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": "In trapezoid $ ABCD$ with $ \\overline{BC}\\parallel\\overline{AD}$ , let $ BC\\equal{}1000$ and $ AD\\equal{}2008$ . Let $ \\angle A\\equal{}37^\\circ$ , $ \\angle D\\eq... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integers \\(a\\) and \\(b\\) such that\n\n\\[ 7a^{3} = 11b^{5} \\]",
"role": "user"
}
] | math | {
"ground_truth": "41503 \\, \\text{,} \\, 539",
"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 hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0$, $b > 0$) with a focal length of $2\\sqrt{6}$, one of its asymptotes is $l$, and the distance from point $(1,... | math | {
"ground_truth": "C: \\frac{x^2}{2} - \\frac{y^2}{4} = 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": "Consider a regular octagon where each side has a length of 8 cm. What is the area, in square centimeters, of the shaded region formed by connecting the midpoints of alternating s... | math | {
"ground_truth": "32 + 16\\sqrt{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": "Find all real $x\\geq-1$ such that for all $a_1,...,a_n\\geq1$ , where $n\\geq2$ the following inequality holds $$ \\frac{a_1+x}{2}*\\frac{a_2+x}{2}*...*\\frac{a_n+x}{2}\... | math | {
"ground_truth": "x \\in [-1, 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": "In the expression $xy^2$, the values of $x$ and $y$ are each decreased by 50%. What is the new value of the expression in terms of its original value?\nA) Increased $\\frac{1}{2}... | math | {
"ground_truth": "\\frac{7}{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": "A regular triangular pyramid is inscribed in a sphere of radius \\( R \\), and its height is \\( \\frac{4R}{3} \\). What is the smallest possible area of a cross-section of the p... | math | {
"ground_truth": "\\frac{2 \\sqrt{2}}{\\sqrt{33}} R^2 ; 3 : 19",
"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 $f(x)$ be a function satisfying $f(3 + x) = f(3 - x)$ for all real numbers $x$. If the equation $f(x) = 0$ has exactly six distinct real roots, calculate the sum of these roo... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=3x+2x^{3}$, where $x\\in (-2,2)$, if $f(a-1)+f(1-2a) < 0$ holds, then the range of the real number $a$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(0, \\frac{3}{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": "What is the least common multiple of 3, 8, 9, and 12?",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the standard equation of the ellipse \\( C \\) is \\( \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1 \\) where \\( a > b > 1 \\). Point \\( P \\) is a moving point on the unit... | math | {
"ground_truth": "[3, 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": "Quantities $a$ and $b$ vary inversely. When $a$ is $800$, $b$ is $0.5$. If the product of $a$ and $b$ increases by $200$ when $a$ is doubled, what is $b$ when $a$ is $1600$?",
... | math | {
"ground_truth": "0.375",
"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 geometric mean of a set of \\(n\\) positive numbers is defined as the \\(n\\)-th root of the product of those numbers.\nYasmeen writes down a set of four numbers which have a... | math | {
"ground_truth": "128",
"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": "Natural numbers, multiples of 3, are painted in two colors: red and blue, such that the sum of a blue and a red number is red, and the product of a blue and a red number is blue.... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with circumcenter $O$ such that $AC = 7$ . Suppose that the circumcircle of $AOC$ is tangent to $BC$ at $C$ and intersects the line $AB$ at ... | math | {
"ground_truth": "\\frac{7}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the area of an ellipse with a major axis of length $2a$ and a minor axis of length $2b$ is $πab$, determine the value of the integral $\\int_{-3}^{3} \\sqrt{1 - \\frac... | math | {
"ground_truth": "\\frac{3π}{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": "If one root of the equation $7x^2 - (m+13)x + m^2 - m - 2 = 0$ is greater than 1 and the other root is less than 1, then the range of the real number $m$ is.",
