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": "If each term of a sequence, after the first term, is inversely proportional to the term preceding it, and the constant of proportionality is consistent throughout, how would the ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A 4x4x4 cube is made of $64$ normal dice, where opposites sum to $7$. Calculate the smallest possible sum of all the values visible on the $6$ faces of the giant cube.",
"rol... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The angles \\( A O B, B O C \\), and \\( C O D \\) are equal to each other, and the angle \\( A O D \\) is three times smaller than each of them. All rays \\( \\mathrm{OA}, \\mat... | math | {
"ground_truth": "36^\\circ, 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": "Solve the following system of equations:\n(1) \\( \\frac{x}{y} + \\frac{y}{x} = 6.\\overline{538461} \\),\n(2) \\( \\frac{1}{x} + \\frac{1}{y} = 0.\\overline{769230} \\).\n\n(Con... | math | {
"ground_truth": "(x, y) = (13, 2) \\text{ or } (x, y) = (2, 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": "In the arithmetic sequence $\\{a_n\\}$, $a_1+a_2=1$, $a_3+a_4=9$, then $a_5+a_6=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the position of the center of gravity of a wire triangle (assuming the wire has a uniform diameter and is made of the same material).",
"role": "user"
}
] | math | {
"ground_truth": "\\vec{P} = \\frac{(b + c) \\vec{A} + (c + a) \\vec{B} + (a + b) \\vec{C}}{2(a + b + c)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The interior of a region is bounded by the graphs of $(x+ay)^3 = 8a^3$ and $(ax-y)^2 = 4a^2$, where $a$ is a positive real number. What is the area of this region in terms of $a$... | math | {
"ground_truth": "\\frac{8a}{a^2+1}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the table, there are $1024$ marbles and two students, $A$ and $B$ , alternatively take a positive number of marble(s). The student $A$ goes first, $B$ goes after that... | math | {
"ground_truth": "k = 4, 24, 40",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many distinct ways can six keys be arranged on a keychain, if I want my house key next to my car key, and my wallet key next to my office key? Two arrangements are not con... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangle with side lengths 9, 12, and 15, determine if this is a right triangle. If it is, calculate the radius R of the circle circumscribed around the triangle.",
"... | math | {
"ground_truth": "7.5",
"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": "Using two red, three blue, and four green small cubes, calculate the number of different towers that can be built using eight of these cubes.",
"role": "user"
}
] | math | {
"ground_truth": "1260",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let x be the smallest real number greater than 0 and less than 30 such that \\(\\cos(3x) = \\cos(2x^2 - x)\\), where the arguments are in degrees. Find x rounded to the nearest i... | 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": "Let $n$ be a positive integer. There are $2018n+1$ cities in the Kingdom of Sellke Arabia. King Mark wants to build two-way roads that connect certain pairs of cities such th... | math | {
"ground_truth": "2 \\mid 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": "The lines $l_1$ and $l_2$ are defined by the equations $x+y\\sqrt{1-\\cos\\theta}+b=0$ and $x\\sin\\theta+y\\sqrt{1+\\cos\\theta}-a=0$, where $\\theta$ is an angle in the third q... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "All of Alice's telephone numbers have the form $555-abc-de$, where $a$, $b$, $c$, $d$, and $e$ are distinct digits, in increasing order, with none being $0$ or $1$. Determine the... | math | {
"ground_truth": "320",
"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 hyperbola $\\frac {x^{2}}{a^{2}}- \\frac {y^{2}}{b^{2}}=1(a＞0, b＞0)$, its asymptotes both touch the circle $x^2+y^2-6x+5=0$. Find the equation of the hyperbola's asympt... | math | {
"ground_truth": "y=± \\frac {2 \\sqrt {5}}{5}x",
