data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( P(x) \\) be an \\( n \\)-th degree polynomial such that \\( P(k) = \\frac{1}{C_{n}^{k}} \\), where \\( k=0,1,2, \\cdots, n \\). Determine \\( P(n+1) \\).",
"role": "u... | math | {
"ground_truth": "P(n+1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Express the following sum as a simple fraction in lowest terms.\n\n$$\\frac{1}{3\\times4} + \\frac{1}{4\\times5} + \\frac{1}{5\\times6} + \\frac{1}{6\\times7} + \\frac{1}{7\\time... | math | {
"ground_truth": "\\frac{2}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the line defined by the parametric equations $\\begin{cases} x=2-t\\sin 30^{\\circ} \\\\ y=-1+t\\sin 30^{\\circ} \\end{cases}$ and the circle ${x}^{2}+{y}^{2}=8$, the line ... | math | {
"ground_truth": "\\frac{\\sqrt{15}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many polynomials of the form $x^5 + ax^4 + bx^3 + cx^2 + dx + 2019$ have the property that whenever $r$ is a root, so is $i \\cdot r$, where $i=\\sqrt{-1}$?",
"role": "us... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,$ $b,$ and $c$ be the roots of the equation $x^3 - 24x^2 + 50x - 14 = 0.$ Find the value of $\\frac{a}{\\frac{1}{a}+bc} + \\frac{b}{\\frac{1}{b}+ca} + \\frac{c}{\\frac{1}{... | math | {
"ground_truth": "\\frac{476}{15}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In eight years Henry will be three times the age that Sally was last year. Twenty five years ago their ages added to $83$ . How old is Henry now?",
"role": "user"
}
] | math | {
"ground_truth": "97",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the following three equations: $x^{2}+4ax-4a+3=0$, $x^{2}+(a-1)x+a^{2}=0$, and $x^{2}+2ax-2a=0$, at least one of the equations has real roots. Determine the range of the re... | math | {
"ground_truth": "a \\leqslant - \\frac {3}{2} \\ \\text{or} \\ a \\geqslant -1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the remainder when the sum \\[82 + 83 + 84 + 85 + 86 + 87 + 88 + 89\\] is divided by 17.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\mathbf{u}$, $\\mathbf{v}$, and $\\mathbf{w}$ such that $\\|\\mathbf{u}\\| = 4,$ $\\|\\mathbf{v}\\| = 5,$ $\\|\\mathbf{w}\\| = 6,$ $\\mathbf{u} \\cdot \\mathbf{v}... | math | {
"ground_truth": "\\|\\operatorname{proj}_{\\mathbf{v}} \\mathbf{u}\\| = \\frac{12}{5}, \\|\\operatorname{proj}_{\\mathbf{w}} \\mathbf{v}\\| = \\frac{5}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of function $y=g(x)$ is known to satisfy $g(x) > 0.3$ for all $x > 2$. The function $g(x)$ has the form $\\frac{x^2}{Ax^2 + Bx + C}$, where $A, B, C$ are integers. Find... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The fifth, sixth, and seventh terms of an arithmetic sequence are 7, 12, and 17, respectively. What is the sum of the first three terms of the sequence?",
"role": "user"
}
... | math | {
"ground_truth": "-24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(a < b < c < d\\) and \\((x, y, z, t)\\) be any permutation of \\((a, b, c, d)\\). How many different values can the expression\n$$\nn = (x - y)^2 + (y - z)^2 + (z - t)^2 +... | math | {
"ground_truth": "n \\text{ can take 3 different values.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two friends collected 300 stamps. One collected 5 stamps per week, the other collected 3 stamps per week. The second boy collected for 20 weeks longer than the first. How many da... | math | {
"ground_truth": "50 \\text{ weeks}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a baby is born every 6 hours and a death occurs every 2 days in the nation of North Southland, calculate the average annual increase in population to the nearest fifty... | math | {
"ground_truth": "1300",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**i.)** Consider a circle $K$ with diameter $AB;$ with circle $L$ tangent to $AB$ and to $K$ and with a circle $M$ tangent to circle $K,$ circle $L$ and $AB.$ C... | math | {
"ground_truth": "80^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, $E$ and $F$ are the midpoints of $\\overline{AB}$ and $\\overline{AC}$ respectively in triangle $ABC$ where $A(0,4), B(6,0),$ and $C(0,-2)$. Find the sum of the s... | math | {
"ground_truth": "\\frac{5}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a classroom, there are 20 female students and 18 male students. Each student is paired with another student of the opposite gender for a project. If the pairings are done rand... | math | {
"ground_truth": "\\frac{1}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four spheres each of radius 2 are arranged such that each sphere is tangent to the other three spheres. These spheres are symmetrically placed around the origin. Find the radius ... | math | {
"ground_truth": "2 + \\sqrt{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assume that the number of offspring for every man can be $0,1,\\ldots, n$ with with probabilities $p_0,p_1,\\ldots,p_n$ independently from each other, where $p_0+p_1+\\cdots... | math | {