"role": "user"... | math | {
"ground_truth": "(-2,4)",
"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": "Given the set $A=\\{x|y= \\sqrt {1-x^{2}}, x\\in \\mathbb{Z}\\}$, and $B=\\{p-q|p\\in A, q\\in A\\}$, find the number of elements in set $B$.",
"role": "user"
}
] | 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": "For any integer $n\\geq 2$ , let $N(n)$ be the maxima number of triples $(a_i, b_i, c_i)$ , $i=1, \\ldots, N(n)$ , consisting of nonnegative integers $a_i$ , $b_i$ and $... | math | {
"ground_truth": "N(n) = \\left\\lfloor \\frac{2n}{3} \\right\\rfloor + 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ T \\equal{} \\int_0^{\\ln2} \\frac {2e^{3x} \\plus{} e^{2x} \\minus{} 1} {e^{3x} \\plus{} e^{2x} \\minus{} e^x \\plus{} 1}dx$ . Evaluate $ e^T$ .",
"role": "user"
}... | math | {
"ground_truth": "\\frac{11}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given eight trees are equally spaced along one side of a straight road, with the distance from the first tree to the fourth being 75 feet, calculate the distance in feet between ... | math | {
"ground_truth": "175",
"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 three lines $l_1: 4x + y = 4$, $l_2: mx + y = 0$, and $l_3: 2x - 3my = 4$ cannot form a triangle, calculate the number of possible values for the real number $m$.",
"role"... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A 12-centimeter length on a map represents $72$ kilometers. How many kilometers does a 17-centimeter length represent?",
"role": "user"
}
] | math | {
"ground_truth": "102",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate plane $(xOy)$, the ratio of the distance from the moving point $S$ to the point $F(1,0)$ and its distance to the line $x=2$ is $\\frac{\\sqrt{2}}{2}$.... | math | {
"ground_truth": "[0,\\frac{1}{2})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the six solutions of $x^6 = -64$ are written in the form $a + bi$, where $a$ and $b$ are real, calculate the product of those solutions with $a > 0$.",
"role": "us... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the three angles of a triangle are $a^\\circ$, $b^\\circ$, and $c^\\circ$ where each is a prime number and $a>b>c$, find the least possible value of $c$.",
"role":... | 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": "Morteza Has $100$ sets. at each step Mahdi can choose two distinct sets of them and Morteza tells him the intersection and union of those two sets. Find the least steps that Ma... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that each of the 25 balls is tossed independently and at random into one of the 5 bins, let $p$ be the probability that some bin ends up with $3$ balls, another with $7$ ba... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At a circular table, there are 5 people seated: Arnaldo, Bernaldo, Cernaldo, Dernaldo, and Ernaldo, each in a chair. Analyzing clockwise, we have:\n\nI. There is 1 empty chair be... | 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": "Max sold glasses of lemonade for 25 cents each. He sold 41 glasses on Saturday and 53 glasses on Sunday. Calculate the total sales for these two days.",
"role": "user"
}
] | math | {
"ground_truth": "\\$23.50",
"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 quadratic polynomial with real coefficients, which has $4 + 2i$ as a root, and where the coefficient of $x^2$ is 3.",
"role": "user"
}
] | math | {
"ground_truth": "3x^2 - 24x + 60",
"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": "An aquarium on a level table has rectangular faces and is 10 inches wide and 8 inches high. When it was tilted, the water in it covered an 8\" x 10\" end but only three-fourths o... | math | {
