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 $-2x^{3}y^{m+3}$ and $9x^{3}y^{5}$ are like terms, then the value of $m$ is ____.",
"role": "user"
}
] | 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": "Find the smallest natural number that starts with the digit 4 and decreases four times by moving this digit to the end of the number.",
"role": "user"
}
] | math | {
"ground_truth": "410256",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, $AB = AC = 7$ units, and $BC = 10$ units. Triangle $ABC$ is isosceles with the vertex angle at $A$.\n\nPoint $P$ is located inside triangle $ABC$ such that it ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all pairs $ (m, n)$ of positive integers such that $ m^n \\minus{} n^m \\equal{} 3$ .",
"role": "user"
}
] | math | {
"ground_truth": "(m, n) = (4, 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": "Point \\( M \\) divides the side \\( BC \\) of parallelogram \\( ABCD \\) in the ratio \\( BM: MC = 1: 3 \\). Line \\( AM \\) intersects diagonal \\( BD \\) at point \\( K \\). F... | math | {
"ground_truth": "\\frac{19}{40}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two spheres touch the plane of triangle $ABC$ at points $A$ and $B$ and are located on opposite sides of this plane. The sum of the radii of these spheres is 13, and the distance... | math | {
"ground_truth": "2 \\sqrt{21} \\approx 9.17",
"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 the function $f(x) = x^2 + 2ax + 2$ is monotonically increasing on the interval $[2, +\\infty)$, then the range of the real number $a$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "[-2, +\\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": "Let $f(x) = x^2 + 8x + q$ for all real numbers $x$, where $q$ is some real number. For what values of $q$ does $f(f(x))$ have exactly 4 distinct real roots?",
"role": "user"
... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Teacher Zhang sawed a piece of wood into 9 small sections, each 4 meters long. If the same piece of wood is sawed into sections that are 3 meters long, how many cuts are needed i... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four congruent rectangles form an arrangement around a smaller, inner square such that each rectangle abuts two sides of the square and the exterior forms a larger square. If the... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $(-9\\cdot 5) - (-7 \\cdot -2) + (11 \\cdot -4)$.",
"role": "user"
}
] | math | {
"ground_truth": "-103",
"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 real numbers $a_1,a_2,a_3$ and $b{}$ are given. The equation \\[(x-a_1)(x-a_2)(x-a_3)=b\\]has three distinct real roots, $c_1,c_2,c_3.$ Determine the roots of the equat... | math | {
"ground_truth": "-a_1, -a_2, -a_3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If a function $f(x)$ satisfies the condition that for any given geometric sequence ${a_n}$, ${f(a_n)}$ is still a geometric sequence, then $f(x)$ is called a \"preserving geometr... | math | {
"ground_truth": "1, 3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a group of students, initially $60\\%$ are girls. Subsequently, three girls leave and three boys arrive, and it is then found that $50\\%$ of the group are girls. Determine... | 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": "A rectangle R1 has one side of length 3 inches and an area of 24 square inches. A rectangle R2, which is similar to R1, has a diagonal measuring 20 inches. Find the area of recta... | math | {
"ground_truth": "\\frac{3200}{73}",
"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 \\( ABC \\) be an isosceles triangle with \\( A \\) as the vertex angle. Let \\( M \\) be the midpoint of the segment \\( [BC] \\). Let \\( D \\) be the reflection of point \... | math | {
"ground_truth": "\\frac{x}{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": "For an integer $m\\geq 1$ , we consider partitions of a $2^m\\times 2^m$ chessboard into rectangles consisting of cells of chessboard, in which each of the $2^m$ cells along... | math | {
"ground_truth": "2^{m+2}(m+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 $m$ be a positive integer. Determine the smallest positive integer $n$ for which there exist real numbers $x_1, x_2,...,x_n \\in (-1, 1)$ such that $|x_1| + |x_2| +...... | math | {
"ground_truth": "n = m + 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 $m$ represent the smallest integer that satisfies the following conditions:\n$\\frac{m}{2}$ is a perfect square.\n$\\frac{m}{3}$ is a perfect cube.\n$\\frac{m}{7}$ is a perfe... | math | {
"ground_truth": "154",
"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": "Simplify first and then evaluate: $\\left(x-2\\right)^{2}+\\left(2+x\\right)\\left(x-2\\right)-2x\\left(2x-1)$, where $x=-2$.",