"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 triangle $XYZ$ has vertices at $X(0, 0)$, $Y(2, 2)$, and $Z(4, 0)$, calculate the area of triangle $XYZ$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $y$ if $y = \\left(\\frac{2023^2 - 2023}{2023}\\right)^2$?",
"role": "user"
}
] | math | {
"ground_truth": "4088484",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular prism has a sum of squares of its side lengths ($x^2 + y^2 + z^2$) equal to 50 and the sum of the products of its dimensions taken two at a time ($xy + yz + zx$) eq... | math | {
"ground_truth": "20\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that for any real numbers \\( x, y \\) and \\( z \\), \\(\\oplus\\) is an operation satisfying\n(i) \\( x \\oplus 0 = 1 \\), and\n(ii) \\( (x \\oplus y) \\oplus z = (z \\op... | math | {
"ground_truth": "2005",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute \\(\\operatorname{tg} x + \\operatorname{tg} y\\), given that\n(1) \\(\\sin 2x + \\sin 2y = a\\),\n(2) \\(\\cos 2x + \\cos 2y = b\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4a}{a^2 + b^2 + 2b}",
"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": "Player A and Player B play a guessing game. First, Player A thinks of a number, denoted as $a$, then Player B guesses the number Player A thought of, denoting their guess as $b$.... | math | {
"ground_truth": "\\frac{7}{25}",
"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 ninth grade class at Parkview High School has 120 students. Each student takes either a science class, a history class, or both. There are 85 ninth graders taking a science c... | math | {
"ground_truth": "C) 55",
"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 sample mean and sample variance using the product method for the given sample distribution with a size of \\(n = 100\\):\n\n| \\( x_{i} \\) | 2 | 3 | 7 | 9 | 11 | 12.5 |... | math | {
"ground_truth": "\\bar{y}_B = 15.86,\\quad D_{B}^{\\prime} = 42.14",
"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 regular dodecagon \\( P_1, P_2, \\ldots, P_{12} \\) is inscribed in a unit circle with center \\( O \\). Let \\( X \\) be the intersection of \\( P_1 P_5 \\) and \\( OP_2 \\), ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the $1234$th digit to the right of the decimal point in $x = .123456789101112...498499500$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Al is diagnosed with algebritis and has been prescribed to take one green pill and one pink pill each day for 18 days. Each green pill costs $2 more than each pink pill, and the ... | math | {
"ground_truth": "21.5",
"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": "Carlos took $60\\%$ of a whole pie and Maria took one quarter of the remainder. What portion of the whole pie was left?",
"role": "user"
}
] | math | {
"ground_truth": "30\\%",
"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 $C$ be a right circular cylinder with height $4$ and radius $2$, along with its interior. For a real $r \\geq 0$, let $T(r)$ denote the set of points in 3-dimensional space t... | math | {
"ground_truth": "\\frac{9}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find two positive integers $a$ and $b$ , when their sum and their least common multiple is given. Find the numbers when the sum is $3972$ and the least common multiple is $... | math | {
"ground_truth": "(1964, 2008)",
"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 company has 1000 employees, among which: senior managers account for 5%, middle managers account for 15%, and general staff account for 80%. In order to understand a certain si... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular pentagon, let \\( M \\) be an arbitrary point inside it (or on its boundary). Number the distances from point \\( M \\) to the sides of the pentagon (or their ext... | math | {
"ground_truth": "r_3 - \\text{maximal at vertices, minimal at midpoints of sides}",
"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": "Rotate the ellipse \\( b^{2} x^{2} + a^{2} y^{2} = a^{2} b^{2} \\) around its minor axis. In the resulting ellipsoid, inscribe the largest volume right circular cylinder. (The cy... | math | {