"ground_truth": "3.75",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that function $f(x)$ is an even function defined on $(−∞,0)∪(0,+∞)$, it is monotonically decreasing on $(0,+∞)$, and $f( \\frac {1}{2}) > 0 > f(- \\sqrt {3})$, determine th... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$ and $B$ be two points on the parabola $y = x^2 + 1,$ such that the tangents at $A$ and $B$ are perpendicular. Find the $y$-coordinate of the point of intersection $P$ of ... | 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": "Calculate the sum of the consecutive integers from 95 to 105.",
"role": "user"
}
] | math | {
"ground_truth": "1100",
"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": "After obtaining his magical staff, Sun Wukong borrowed weapons for the other monkeys. It is known that Sun Wukong borrowed a total of 600 jin (a unit of weight), with each weapon... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sets \\( T = \\{0, 1, 2, 3, 4, 5, 6\\} \\) and \\( M = \\left\\{ \\left. \\frac{a_{1}}{7} + \\frac{a_{2}}{7^{2}} + \\frac{a_{3}}{7^{3}} + \\frac{a_{4}}{7^{4}} \\right| ... | math | {
"ground_truth": "\\frac{1}{7} + \\frac{1}{7^2} + \\frac{0}{7^3} + \\frac{4}{7^4}",
"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": "An angle is formed at the origin by the graphs of the lines y = 2x and y = 4x. The equation of the angle bisector of the acute angle formed is y = kx. Find the value of k.",
... | math | {
"ground_truth": "-\\frac{12}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the function $f(x) = x|x - a|$ ($a > 0$) has a minimum value of 2 on the interval $[1, 2]$, then $a = $ ___.",
"role": "user"
}
] | math | {
"ground_truth": "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": "There are 32 students applying to participate in an international exchange event, but only 2 can be selected. The selection method is as follows: the 32 students stand in a line ... | math | {
"ground_truth": "16 \\text{ or } 32",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\{a\\_n\\}$, where $a\\_1=1$, the sum of the first $n$ terms is denoted by $S\\_n$, and it satisfies the equation $2S\\_n=(n+1)a\\_n$, $(n∈N*)$.\n(1) Find th... | math | {
"ground_truth": "λ \\text{ is } (-∞,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": "Determine the work (in joules) performed in lifting a satellite from the surface of the Earth to a height of $H$ km. The mass of the satellite is $m$ tons, the radius of the Eart... | math | {
"ground_truth": "1.6452722063 \\times 10^{10} \\, \\text{J}",
"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 number $m$ is added to the set $\\{2, 5, 8, 11\\}$ to make the mean of the set of five numbers equal to its median. Determine the number of possible values of $m$ that satisfy ... | 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": "Given $x-2y=-1$, the value of the algebraic expression $6+2x-4y$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any real numbers $a$ and $b$, given that $|a-b| \\leqslant 1$, $|2a-1| \\leqslant 1$, and it always holds that $|4a-3b+2| \\leqslant m$, find the range of values for the real... | math | {
"ground_truth": "m \\geqslant 6",
"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 slope angle $\\alpha$ of line $l$ satisfies $3\\sin\\alpha=4\\cos\\alpha$, and its intercept on the x-axis is 2. The equation of line $l$ is \\_\\_\\_\\_\\_\\_.",
"role":... | math | {
"ground_truth": "4x-3y-8=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": "Let $a_1 = 2,$ and for $n\\ge 1,$ let $a_{n+1} = 2a_n + 1.$ Find the smallest value of an $a_n$ that is not a prime number.",
"role": "user"
}
] | math | {
"ground_truth": "95",
"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 price of three tires and one tire at half price is $345.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"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 smallest integer $y$ such that $|5y^2 - 56y + 12|$ is prime?",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of the region enclosed by the graph of $|x-70|+|y|=\\left|\\frac{x}{3}\\right|.$",
"role": "user"
}
] | math | {
"ground_truth": "1224.975",
"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 Billy Bob counts a total of 29 wheels and observes 10 children riding past his house, using bicycles, tricycles, and scooters, determine the number of tricycles among the chil... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mary can mow a lawn in three hours and Tom can mow the same lawn in six hours. If Mary works for 1 hour alone, what fractional part of the lawn remains to be mowed?",