"ground_truth": "p_0 = 1 - p_1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of \\( n \\) if \\( 15 \\) quarters and \\( 18 \\) nickels equal the value of \\( 7 \\) quarters and \\( n \\) nickels.",
"role": "user"
}
] | math | {
"ground_truth": "58",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $2268$ needs to be written as a product of two positive integers whose difference is as small as possible, what is that difference?\nA) 10 \nB) 12 \nC) 14 \nD) 16 \nE) 18"... | math | {
"ground_truth": "B) 12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For every positive integer $n$ , determine the greatest possible value of the quotient $$ \\frac{1-x^{n}-(1-x)^{n}}{x(1-x)^n+(1-x)x^n} $$ where $0 < x < 1$ .",
"role": "u... | math | {
"ground_truth": "2^n - 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integer $n$ cannot be divided by $2$ and $3$ , there are no nonnegative integers $a$ and $b$ such that $|2^a-3^b|=n$ . Find the minimum value of $n$ .",
"... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of the tangent line to the function f(x) = x cos x at the point (0, f(0)), find its equation.",
"role": "user"
}
] | math | {
"ground_truth": "x - y = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function \\( f(x) \\) satisfies\n\\[ f(x + f(x)) = 4f(x) \\] for all \\( x, \\) and \\( f(1) = 3. \\) Find \\( f(21). \\)",
"role": "user"
}
] | math | {
"ground_truth": "192",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the indefinite integral:\n\n$$\n\\int \\frac{3 x^{5}-12 x^{3}-7}{x^{2}+2 x} d x\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3x^4}{4} - 2x^3 - \\frac{7}{2} \\ln|x| + \\frac{7}{2} \\ln|x + 2| + C",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A robot vacuum cleaner \"Orthogonal\" decides to clean the coordinate plane. It starts from point $O$ located at the origin and travels a straight distance $X_{1}$. At the point ... | math | {
"ground_truth": "\\pi n (d + a^2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that N is a two-digit positive integer such that the sum of N and the number obtained by reversing the digits of N is a palindrome, and that N and its reversed number are b... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Anna and Bob, with Anna starting first, alternately color the integers of the set $S = \\{1, 2, ..., 2022 \\}$ red or blue. At their turn each one can color any uncolored numbe... | math | {
"ground_truth": "3m - 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation \\(a^{\\log_{\\sqrt{b}}{x}} - 5a^{\\log_b{\\alpha}} + 6 = 0\\).",
"role": "user"
}
] | math | {
"ground_truth": "x = b^{\\log_{a} 3} \\quad \\text{or} \\quad x = b^{\\log_{a} 2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the least number of colors needed to shade the tessellation shown, such that no two tiles sharing a side are the same color, if the tessellation consists of hexagons (sim... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that in $\\triangle{ABC}$, $AX=XY=YB=BC$, and $m\\angle{ABC}=120^{\\circ}$, calculate the measure of $\\angle{BAC}$.",
"role": "user"
}
] | math | {
"ground_truth": "15^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the center of gravity of the arc \\(AB\\):\n\na) \\(AB: x^{2/3} + y^{2/3} = a^{2/3}\\) (astroid), \\(A(0, a)\\), \\(B(a, 0)\\), with linear density at each point of the arc ... | math | {
"ground_truth": "\\left( 0, 0, H \\sqrt{1 + \\frac{H^2}{4\\pi^2}} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio of $3:2:1$, respectively, determine the fract... | math | {
"ground_truth": "\\frac{5}{18}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If a quadrilateral \\(ABCD\\) has each side length being a positive integer, the perimeter \\(p\\), \\(\\angle B\\) and \\(\\angle C\\) are right angles, \\(AB = 2\\), and \\(CD ... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a line $l$: $y=k(x-2)$ where $k > 0$, which intersects with a parabola $C$: $y^{2}=8x$ at points $A$ and $B$, with $F$ being the focus of parabola $C$. If $|AF|=2|BF|$, det... | math | {
"ground_truth": "2 \\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 47 students in a class, with the classroom arranged in 6 rows and 8 columns. Each seat can be denoted as \\((i, j)\\) where \\(i\\) is the row number and \\(j\\) is the... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sample data of the weight (unit: $g)$ of a certain brand of milk is as follows: $110.2$, $109.7$, $110.8$, $109.1$, $108.9$, $108.6$, $109.8$, $109.6$, $109.9$, $111.2$, $110... | math | {
"ground_truth": "110.8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( \\log_8 (x-3) = \\frac{1}{3} \\), find \\( \\log_{64} x \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\log_{64} 5 = \\frac{\\log_10 5}{6 \\cdot \\log_10 2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square of side length $2$ and a circle of radius $\\frac{1}{2}$ share the same center. Within this configuration, an inner square also shares the center, its side length being ... | math | {