"ground_truth": "S_h : S_e = \\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": "The sum of the base-$10$ logarithms of the divisors of $10^n$ is $792$. What is $n$?",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x)$ is differentiable at $x_0$, find the limit of the difference quotient $\\lim\\_{\\Delta x \\to 0} \\frac{f(x_0 - \\Delta x) - f(x_0)}{\\Delta x}$."... | math | {
"ground_truth": "-f'(x\\_0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with center $C$ is tangent to the positive $x$-axis and $y$-axis and externally tangent to a circle centered at $(5,0)$ with a radius of $2$. What is the sum of all poss... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a certain scenic area in Xi'an, the ticket price is $50$ yuan per person. To attract tourists, a special rule is set: on non-holidays, tickets are sold at a 40% discount; on h... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a regular hexagon with side length 2 units is on a plane and squares of side length 2 units are constructed outside the hexagon and on new sides of the squares, find t... | math | {
"ground_truth": "42\\sqrt{3} - 72",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a fixed point $A(1,0)$, point $B$ moves on the line $x-y=0$. When the length of segment $AB$ is the shortest, the coordinates of point $B$ are \\_\\_\\_\\_.",
"role": "... | math | {
"ground_truth": "\\left( \\dfrac{1}{2}, \\dfrac{1}{2}\\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": "A triangle has sides of lengths 7 and 9 units. The length of the third side is $y$ units, where $y$ is an integer. What is the largest possible perimeter of the triangle?",
"... | math | {
"ground_truth": "31 \\text{ units}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the set of solutions for $x$ in the inequality $\\dfrac{x+1}{x+2}>\\dfrac{3x+4}{2x+9}$ when $x\\neq 2$ , $x\\neq -\\dfrac{9}{2}$ .",
"role": "user"
}
] | math | {
"ground_truth": "x \\in (-\\frac{9}{2}, -2) \\cup \\left(\\frac{1-\\sqrt{5}}{2}, \\frac{1+\\sqrt{5}}{2}\\right)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x)$ is an odd function defined on $\\mathbb{R}$, and when $x > 0$, $f(x)=x^{2}-ax+a$, where $a \\in \\mathbb{R}$. \n$(1) f(-1)=$ _______ ; \n$(2)$ If... | math | {
"ground_truth": "(-\\infty,0] \\cup [4,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f(x) = 2\\sqrt{3}\\sin{x}\\cos{x} + 2\\cos^2{x} - 1$ is translated $\\phi (\\phi > 0)$ units to the right, resulting in a graph that is symmetric about the y-axis. ... | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define the function \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) by\n\\[ \nf(x)=\\left\\{\\begin{array}{ll}\n\\frac{1}{x^{2}+\\sqrt{x^{4}+2 x}} & \\text{ if } x \\notin (-\\sq... | math | {
"ground_truth": "932",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 30 people standing in a row, each of them is either a knight who always tells the truth or a liar who always lies. They are numbered from left to right. Each person wit... | math | {
"ground_truth": "28",
"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 \\( O \\) and \\( A \\) be two points in the plane with \\( OA = 30 \\), and let \\( \\Gamma \\) be a circle with center \\( O \\) and radius \\( r \\). Suppose that there ex... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$\\frac{2+4+6+8}{1+3+5+7} - \\frac{1+3+5+7}{2+4+6+8}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2+4+6+8}{1+3+5+7} - \\frac{1+3+5+7}{2+4+6+8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the complex number $z=(3-2i)(1+i)$, calculate the imaginary part of $z$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two circles have radius $2$ and $3$ , and the distance between their centers is $10$ . Let $E$ be the intersection of their two common external tangents, and $I$ be the i... | math | {
"ground_truth": "24",
"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 $f(x)=\\frac{a^3}{2}x^2-alnx$ where $a\\neq0$. \n$(1)$ If $a=1$, find the extreme value of $f(x)$. \n$(2)$ Discuss the monotonicity of the function $f(x)$.",... | math | {