"role":... | math | {
"ground_truth": "\\frac{2}{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": "Calculate the result of the expression: \n\\[\n\\frac{\\frac{1}{1}-\\frac{1}{3}}{\\frac{1}{1} \\times \\frac{1}{2} \\times \\frac{1}{3}} + \\frac{\\frac{1}{2}-\\frac{1}{4}}{\\fra... | math | {
"ground_truth": "108",
"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": "Piravena needs to travel from city $D$ to city $E$, then from $E$ to city $F$, and finally from $F$ back to $D$. Each leg of the journey is undertaken by either bus or train. The... | math | {
"ground_truth": "10560.992",
"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": "Alice thinks of a number. She triples it, adds 15, multiplies by 3, and ends up with 135. What was her original number?",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f: N \\to N_0$ is such that $f (2) = 0, f (3)> 0, f (6042) = 2014$ and $f (m + n)- f (m) - f (n) \\in\\{0,1\\}$ for all $m,n \\in N$ . Determine $f (2014)... | math | {
"ground_truth": "671",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the octagon COMPUTER exhibited below, all interior angles are either \\(90^{\\circ}\\) or \\(270^{\\circ}\\) and we have \\(CO=OM=MP=PU=UT=TE=1\\).\n\nPoint \\(D\\) (not to sc... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(2) If $7$ products are sampled from samples with quality index values $m\\geqslant 85$ using stratified sampling, and then $3$ products are randomly selected from these $7$ prod... | math | {
"ground_truth": "\\frac{6}{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( z_1 \\) and \\( z_2 \\) be the complex roots of \\( z^2 + pz + q = 0 \\), where \\( p \\) and \\( q \\) are complex numbers. In the complex plane, the points 0, \\( z_1 \... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a simple graph with 300 vertices no two vertices of the same degree are adjacent (boo hoo hoo). \nWhat is the maximal possible number of edges in such a graph?",
"role": "... | math | {
"ground_truth": "42550",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,b,c$ be positive real numbers. Find all real solutions $(x,y,z)$ of the system:\n\\[ ax+by=(x-y)^{2}\n by+cz=(y-z)^{2}\n cz+ax=(z-x)^{2}\\]",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0, 0), (0, 0, c), (a, 0, 0), (0, b, 0)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain electric car factory plans to produce 2100 electric cars in a week, with an average daily production plan of 300 cars. Due to various reasons, the actual daily producti... | math | {
"ground_truth": "2109a + 9b",
"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 frustum of a cone with the areas of its two bases being $4\\pi$ and $25\\pi$ respectively, and the height of the frustum is 4, find the volume and the lateral surface are... | math | {
"ground_truth": "35\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all sets $ A$ of nonnegative integers with the property: if for the nonnegative intergers $m$ and $ n $ we have $m+n\\in A$ then $m\\cdot n\\in A.$",
"role": "u... | math | {
"ground_truth": "\\emptyset, \\{0\\}, \\{0, 1\\}, \\{0, 1, 2\\}, \\{0, 1, 2, 3\\}, \\{0, 1, 2, 3, 4\\}, \\mathbb{Z}_{\\ge 0}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the product of the least common multiple and the greatest common factor of $30$ and $75$?",
"role": "user"
}
] | math | {
"ground_truth": "2250",
"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": "Twelve points are positioned on the positive x-axis, \\(X^+\\), and six points are placed on the positive y-axis, \\(Y^+\\). Each point on \\(X^+\\) is connected with a line segm... | math | {
"ground_truth": "C) 990",
"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 number $r$ can be expressed as a four-place decimal $0.abcd$, where $a, b, c, d$ represent digits. It is desired to approximate $r$ by a fraction whose numerator is 1 or 2 an... | math | {