"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": "On Wednesday, I worked $t+2$ hours and earned $4t-5$ dollars per hour. My cousin Maria worked $2t+1$ hours but only earned $2t+3$ dollars an hour. At the end of the day, I had ea... | math | {
"ground_truth": "-\\frac{16}{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": "Michael's school offers 10 different math classes, but he must take \"Calculus 1\" as it's a prerequisite for other advanced courses. In total, Michael needs to select 4 math cla... | math | {
"ground_truth": "84",
"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 the Cartesian coordinate system, the vertices of triangle ABC are $A(2,1)$, $B(-2,3)$, and $C(-3,0)$. \n$(1)$ Find the equation of the line containing side $BC$. \n$(2)$ Fin... | math | {
"ground_truth": "x + 3y - 5 = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Patrick started walking at a constant rate along a straight road from school to the park. One hour after Patrick left, Tanya started running along the same road from school to th... | math | {
"ground_truth": "277",
"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": "Cut $2003$ disjoint rectangles from an acute-angled triangle $ABC$ , such that any of them has a parallel side to $AB$ and the sum of their areas is maximal.",
"role": ... | math | {
"ground_truth": "\\frac{n}{n+1} \\cdot \\text{area}(\\triangle ABC)",
"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 circumferences of radius $1$ that do not intersect, $c_1$ and $c_2$ , are placed inside an angle whose vertex is $O$ . $c_1$ is tangent to one of the rays of the angl... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the expression \\(2^{-2} \\times 2^{-1} \\times 2^{0} \\times 2^{1} \\times 2^{2}\\), calculate its numerical value.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point is randomly dropped on the interval $[5, 7]$, and let $k$ be the resulting value. Find the probability that the roots of the equation $\\left(k^{2}-3k-4\\right)x^{2}+(3k-... | math | {
"ground_truth": "\\frac{1}{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": "In triangle $ABC$ , $AB=13$ , $BC=14$ and $CA=15$ . Segment $BC$ is split into $n+1$ congruent segments by $n$ points. Among these points are the feet of the altitud... | math | {
"ground_truth": "27",
"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 meteorologist predicts that for each day from Monday to Sunday next week, there is a $30\\%$ chance of sun, a $40\\%$ chance of getting 3 inches of rain, and a $30\\%$ chance o... | math | {
"ground_truth": "25.2 \\text{ inches}",
"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 functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) of a real variable with real values, such that for all \\( x, y \\in \\mathbb{R} \\):\n\n$$\n(x-2) f(y) + f(y +... | math | {
"ground_truth": "f(x) = 0 \\text{ or } f(x) = x - 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Three-digit powers of 3 and 7 are used in this \"cross-number\" puzzle, find the only possible digit for the outlined square.",
"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": "Let $A$ be the number of 2019-digit numbers, that is made of 2 different digits (For example $10\\underbrace{1...1}_{2016}0$ is such number). Determine the highest power of 3... | math | {
"ground_truth": "\\nu_3(A) = 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 coefficient of $x^5$ in the expansion of $\\left(\\frac{x^2}{3}-\\frac{3}{x}\\right)^7$ is $-\\frac{35}{3}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{35}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(y = \\sqrt{4+\\sqrt{4+\\sqrt{4+\\sqrt{4+\\cdots}}}}\\). Determine \\(y\\).\nA) \\( \\frac{1 - \\sqrt{17}}{2} \\)\nB) \\( \\frac{1 + \\sqrt{17}}{2} \\)\nC) \\( \\sqrt{17} \... | math | {
"ground_truth": "B) \\( \\frac{1 + \\sqrt{17}}{2} \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, we have $\\frac {\\cos B}{\\cos C} = -\\frac {b}{2a+c}$,\n1. Find the angle $B$.\n2. Given $b= \\sqrt {13}$ and $a+c=4$, find the area $S_{\\triangle ABC}$.",
... | math | {
"ground_truth": "\\frac{3\\sqrt{3}}{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": "The numbers from 1 to 9 are divided into three groups of three numbers, and then the numbers in each group are multiplied. $A$ is the largest of the three products. What is the s... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two wooden sticks have lengths of 5 and 7, respectively. To choose a third wooden stick to form a triangle, if the length of the third wooden stick is chosen to be an even number... | 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": "When a number is divided by 9, the remainder is 3. What is the remainder when five times the number minus 12 is divided by 9?",
"role": "user"
}
] | 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": "How can it be expressed using a single equality sign that each of the three real numbers \\(a, b, c\\) is separately equal to zero?",