"ground_truth": "\\text{decreasing on } (0,\\frac{1}{a}) \\text{ and increasing on } (\\frac{1}{a},+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a $ 4\\times 4$ squares table. How many ways that we can fill the table with $ \\{0,1\\}$ such that two neighbor squares (have one common side) have product which is eq... | math | {
"ground_truth": "511",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the units digit of the number \\( 2015^{2} + 2015^{0} + 2015^{1} + 2015^{5} \\)?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine $x$ for the pair $(49, 8, x)$, if $x$ is defined by the relation $\\sqrt{49} + \\sqrt[3]{8} = x$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangle $ABCD$ has dimensions $3 \\times 2$, where $AB = 3$ and $AD = 2$. Point $E$ is the midpoint of $\\overline{AB}$, and point $F$ is the midpoint of $\\overline{CD}$. Li... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ordered pairs of integers $(a,b)$ satisfy all of the following inequalities? \n\n\\begin{eqnarray*} a^2 + b^2 &<& 16 a^2 + b^2 &<& 8a a^2 + b^2 &<& 8b \\end{eqnarray... | 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": "Two of the altitudes of an acute triangle divide the sides into segments of lengths $7, 4, 3$ and $y$ units, as shown. What is the value of $y$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{12}{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 the sum of two numbers is 15 and their product is 56, calculate the sum of their reciprocals.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{15}{56}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an integer coefficient polynomial\n$$\nf(x)=x^{5}+a_{1} x^{4}+a_{2} x^{3}+a_{3} x^{2}+a_{4} x+a_{5}\n$$\n\nIf $f(\\sqrt{3}+\\sqrt{2})=0$ and $f(1)+f(3)=0$, then $f(-1)=$ $\... | math | {
"ground_truth": "24",
"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 two employees, A and B, living 5000m away from their company, and that A leaves at 7:00 AM while B leaves at 7:10 AM, with B's cycling speed being 1.5 times ... | math | {
"ground_truth": "\\frac{5000}{x} - \\frac{5000}{1.5x} = 10",
"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 number of proper subsets of the set $\\left\\{x \\left\\lvert\\,-1 \\leqslant \\log _{\\frac{1}{x}} 10<-\\frac{1}{2}\\right., x \\in N\\right\\}$ is ___",
"role": "user"
... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a geometric sequence {a<sub>n</sub>} where all terms are positive, vectors $$\\overrightarrow {a}=(a_{4},a_{3})$$ and $$\\overrightarrow {b}=(a_{7},a_{8})$$ are known, and ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We have two regular pyramids with $2n$ sides $(n \\geq 2)$ (base: regular polygon, sides: equal). Their congruent bases are aligned to form a convex polyhedron with triangular fa... | math | {
"ground_truth": "2(n+1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a right triangle with $\\angle{ACB}=90^{\\circ}$ . $D$ is a point on $AB$ such that $CD\\perp AB$ . If the area of triangle $ABC$ is $84$ , what is the sm... | math | {
"ground_truth": "1008",
"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 $$ \\left(\\frac{1+1}{1^2+1}+\\frac{1}{4}\\right)\\left(\\frac{2+1}{2^2+1}+\\frac{1}{4}\\right)\\left(\\frac{3+1}{3^2+1}+\\frac{1}{4}\\right)\\cdots\\left(\\frac{202... | 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": "The excellent student Polycarp filled the cells of a table with digits so that the sum of the digits in any three adjacent cells was always 15. However, the failing student Kolka... | math | {
"ground_truth": "6,5,4,6,5,4,6,5,4,6,5,4,6,5,4",
"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": "Solve the quadratic equation $(x-h)^2 + 4h = 5 + x$ and find the sum of the squares of its roots. If the sum is equal to $20$, what is the absolute value of $h$?\n**A)** $\\frac{... | math | {
"ground_truth": "\\frac{\\sqrt{22}}{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": "Given a blue ball and a yellow ball are randomly and independently tossed into bins numbered with the positive integers, where the probability that each ball is tossed into bin $... | 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": "The graph of the function $f(x) = a^x - 3$ ($a > 0$ and $a \\neq 1$) must pass through a fixed point $P$. The coordinates of point $P$ are.",