"ground_truth": "833",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the minimum number of digits to the right of the decimal point required to express the fraction $\\frac{987654321}{2^{30} \\cdot 5^2}$ as a decimal.\nA) 2 \nB) 28 \... | math | {
"ground_truth": "C) 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": "$(1)$ Calculate: $18+|-\\sqrt{2}|-\\left(2012-\\pi \\right)^{0}-4\\sin 45^{\\circ}$; \n$(2)$ Solve the equation: $\\frac{4x}{x^{2}-4}-\\frac{2}{x-2}=1$.",
"role": "user"
}... | math | {
"ground_truth": "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": "Determine the positive prime numbers \\( p \\) and \\( q \\) if\n\n\\[ p + p^{2} + p^{4} - q - q^{2} - q^{4} = 83805 \\]",
"role": "user"
}
] | math | {
"ground_truth": "p = 17, q = 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $(4 - 3i)^2$. (Your answer should be of the form $a+bi$.)",
"role": "user"
}
] | math | {
"ground_truth": "7 - 24i",
"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 propositions $p$ and $q$: Proposition $p$: The equation $x^{2}+mx+1=0$ with real number $x$ has two different negative roots; Proposition $q$: The equation $4x^{2}+4(m-2)x+... | math | {
"ground_truth": "m \\geq 3 \\text{ or } 1 < m \\leq 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "One participant in the game was given 30 questions. For each correct answer, they were awarded 7 points, and for each wrong answer (or no answer), 12 points were deducted. How ma... | math | {
"ground_truth": "23",
"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": "Construct a triangle given the circumradius $r$, the difference between the two angles adjacent to side $a$: $\\beta - \\gamma$, and the segment $K A_{1}$, where $K$ is the cente... | math | {
"ground_truth": "1 \\text{ or } 2 \\text{ solutions}",
"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 isosceles triangle $\\triangle ABC$, $\\angle A=120^{\\circ}$. The angle between vectors $\\overrightarrow{AB}$ and $\\overrightarrow{BC}$ is $\\_\\_\\_\\_\\_\\_\\_\\_$.",
... | math | {
"ground_truth": "150^{\\circ}",
"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": "Calculate $i + i^2 + i^3 + \\ldots + i^{2014}$ (where $i$ is the imaginary unit).",
"role": "user"
}
] | math | {
"ground_truth": "-1 + i",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of permutations of $\\{1,2,...,n\\}$ like $\\{a_1,...,a_n\\}$ st for each $1 \\leq i \\leq n$ : $$ a_i | 2i $$",
"role": "user"
}
] | math | {
"ground_truth": "2^{\\lfloor n/2 \\rfloor}",
"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 sets of two or more consecutive positive integers have a sum of 36?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 $ABCDV$ be a regular quadrangular pyramid with $V$ as the apex. The plane $\\lambda$ intersects the $VA$ , $VB$ , $VC$ and $VD$ at $M$ , $N$ , $P$ , $Q$ resp... | math | {
"ground_truth": "2:1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ m\\geq n\\geq 4$ be two integers. We call a $ m\\times n$ board filled with 0's or 1's *good* if\r\n\r\n1) not all the numbers on the board are 0 or 1;\r\n\r\n2) the su... | math | {
"ground_truth": "(4 + m, 4)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $m$ and $n$ are positive integers satisfying $mn-2m-3n-20=0$, calculate the minimum value of $m+n$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are two circles with the same center. The smaller circle has a diameter of 2 inches and is painted yellow. The larger circle has a diameter of 6 inches. The ring formed bet... | math | {
"ground_truth": "E) 8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=x^{2}+a|x-1|$, where $a$ is a constant.\n(1) When $a=2$, find the minimum and maximum values of the function $f(x)$ on $[0,2]$;\n(2) If the function $f(x... | math | {
"ground_truth": "[-2,0]",
"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": "Let $x,$ $y,$ $z$ be positive real numbers such that\n\\[\\left( \\frac{x}{y} + \\frac{y}{z} + \\frac{z}{x} \\right) + \\left( \\frac{y}{x} + \\frac{z}{y} + \\frac{x}{z} \\right)... | math | {