"ground_truth": "0.76",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all pairs $(p, q)$ of prime numbers such that $p^p + q^q + 1$ is divisible by $pq.$",
"role": "user"
}
] | math | {
"ground_truth": "(2, 5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the recurrence relation \\( x_{k+1} = x_k + \\frac{1}{3} \\) for \\( k = 1, 2, \\dots, n-1 \\) and \\( x_1 = 2 \\), find the sum \\( x_1 + x_2 + \\dots + x_n \\).\n**A)** \... | math | {
"ground_truth": "**B)** \\( \\frac{n(n+11)}{6} \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the expression $\\frac {x^2-1}{x-1}$, find the limit as $x$ approaches $1$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "<u>Round 9</u>**p25.** Let $S$ be the set of the first $2017$ positive integers. Find the number of elements $n \\in S$ such that $\\sum^n_{i=1} \\left\\lfloor \\frac{n}{i... | math | {
"ground_truth": "163^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given triangle $PQR$, we have $PQ = 30$, $QR = 50$, and $PR = 54$. Points $S$ and $T$ are on $PQ$ and $PR$ respectively, with $PS = 18$ and $PT = 24$. Calculate the ratio of the ... | math | {
"ground_truth": "\\frac{6}{19}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the probability \\( p \\) of an event occurring in each of 49 independent trials if the most likely number of occurrences of the event in these trials is 30?",
"role"... | math | {
"ground_truth": "0.6 < p \\leq 0.62",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers $1,2,...,100$ are written in a board. We are allowed to choose any two numbers from the board $a,b$ to delete them and replace on the board the number $a+b-1$ . ... | math | {
"ground_truth": "4951",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that one must cover a $k\\times k$ square with $T$ tetrominos, find the sum of all $k\\leq25$ such that $k^{2}=T$.",
"role": "user"
}
] | math | {
"ground_truth": "84",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A club has 18 members divided into three departments: 6 in Department A, 7 in Department B, and 5 in Department C. The club needs to choose 3 members to form a new committee, ens... | math | {
"ground_truth": "210",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The tangent line to the graph of the function $y = x^2$ ($x > 0$) at the point $(a_k, a_k^2)$ intersects the x-axis at the point with the x-coordinate $a_{k+1}$, where $k \\in \\... | math | {
"ground_truth": "133",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the integer, the cube of which, when 135,002 is added to it, results in the cube of a slightly larger integer?",
"role": "user"
}
] | math | {
"ground_truth": "149 \\text{ and } -151",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer divisor of $10!$ is chosen at random. What is the probability that the divisor chosen is a perfect square?\nA) $\\frac{1}{5}$\nB) $\\frac{1}{6}$\nC) $\\frac{1}... | math | {
"ground_truth": "\\textbf{(D) } \\frac{1}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle XYZ, the measure of angle $Z$ is three times the measure of angle $Y$. If the measure of angle $Y$ is $30^\\circ$, find the measure of angle $X$.",
"role": "user"... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider $15!$ (15 factorial). A positive integer divisor of $15!$ that is also divisible by 13 is chosen at random. What is the probability that this divisor is a perfect square... | math | {
"ground_truth": "D) 22",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the coefficient of $x^2$ when $3x^3 - 4x^2 - 9x + 2$ is multiplied by $2x^2 - 8x + 3$ and the like terms are combined?",
"role": "user"
}
] | math | {
"ground_truth": "68",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a machine that when a positive integer $N$ is entered, the machine's processing rule is:\n\n- If $N$ is odd, output $4N + 2$.\n- If $N$ is even, output $N / 2$.\n\nUsing... | math | {
"ground_truth": "640",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of circle $\\omega$ where points $P=(7,15)$ and $Q=(11,9)$ lie on $\\omega$. Suppose that the tangent lines to $\\omega$ at $P$ and $Q$ intersect at a point on the ... | math | {
"ground_truth": "\\textbf{(A)} 709\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $XYZ$, $XY = 10$. The length of median $XM$ is 6. Let $R$ be the largest possible value of $XZ^2 + YZ^2$, and let $r$ be the smallest possible value. Find $R - r$.",
... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The set $\\{[x]+[2x]+[3x] \\mid x \\in \\mathbf{R}\\} \\bigcap \\{1, 2, \\cdots, 100\\}$ contains how many elements, where $[x]$ represents the greatest integer less than or equa... | math | {