"role": "user"
}
] | math | {
"ground_truth": "(0, -2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence $\\{a_n\\}$ where $$ a_n = \\begin{cases} 2^{n-1} & \\text{if } n \\text{ is an odd positive integer} \\\\ 2n-1 & \\text{if } n \\text{ is an even positive integ... | math | {
"ground_truth": "377",
"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 values of the parameter \\( a \\), for each of which there exists a number \\( b \\) such that the system\n\n$$\n\\left\\{\\begin{array}{l}\ny=x^{2}+a \\\\\nx^{2}+y^{2}+... | math | {
"ground_truth": "a \\leq \\sqrt{2} + \\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": "The ratio of $w$ to $x$ is $5:4$, the ratio of $y$ to $z$ is $4:3$, and the ratio of $z$ to $x$ is $1:8$. What is the ratio of $w$ to $y$?\nA) $12:1$\nB) $8:3$\nC) $15:2$\nD) $10... | math | {
"ground_truth": "15:2",
"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": "The integers \\(1, 2, 4, 5, 6, 9, 10, 11, 13\\) are to be placed in the circles and squares below with one number in each shape.\n\n![](https://cdn.mathpix.com/cropped/2024_04_20... | 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": "Quarter circles of radius 1' form a pattern as shown below. What is the area, in square feet, of the shaded region in a 3-foot length of this pattern? The quarter circles' flat s... | math | {
"ground_truth": "\\frac{3}{4}\\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": "If $m=\\int_{0}^{\\frac{\\pi }{2}}{\\sqrt{2}\\sin \\left( x+\\dfrac{\\pi }{4} \\right)dx}$, then the coefficient of the $x$ term in the expansion of the binomial $\\left( \\sqrt{... | math | {
"ground_truth": "60",
"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": "Each edge length of a rectangular solid is a different prime number. If one dimension is 3 units, another is 5 units, and the third is 17 units, determine the total surface area ... | math | {
"ground_truth": "302",
"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 smallest solution of the equation $x^4 - 64x^2 + 576 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "-2\\sqrt{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": "A triangle is partitioned into two smaller triangles and a quadrilateral by drawing two lines from one vertex to the midpoints of the two opponent sides. The areas of the triangl... | math | {
"ground_truth": "\\textbf{B) }8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S_1$ and $S_2$ be two spheres with distinct radii that touch externally. The spheres lie inside a cone $C$ , and each sphere touches the cone in a full circle. Inside t... | math | {
"ground_truth": "n = 7, 8, 9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ordered triples $(a,b,c)$ of integers with $1\\le a\\le b\\le c\\le 60$ satisfy $a\\cdot b=c$ ?",
"role": "user"
}
] | math | {
"ground_truth": "134",
"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 complex number $z= \\frac {(1-i)^{2}+3(1+i)}{2-i}$:\n(1) Find the real and imaginary parts of the complex number $z$;\n(2) If $z^{2}+az+b=1-i$, find the values of the r... | math | {
"ground_truth": "a = -3, \\ b = 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $p = \\binom{20}{6}$ and $q = \\binom{20}{5}$, compute the sum $p+q$.",
"role": "user"
}
] | math | {
"ground_truth": "62016",
"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 Bulls are playing the Heat in the NBA finals. To win the championship, a team needs to secure 4 victories before the opponent does. If the Heat win each game with a probabili... | math | {
"ground_truth": "\\frac{540}{16384}",
"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 smallest integer value of $N$ so that when $(a+b+c+d+e+1)^N$ is expanded and like terms are combined, the expression contains exactly $3003$ terms that include all five ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $3 - (-3)^{-3}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{82}{27}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $Q$ be the plane passing through the origin with the normal vector $\\begin{pmatrix} 2 \\\\ -1 \\\\ 2 \\end{pmatrix}$. Find the matrix $\\mathbf{Q}$ such that for any vector ... | math | {