"ground_truth": "\\frac{81}{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": "Real numbers $x$ and $y$ satisfy $x^2+y^2=4$. Find the maximum value of $x^2+8y+3$.",
"role": "user"
}
] | math | {
"ground_truth": "19",
"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": "Four coplanar squares with side lengths of 3, 5, 7, and 9 units, respectively, are placed sequentially, each sharing one side lying on line $CD$. A segment connects the bottom le... | math | {
"ground_truth": "119.25 \\text{ square 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 all non-negative integers $a, b, c$ such that the roots of equations: $\\begin{cases}x^2 - 2ax + b = 0 \nx^2- 2bx + c = 0 \nx^2 - 2cx + a = 0 \\end{cases}$ are non-negat... | math | {
"ground_truth": "(1, 1, 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)(xy+xz+yz)=49$$ and that $$x^2(y+z)+y^2(x+z)+z^2(x+y)=19$$ for real numbers $x$, $y$, and $z$, find the value of $xyz$.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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": "Each vertex of this parallelogram has integer coordinates. The vertices of the parallelogram are placed at points $(1,3)$, $(6,3)$, $(4,0)$, and $(-1,0)$. Find the sum of the per... | math | {
"ground_truth": "25 + 2\\sqrt{13}",
"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 parallelepiped with dimensions \\( m \\times n \\times k \\) is divided into unit cubes. How many parallelepipeds in total (including the original one) are formed?"... | math | {
"ground_truth": "\\frac{m n k (m+1)(n+1)(k+1)}{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 random variable $X \\sim N(1,\\sigma^{2})$, if $P(0 < X < 3)=0.5$ and $P(0 < X < 1)=0.2$, calculate the probability $P(X < 3)$.",
"role": "user"
}
] | math | {
"ground_truth": "0.8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $p = 1+\\frac{1}{2}+\\frac{1}{2^2}+\\frac{1}{2^3}+\\frac{1}{2^4}+\\frac{1}{2^5}. $ For nonnegative reals $x, y,z$ satisfying $(x-1)^2 + (y-1)^2 + (z-1)^2 = 27,$ find th... | math | {
"ground_truth": "40.4",
"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": "Translate the given problem from Chinese to English.",
"role": "user"
}
] | math | {
"ground_truth": "4x + y = 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": "Determine the values of $k$ such that the quadratic equation $3x^2 - kx + 2x + 15 = 0$ has real and equal roots.\nA) $2\\sqrt{5} \\text{ and } -2\\sqrt{5}$\nB) $6\\sqrt{5}+2 \\te... | math | {
"ground_truth": "6\\sqrt{5}+2 \\text{ and } -6\\sqrt{5}+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": "If the volume of the gas expands by $4$ cubic centimeters for every $3^\\circ$ rise in temperature, determine the volume of the gas in cubic centimeters when the temperature was ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integers $n$ greater than or equal to $4$ that satisfy the following conditions:\n\n\n- Take an arbitrary convex $n$ -gon $P$ on the coordinate plane whose vertic... | math | {
"ground_truth": "n = 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": "Find an integer $n$ , where $100 \\leq n \\leq 1997$ , such that \\[\\frac{2^{n}+2}{n}\\] is also an integer.",
"role": "user"
}
] | math | {
"ground_truth": "66, 198, 398, 798",
"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 a geometric sequence $\\{an\\}$ where each term is positive and $a_{5}a_{6}=81$, find the value of ${\\log _{\\frac{1}{3}}}{a_{1}} + {\\log _{\\frac{1}{3}}}{a_{2}} + {\\log... | math | {
"ground_truth": "-20",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The total length of a certain highway is 155 kilometers. On a road map with a scale of 1:500000, the length should be ______ centimeters.",
"role": "user"
}
] | math | {
"ground_truth": "31",
"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": "Formulate a second-degree equation whose roots are one unit greater than the roots of the equation \\(a x^{2} + b x + c = 0\\).",
"role": "user"
}
] | math | {
"ground_truth": "a y^2 + (b-2a) y + (a - b + c) = 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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