"ground_truth": "67",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A number $p$ is $perfect$ if the sum of its divisors, except $p$ is $p$ . Let $f$ be a function such that:\r\n\r $f(n)=0$ , if n is perfect\r $f(n)=0$ , if the last digi... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be an isosceles right-angled triangle. Point $D$ is chosen on the prolongation of the hypothenuse $AB$ beyond point $A$ so that $AB = 2AD$ . Points $M$ and ... | math | {
"ground_truth": "45^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a > 1, b > 1$, and $\\lg (a+b) = \\lg a + \\lg b$, calculate the value of $\\lg (a-1) + \\lg (b-1)$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $m$ and $n$ two given integers. Ana thinks of a pair of real numbers $x$ , $y$ and then she tells Beto the values of $x^m+y^m$ and $x^n+y^n$ , in this order. Beto's... | math | {
"ground_truth": "(m, n) = (2k+1, 2t(2k+1))",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "[IMO 2007 HKTST 1](http://www.mathlinks.ro/Forum/viewtopic.php?t=107262)\r\nProblem 1\r\n\r\nLet $p,q,r$ and $s$ be real numbers such that $p^{2}+q^{2}+r^{2}-s^{2}+4=0$ . Fi... | math | {
"ground_truth": "-2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An insect lives on the surface of a regular cube with edges of length 1. It wishes to travel from one vertex to the center of a face that does not share that vertex. What is the ... | math | {
"ground_truth": "1 + \\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "After Natasha eats half of the peaches in the jar, the level of the compote decreases by one third. By what fraction (of the resulting level) will the compote level decrease if h... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a set of consecutive positive integers beginning with $1$, and the average of the remaining numbers is $35\\frac{7}{17}$ after one number is erased, determine the number th... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let points \\( P \\) and \\( Q \\) be on the graphs of the functions \\( y = 2^{x} \\) and \\( y = \\log_{2} x \\) respectively. Find the minimum value of \\( |PQ| \\).",
"ro... | math | {
"ground_truth": "\\frac{1 + \\ln (\\ln 2)}{\\ln 2} \\sqrt{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that each interior angle of a polygon $P$ is $9$ times the corresponding exterior angle, find the total sum of the interior angles $S$ of the polygon, and determine whether... | math | {
"ground_truth": "S=3240^\\circ \\text{ and } P \\text{ may or may not be regular}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\left\\{a_{n}\\right\\}$, the odd-numbered terms form an arithmetic sequence with a common difference $d_{1}$, and the even-numbered terms form an arithmetic... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = (x^2 - 1)(x^2 + ax + b)$, its graph is symmetric about the line $x = 3$. Determine the range of the function $f(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "[-36, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many multiples of 12 are there between 10 and 250?",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A tank when four-fifths full weighs $p$ kilograms, and when two-thirds full it weighs $q$ kilograms. Determine the total weight when the tank is completely full. The combined wei... | math | {
"ground_truth": "\\frac{5}{2}p + \\frac{3}{2}q",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Noah is preparing orange juice for a family gathering using his special recipe. The recipe calls for three times as much water as sugar, and the sugar should be three times the a... | math | {
"ground_truth": "C) 36",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "One angle of a parallelogram is 135 degrees, and two consecutive sides have lengths of 10 inches and 17 inches. What is the area of the parallelogram? Express your answer in simp... | math | {
"ground_truth": "85\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an equilateral $\\triangle ABC$ with side length $2$ and point $D$ on ray $\\overrightarrow{BC}$ such that $CD = 4$, find $\\tfrac{AE}{AF}$, where $E$ and $F$ lie on $\\ove... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The lines $x = \\frac{1}{3}y + c$ and $y = \\frac{1}{3}x + d$ intersect at the point $(3,3)$. What is $c + d$?\nA) 2\nB) 3\nC) 4\nD) 5\nE) 6",
"role": "user"
}
] | math | {
"ground_truth": "C) 4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)=cx(x-1)$ , where $c$ is a positive real number. We use $f^n(x)$ to denote the polynomial obtained by composing $f$ with itself $n$ times. For every positive ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number $K$ is divisible by 7 and its binary representation is given by:\n\n$$\nK = 10110101010101xyz110\n$$\n\nDetermine the digits $x$, $y$, and $z$.",
"role": "user"
... | math | {
"ground_truth": "0, 1, 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the maximum number of acute angles in a non-convex $n$-gon?",
"role": "user"
}
] | math | {
