two and nine inclusive does the representation of $780_{10}$ have a final digit of 1?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\(a, b, c, d\\) are within the interval \\(\\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right]\\), and \\(\\sin a + \\sin b + \\sin c + \\sin d = 1\\), and \\(\\cos 2a +... | math | {
"ground_truth": "\\frac{\\pi}{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": "Four friends, Art, Roger, Paul, and Trisha, each bake cookies of different shapes but with the same thickness using the same amount of dough.\n- Art's cookies are trapezoids, and... | math | {
"ground_truth": "C) 56 cents",
"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 socks cost $4 per pair, and each T-shirt costs $5 more than a pair of socks, and each member needs one pair of socks and a shirt for home games and another pair of soc... | math | {
"ground_truth": "91",
"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": "One day, the weather forecast shows that the temperature in Gaochun ranges from -2 to 9°C. What is the temperature difference in Gaochun on that day?",
"role": "user"
}
] | math | {
"ground_truth": "11",
"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": "Alice and Tom each have two fair coins and another coin that comes up heads with a probability of $\\frac{2}{5}$. Alice flips the three coins, and then Tom repeats the same. The ... | math | {
"ground_truth": "139 + 392 = 531",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the axial section of a cone is an equilateral triangle, find the ratio of the lateral surface area to the total surface area of this cone.",
"role": "user"
}
] | math | {
"ground_truth": "\\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": "Given the sequence of 0s and 1s has a length of 22 and begins and ends with 0, contains no two consecutive 0s, and contains exactly one occurrence of three consecutive 1s, calcul... | 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": "If $n$ is a positive integer and $a, b$ are relatively prime positive integers, calculate $(a + b,a^n + b^n)$ .",
"role": "user"
}
] | math | {
"ground_truth": "(a + b, a^n + b^n) = \\begin{cases} \na + b & \\text{if } n \\text{ is odd} \\\\\n(2, a + b) & \\text{if } n \\text{ is even}\n\\end{cases}",
"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 Daphne's four friends visit her every 4, 6, 8, and 10 days respectively, all four friends visited her yesterday, calculate the number of days in the next 365-day period whe... | math | {
"ground_truth": "129",
"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 iterative process is used to find an average of the numbers -1, 0, 5, 10, and 15. Arrange the five numbers in a certain sequence. Find the average of the first two numbers, th... | math | {
"ground_truth": "8.875",
"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": "Draw five lines \\( l_1, l_2, \\cdots, l_5 \\) on a plane such that no two lines are parallel and no three lines pass through the same point.\n(1) How many intersection points ar... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "You have $8$ friends, each of whom lives at a different vertex of a cube. You want to chart a path along the cube’s edges that will visit each of your friends exactly once. You... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the product $\\dfrac{3}{2}\\cdot \\dfrac{4}{3}\\cdot \\dfrac{5}{4}\\cdot \\dfrac{6}{5}\\cdot \\ldots\\cdot \\dfrac{a}{b} = 9$, determine the sum of $a$ and $b$.",
"role... | math | {
"ground_truth": "35",
"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": "Schoolchildren Chukov and Gekov are skating at constant speeds around a closed loop ice rink. If Chukov skates clockwise and Gekov skates counterclockwise, their meetings occur f... | math | {
"ground_truth": "10 \\ \\text{m/s} \\ \\text{or} \\ 3.6 \\ \\text{m/s}",
"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": "For some positive integer $m$, the number $120m^3$ has $120$ positive integer divisors, including $1$ and the number $120m^3$. How many positive integer divisors does the number ... | math | {
"ground_truth": "75",
"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 a \"clearance game,\" the rules stipulate that in round \\( n \\), a dice is to be rolled \\( n \\) times. If the sum of the points of these \\( n \\) rolls is greater than \\... | math | {
"ground_truth": "\\frac{100}{243}",
"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 $a$ and $b$ are both positive real numbers, and $a\\cdot b=3$, then the minimum value of $\\frac{{a}^{2}+{b}^{2}+22}{a+b}$ is ______.",
"role": "user"
}
] | 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": "Find the coefficient of $x$ in the expansion of $x\\left( \\sqrt{x} - \\frac{1}{x}\\right)^9$.",
"role": "user"
}
] | math | {
"ground_truth": "-84",
"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 value of the fraction $\\dfrac{x^{2}-4}{x^{2}-4x+4}$ is $0$, calculate the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{C: } \\pm 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": "Let $\\alpha,\\beta$ be the distinct positive roots of the equation of $2x=\\tan x$ .\r\nEvaluate\r\n\r\n\\[\\int_0^1 \\sin \\alpha x\\sin \\beta x\\ dx\\]",