"role": "user"
}
] | math | {
"ground_truth": "a^2 + b^2 + c^2 = 0",
"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_{2}=-1$, and the sum of the first $n$ terms of $\\{a_{n}\\}$ is $S_{n}$, satisfying $S_{9}=5S_{5}$. \n$(1)$ Find the general formula... | math | {
"ground_truth": "\\frac{80}{9}",
"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": "In a school, there are 30 students in the first year and 40 students in the second year who have chosen the basketball course. A stratified sampling method is used to draw a samp... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a music school, there are $4$ times as many boys as girls and $7$ times as many girls as teachers. Let $b, g, t$ represent the number of boys, girls, and teachers, respectivel... | math | {
"ground_truth": "\\frac{9b}{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": "An isosceles triangle has two sides measuring 15 cm and one side measuring 24 cm. If a similar triangle has its longest side measuring 72 cm, find the perimeter of this larger tr... | math | {
"ground_truth": "162 \\text{ cm}",
"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": "Suppose $xy-5x+2y=30$ , where $x$ and $y$ are positive integers. Find the sum of all possible values of $x$",
"role": "user"
}
] | math | {
"ground_truth": "31",
"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": "Compute the value of \\(262^2 - 258^2\\) and add \\(150\\) to the result.",
"role": "user"
}
] | math | {
"ground_truth": "2230",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P_1$ be a regular $r~\\mbox{gon}$ and $P_2$ be a regular $s~\\mbox{gon}$ $(r\\geq s\\geq 3)$ such that each interior angle of $P_1$ is $\\frac{5}{4}$ as large as each interi... | math | {
"ground_truth": "130",
"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 three positive numbers \\( a, b, \\mathrm{and} c \\) satisfying \\( a \\leq b+c \\leq 3a \\) and \\( 3b^2 \\leq a(a+c) \\leq 5b^2 \\), what is the minimum value of \\(\\fra... | math | {
"ground_truth": "-\\frac{18}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A line segment begins at \\( (3, -2) \\) and is 12 units long. It ends at the point \\( (x, 7) \\) where \\( x < 0 \\). What is the value of \\( x \\)?",
"role": "user"
}
] | math | {
"ground_truth": "-4.94",
"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 $a+b=1$, find the maximum value of $ab$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "Let \\( x_{1}, x_{2}, \\cdots, x_{n} \\) be a sequence of positive integers where each term is not greater than \\( M \\) and satisfies\n\\[ x_{k} = \\left| x_{k-1} - x_{k-2} \\r... | 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": "Isabella has a sheet of paper in the shape of a right triangle with sides of length 3, 4, and 5. She cuts the paper into two pieces along the altitude to the hypotenuse, and rand... | math | {
"ground_truth": "64",
"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 proposition \"There exists an $x \\in \\mathbb{Z}$ such that $x^{2}+2x+m < 0$\", find the negation of this proposition.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{For all $x \\in \\mathbb{Z}$, $x^{2}+2x+m \\geqslant 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": "If \\( y = -3x^2 + 4x + 6 \\) and \\( x \\) is a real number, what is the maximum value possible for \\( y \\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{22}{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": "Compute the sum $g \\left(\\frac{1}{2021} \\right) - g \\left(\\frac{2}{2021} \\right) + g \\left(\\frac{3}{2021} \\right) - g \\left(\\frac{4}{2021} \\right) + \\cdots - g \\lef... | 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": "In triangle $ABC$ , let $I, O, H$ be the incenter, circumcenter and orthocenter, respectively. Suppose that $AI = 11$ and $AO = AH = 13$ . Find $OH$ .\n\n*Proposed by Kevi... | math | {
"ground_truth": "10",
"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": "Evaluate the value of the expression \\[(3^{1002}+7^{1003})^2 - (3^{1002}-7^{1003})^2\\] and express your answer in the form of $m\\cdot10^{1003}$ for some integer $m$.",
"ro... | math | {
"ground_truth": "1372",
"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": "Factorize: $3x^{2}y-6x=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "3x(xy-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 $H = \\log \\frac{2+x}{2-x}$. Find a new function $K$ by replacing each $x$ in $H$ by $\\frac{4x - x^3}{1 + 4x^2}$ and simplify.",
"role": "user"
}
] | math | {
"ground_truth": "3H",
"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": "Four spheres in three-dimensional space intersect at different points. What is the maximum number of points on the spheres that a line passing through all four spheres can touch?... | math | {
"ground_truth": "8",