"ground_truth": "\\left\\lfloor \\frac{2n}{3} \\right\\rfloor + 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $F_1 = (0,2)$ and $F_2= (6,2).$ Then the set of points $P$ such that\n\\[PF_1 + PF_2 = 10\\] form an ellipse. The equation of this ellipse can be expressed as\n\\[\\frac{(x -... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest positive integer $n$ such that there exist $n$ distinct positive integers $x_{1}, x_{2}, \\cdots, x_{n}$ satisfying\n$$\nx_{1}^{2}+x_{2}^{2}+\\cdots+x_{n}^{2}=20... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**p1.** Sujay sees a shooting star go across the night sky, and took a picture of it. The shooting star consists of a star body, which is bounded by four quarter-circle arcs, and... | math | {
"ground_truth": "\\frac{4}{165}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence of digits\n\\[\n1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 \\dots\n\\]\nis obtained by writing the positive integers in order. If the $10^n$ ... | math | {
"ground_truth": "f(1987) = 1984",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A quantity of grey paint has a mass of 12 kg. The grey paint is a mixture of black paint and white paint, of which 80% by mass is white paint. More white paint is added until the... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are four rectangular containers labeled $A$, $B$, $C$, and $D$. The base areas of $A$ and $B$ are both $x^{2}$, with heights $x$ and $y$ respectively. The base areas of $C$... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rise of $600$ feet is required to get a railroad line over a mountain. The grade can be kept down by lengthening the track and curving it around the mountain peak. Determine th... | math | {
"ground_truth": "10000",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"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 how many distinguishable ways can $10$ distinct pool balls be formed into a pyramid ( $6$ on the bottom, $3$ in the middle, one on top), assuming that all rotations of th... | math | {
"ground_truth": "403200",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\bigtriangleup ABC$, D is a point on side $\\overline{AC}$ such that $\\frac{BD}{DC} = 2$ and $\\angle BCD$ measures $60^\\circ$. What is the degree measure of $\\angle ADB$... | math | {
"ground_truth": "The final answer is **(C) 120°**.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse $\\frac {x^{2}}{a^{2}} + \\frac {y^{2}}{b^{2}} = 1$ ($a > b > 0$) and a line $l: y = -\\frac { \\sqrt {3}}{3}x + b$ intersect at two distinct points P and Q. The... | math | {
"ground_truth": "-\\frac {7}{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many squares would be in the 100th diagram of a sequence where the first four diagrams contain 1, 7, 19, and 37 squares respectively.",
"role": "user"
}
] | math | {
"ground_truth": "30301",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many different orders can the characters $P \\ U \\ M \\ \\alpha \\ C$ be arranged such that the $M$ is to the left of the $\\alpha$ and the $\\alpha$ is to the... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are $8$ different products, among which $3$ are defective, they are tested one by one until all defective products are found.\n$(1)$ If the first defective produ... | math | {
"ground_truth": "936",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the product $\\left(1 - \\frac{1}{3}\\right)\\left(1 - \\frac{1}{4}\\right)\\cdots\\left(1 - \\frac{1}{12}\\right)$.\nA) $\\frac{1}{6}$ \nB) $\\frac{1}{5}$ \nC) $\\fr... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$5^m = 5 \\cdot 25^5 \\cdot 125^3$. Find the value of $m$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\bigtriangleup ABC$ is isosceles with $AB=BC=30$ and $AC=50$, calculate the area of $\\bigtriangleup ABC$.",
"role": "user"
}
] | math | {
"ground_truth": "414.67",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Charlie and Dana each have a sheet of paper. Charlie's sheet measures 7 inches by 9 inches, and Dana's sheet measures 5 inches by 10 inches. Charlie forms a cylinder by taping th... | math | {
"ground_truth": "867.25",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the numbers $1, 2, \\dots, 16$ are randomly placed into the $16$ squares of a $4 \\times 4$ grid, find the probability that the sum of the numbers in each row and each colu... | math | {
"ground_truth": "\\frac{1}{3584}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the letters in the word BANANA, find the number of distinguishable rearrangements in which all the vowels are at the end and in alphabetical order.",
"role": "user"
}... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We created a rectangular thread grid consisting of squares. The number of knots along the two sides of the rectangle is $k$ and $n$, respectively. We tied a bead to each knot. Fo... | math | {
"ground_truth": "n \\cdot k \\text{ must be even, and both } n \\text{ and } k \\geq 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
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