"role": "user... | math | {
"ground_truth": "0",
"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": "(Optional 4-5: Inequality Lecture) Given the function $f(x)=|x+3|+|x-a| (a > 0)$.\n(I) When $a=4$, it is known that $f(x)=7$, find the range of $x$;\n(II) If the solution set of ... | math | {
"ground_truth": "a=1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagonals of a rhombus are $12$ inches and $30$ inches. What is the perimeter of the rhombus, in inches?",
"role": "user"
}
] | math | {
"ground_truth": "4\\sqrt{261}",
"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 ordered pair \\((x, y)\\) if:\n\\[\nx + 2y = (7 - x) + (7 - 2y)\n\\]\n\\[\nx - y = 2(x - 2) - (y - 3)\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "(1, 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": "Let $S_1, S_2, \\dots, S_{2^n - 1}$ be the nonempty subsets of $\\{1, 2, \\dots, n\\}$ in some order, and let $M$ be the $(2^n - 1) \\times (2^n - 1)$ matrix whose $(i, ... | math | {
"ground_truth": "(-1)^{[n \\neq 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 values of the polynomial $P(x) = 2x^3-30x^2+cx$ for any three consecutive integers are also three consecutive integers. Find these values.",
"role": "user"
}
] | math | {
"ground_truth": "c = 149",
"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": "Three circles $C_i$ are given in the plane: $C_1$ has diameter $AB$ of length $1$ ; $C_2$ is concentric and has diameter $k$ ( $1 < k < 3$ ); $C_3$ has center $A$ ... | math | {
"ground_truth": "\\frac{XB}{BY} = 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": "An equilateral triangle is constructed externally on the side \\(AB\\) of triangle \\(ABC\\). Find the distance between its center and vertex \\(C\\), given \\(AB=c\\) and \\(\\a... | math | {
"ground_truth": "\\frac{c \\sqrt{3}}{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": "Is there a 6-digit number that becomes 6 times larger when its last three digits are moved to the beginning of the number, keeping the order of the digits?",
"role": "user"
... | math | {
"ground_truth": "142857",
"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": "$A$ and $B$ are two opposite vertices of an $n \\times n$ board. Within each small square of the board, the diagonal parallel to $AB$ is drawn, so that the board is divide... | math | {
"ground_truth": "n = 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 product of three consecutive page numbers in a book is 136,080. What is the sum of these three page numbers?",
"role": "user"
}
] | math | {
"ground_truth": "144",
"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": "David notices that his kitchen clock, which runs fast, and his cellphone (which is accurate) both indicate 8:00 AM when he starts his morning routine. After he finishes breakfast... | math | {
"ground_truth": "B) 12:40 PM",
"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 $S_n$ be the sum of the first $n$ terms of the sequence $\\{a_n\\}$. Given that $a_n > 0$ and $4S_n = (a_n + 3)(a_n - 1)$ for $n \\in \\mathbb{N}^*$. Find the general formula... | math | {
"ground_truth": "2n + 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "ABC is a triangle with side lengths |BC| = a, |CA| = b, |AB| = c, circumradius R, and inradius r. Given that a ≤ b ≤ c, determine the values of angle C for which a + b - 2(r + R)... | math | {
"ground_truth": "\\text{Positive for } C < 90^\\circ \\text{, zero for } C = 90^\\circ \\text{, and negative for } C > 90^\\circ \\text{.}",
"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": "Express 12.06 million in scientific notation.",
"role": "user"
}
] | math | {
"ground_truth": "1.206 \\times 10^{7}",
"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": "Solve the equation \\(\\sqrt{2 + \\cos 2x - \\sqrt{3} \\tan x} = \\sin x - \\sqrt{3} \\cos x\\). Find all its roots that satisfy the condition \\(|x-3|<1\\).",
"role": "user"... | math | {
"ground_truth": "\\frac{3\\pi}{4}, \\pi, \\frac{5\\pi}{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": "Calculate the value of the expression $5^5+5^5+5^5+5^5+5^5 = ?$\nA) $5^5$ \nB) $5^{10}$ \nC) $5^6$ \nD) $25^5$ \nE) $5^{25}$",
"role": "user"
}
] | math | {
"ground_truth": "C) 5^6",
"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": "There are $n$ seats in a bus, and all tickets have been sold to $n$ passengers. The Absent-Minded Scientist enters first and sits in a randomly chosen seat without looking at the... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two variables \\( x \\) and \\( y \\) are inversely proportional; what can be said about their reciprocals?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{x} \\text{ is inversely proportional to } \\frac{1}{y}.",
"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": "Max bought a new skateboard and paid $20\\%$ of the cost upfront, which was $\\$60$. What was the price of the skateboard?",
"role": "user"
}
] | math | {
"ground_truth": "\\$300",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
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