"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": "Three vertices of parallelogram $ABCD$ are $A(1,2), B(-4,2), D(5,-4)$ with $A$ and $D$ diagonally opposite. Find the sum of the coordinates of vertex $C$.",
"role": "user"
... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( 100 \\leq a \\leq 300 \\) and \\( 1200 \\leq b \\leq 2400 \\), calculate the largest value of the quotient \\( \\frac{b}{a} \\).",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three standard dice are rolled. What is the expected number of 6's obtained? Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a circle is divided into 12 sectors with central angles of integers forming an arithmetic sequence, calculate the degree measure of the smallest possible sector angle.... | 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": "Calculate\n\nGiven $2x+y=6$, find the value of $\\left[(x-y)^{2}-(x+y)^{2}+y(2x-y)\\right]÷(-2y)$.",
"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": "Let \\\\(\\alpha\\\\) and \\\\(\\beta\\\\) be acute angles, and satisfy \\\\(\\sin^2\\alpha + \\sin^2\\beta = \\sin(\\alpha + \\beta)\\\\), then \\\\(\\alpha + \\beta =\\\\) \\_\... | math | {
"ground_truth": "\\frac{\\pi}{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": "$(1)\\sqrt{5}-27+|2-\\sqrt{5}|-\\sqrt{9}+(\\frac{1}{2})^{2}$；<br/>$(2)2\\sqrt{40}-5\\sqrt{\\frac{1}{10}}-\\sqrt{10}$；<br/>$(3)(3\\sqrt{12}-2\\sqrt{\\frac{1}{3}}-\\sqrt{48})÷4\\sq... | math | {
"ground_truth": "2+2\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $T_1$ be a triangle with side lengths $2021$, $2022$, and $2023$. For $n \\geq 1$, if $T_n = \\Delta ABC$ and $D, E$, and $F$ are the points of tangency of the incircle of $\... | math | {
"ground_truth": "\\frac{1516.5}{128}",
"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$ is irrational , but $a$ and $a^3-6a$ are roots of square polynomial with integer coefficients.Find $a$",
"role": "user"
}
] | math | {
"ground_truth": "a \\in \\left\\{-1 - \\sqrt{2}, -\\sqrt{5}, 1 - \\sqrt{2}, -1 + \\sqrt{2}, \\sqrt{5}, 1 + \\sqrt{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": "Compute the area of the smallest convex polygon S that contains the region R formed by the union of a unit square and 8 equilateral triangles constructed on each side of the squa... | 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": "Find all pairs of positive integers $(m, n)$ such that $m^2-mn+n^2+1$ divides both numbers $3^{m+n}+(m+n)!$ and $3^{m^3+n^3}+m+n$ .\n\n*Proposed by Dorlir Ahmeti*",
"r... | math | {
"ground_truth": "(2, 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": "A quadratic polynomial $q(x)$ with real coefficients is called **respectful** if it can be expressed as $q(x) = x^2 + ax + b$. This polynomial is uniquely defined such that $q(q(... | math | {
"ground_truth": "**A)** 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": "Jane plans a journey that begins when the clock hands are together between 10 a.m. and 11 a.m. and ends when the hands are exactly 180 degrees apart between 5 p.m. and 6 p.m. How... | math | {
"ground_truth": "C) 7 hr. 30 sec.",
"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 $|a^{3}-27|+\\left(b+2\\right)^{2}=0$, then $a+b=\\_\\_\\_\\_\\_\\_$.",
"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": "We say an integer $n$ is naoish if $n \\geq 90$ and the second-to-last digit of $n$ (in decimal notation) is equal to $9$ . For example, $10798$ , $1999$ and $90$ are... | math | {
"ground_truth": "8",
"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 $50$-question multiple choice math contest with a scoring system of $4$ points for a correct answer, $0$ points for an answer left blank, and $-1$ point for an incorrect ... | math | {
"ground_truth": "29",
"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": "What is the smallest number of weights in a set that can be divided into 3, 4, and 5 piles of equal mass?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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 expression:\n$$\nK=(x-a)^{2}+(x-b)^{2}+(x-c)^{2}\n$$\n\nwhere \\( a, b, \\) and \\( c \\) are given real numbers, and \\( x \\) is any real number. What is the minimum ... | math | {
"ground_truth": "\\frac{(a-b)^2 + (b-c)^2 + (a-c)^2}{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": "Suppose that in triangle $ABC$ it is known that \\(\\cos 2A + \\cos 2B + \\cos 2C = 0\\). Two sides of the triangle have lengths 8 and 15. Find the maximum length of the third si... | math | {
"ground_truth": "\\sqrt{289 - 120\\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": "Rebecca and Mark need to travel from the southwest corner to the northeast corner of a rectangular park, which has a length of 3 units and a width of 4 units. Rebecca walks due e... | math | {
"ground_truth": "29\\%",
"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 sequence $\\{a\\_n\\}$ with its first $n$ terms sum $S\\_n$, and $a\\_1=1$, $a_{n+1}=3S\\_n (n\\in\\mathbb{N}^*)$.\n\n1. Find the general term formula for the sequence $\... | math | {