"ground_truth": "\\begin{pmatrix} \\frac{5}{9} & \\frac{2}{9} & -\\frac{4}{9} \\\\ \\frac{2}{9} & \\frac{8}{9} & \\frac{2}{9} \\\\ -\\frac{4}{9} & \\frac{2}{9} & \\frac{5}{9} \\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": "The number $734{,}851{,}474{,}594{,}578{,}436{,}096$ is equal to $n^6$ for some positive integer $n$ . What is the value of $n$ ?",
"role": "user"
}
] | math | {
"ground_truth": "3004",
"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) Solve the system of equations $\\begin{cases}\n1 - x_1x_2 = 0 \n1 - x_2x_3 = 0 \n...\n1 - x_{14}x_{15} = 0 \n1 - x_{15}x_1 = 0 \\end{cases}$ b) Solve the system of equations ... | math | {
"ground_truth": "x_1 = x_2 = \\cdots = x_{15} = \\pm 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": "Given that $x$, $y$, $z$ are positive integers, $x+y+z=30$ and $\\gcd(x,y)+\\gcd(y,z)+\\gcd(z,x)=12$, determine the sum of all possible distinct values of $x^2+y^2+z^2$.",
"r... | math | {
"ground_truth": "710",
"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 smallest positive integer \\( n \\) such that in any 2-coloring of \\( K_n \\), there exist two monochromatic triangles of the same color that do not share any edge.\n(1... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive integer \\( n \\), a finite sequence of positive integers \\( a_{1}, a_{2}, \\cdots, a_{m} \\) is called an \"n-even sequence\" if \\( n = a_{1} + a_{2} + \\cdot... | math | {
"ground_truth": "2^{n-2} + 2^{\\left\\lfloor \\frac{n}{2} \\right\\rfloor - 1}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $f$ men can build a wall with $b$ bricks in $c$ days, determine the number of days $b$ men would take to build the same wall if each man's building rate doubles.",
"role":... | math | {
"ground_truth": "\\frac{2f \\times c}{b}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sides of a triangle have lengths of $13$, $84$, and $85$. Find the length of the shortest altitude.",
"role": "user"
}
] | math | {
"ground_truth": "12.8470588235",
"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 sum of the ages of four people, A, B, C, and D, is 100 years. A is 32 years old, and the sum of A and B's ages is three times the sum of the other two people's ages. C is 3 y... | math | {
"ground_truth": "43 + 11 = 54",
"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 $T$ be a set of $8$ integers taken from $\\{1,2,\\dots,18\\}$ with the property that if $x$ and $y$ are elements of $T$ with $x<y$, then $y$ is neither a multiple of $x$ nor ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Michael walks at 6 feet per second on a long straight path. Trash pails are located every 240 feet. A garbage truck traveling at 10 feet per second in the same direction as Micha... | math | {
"ground_truth": "A) Every 120 seconds starting at 120 seconds",
"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 \\begin{align*}\nf(x) &= 3x + 6 \\\\\ng(x) &= \\sqrt{f(x)} - 2 \\\\\nh(x) &= f(g(x))\n\\end{align*} What is $h(3)$?",
"role": "user"
}
] | math | {
"ground_truth": "3\\sqrt{15}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Team A has 37 people, Team B has 23 people. Now, x people are transferred from Team B to Team A, so that the number of people in Team A is exactly twice the number of people in T... | math | {
"ground_truth": "37 + x = 2 \\times (23 - x)",
"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 $\\sin{2x}\\sin{4x}=\\cos{2x}\\cos{4x}$, determine one possible value for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "15^\\circ",
"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": "Triangle $PQR$ has side lengths $PQ=13, QR=14,$ and $RP=15$. Circle $\\omega_1$ passes through $Q$ and is tangent to line $RP$ at $P$. Circle $\\omega_2$ passes through $R$ and i... | math | {
"ground_truth": "\\frac{25\\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": "The NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limited number of moves: it can either move two squares to the ... | math | {
"ground_truth": "252",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
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