"ground_truth": "\\frac{(3n-1)\\cdot 4^{n-1} + 1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $0 < a < 1$, determine the solution set for the inequality $(a-x)(x-\\frac{1}{a}) > 0$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x | a < x < \\frac{1}{a}\\}",
"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": "Reconstruct the multiplication example.",
"role": "user"
}
] | math | {
"ground_truth": "90625",
"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 expression $(1+x)^{2011} = a_0 + a_1x + \\ldots + a_{2011}x^{2011}$, calculate the value of $a_0 + a_2 + a_4 + \\ldots + a_{2010}$.",
"role": "user"
}
] | math | {
"ground_truth": "2^{2010}",
"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 store increased the original price of a shirt by a certain percent, then added a 5% tax on the new price, and finally decreased the price by the same percent as the initial inc... | math | {
"ground_truth": "C) 52.5%",
"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": "Samantha leaves her house at 7:00 a.m., attends 8 classes, each lasting 55 minutes, and spends a total of 1 hour and 45 minutes on other school-related activities throughout the ... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The cost of five water bottles is \\ $13, rounded to the nearest dollar, and the cost of six water bottles is \\$ 16, also rounded to the nearest dollar. If all water bottles cos... | math | {
"ground_truth": "11",
"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 expression $\\frac{x^2 - 4x + 3}{x^2 - 6x + 8} \\div \\frac{x^2 - 6x + 5}{x^2 - 8x + 15},$ when simplified is:\nA) $\\frac{(x-3)(x-1)}{(x-2)(x-4)}$\nB) $\\frac{1}{x-3}$\nC) $... | math | {
"ground_truth": "\\frac{1}{(x-2)(x-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": "How many three-digit numbers remain if we exclude all three-digit numbers in which there are exactly two identical digits that are adjacent?",
"role": "user"
}
] | math | {
"ground_truth": "738",
"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 two vectors in the plane, $\\overrightarrow{a}$ and $\\overrightarrow{b}$, with an angle of $60^{\\circ}$ between them, and $|\\overrightarrow{a}|=2$, $|\\overrightarrow{b}... | 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": "One team can complete the entire field in 12 days. The other team requires 75% of this time to complete the same work. After the first team worked alone for 5 days, the second te... | math | {
"ground_truth": "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": "Pinegrove Middle School has the same number of boys and girls. $\\frac{4}{5}$ of the boys and $\\frac{1}{2}$ of the girls attended a science lecture. Additionally, $\\frac{1}{10}... | math | {
"ground_truth": "\\frac{16}{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": "In an isosceles triangle, one of the angles is $80^{\\circ}$. What are its other angles? (Specify all possibilities.)",
"role": "user"
}
] | math | {
"ground_truth": "80^\\circ, 80^\\circ, 20^\\circ \\text{ or } 80^\\circ, 50^\\circ, 50^\\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": "There are 300 sprinters registered for a 200-meter dash at a local track meet, where the track has only 8 lanes. In each race, 3 of the competitors advance to the next round, whi... | math | {
"ground_truth": "60",
"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 following indefinite integrals.\r\n\r\n[1] $\\int \\frac{x}{\\sqrt{5-x}}dx$ \r\n\r\n[2] $\\int \\frac{\\sin x \\cos ^2 x}{1+\\cos x}dx$ \r\n\r\n[3] $\\int (\\sin... | math | {
"ground_truth": "x - \\frac{1}{4} \\sin 2x - \\frac{1}{8} \\sin 4x + \\frac{4}{3} \\sin^3 x + C",
"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 $\\log_8 x = 3.25$, find the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "32 \\sqrt[4]{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": "Determine how many positive integer divisors of $150^{12}$ are either perfect squares or perfect cubes (or both).\nA) 713\nB) 715\nC) 717\nD) 719\nE) 721",
"role": "user"
}... | math | {
"ground_truth": "C) 717",
"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 construction supervisor noticed that one of his bricklayers would take 8 hours to construct a particular wall, while the other would need 12 hours. He also saw that when they w... | math | {
"ground_truth": "C) 288",
"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 set $S$ of positive integers is $\\textit{sum-complete}$ if there are positive integers $m$ and $n$ such that an integer $a$ is the sum of the elements of some nonemp... | math | {
"ground_truth": "223",
"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 solution set for the inequality $\\frac{x-1}{x} > 1$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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