data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the absolute value of a number is $4$, then the number is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\pm 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four friends make cookies from the same amount of dough with the same thickness. Art's cookies are circles with a radius of 2 inches, and Trisha's cookies are squares with a side... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a board with $n$ rows and $4$ columns. In the first line are written $4$ zeros (one in each house). Next, each line is then obtained from the previous line by perf... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the real numbers \\(a\\) and \\(b\\) such that \\((X - 1)^{2}\\) divides \\(a X^{4} + b X^{3} + 1\\).",
"role": "user"
}
] | math | {
"ground_truth": "a = 3, \\, b = -4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three cyclists are initially $8$ miles apart and start at the same time. If they all travel in the same direction, the fastest and the slowest would take $4$ hours to meet. If th... | math | {
"ground_truth": "\\frac{5}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A semicircle with diameter \\( AB \\) and center at point \\( O \\) is divided by points \\( C \\) and \\( D \\) into three parts such that point \\( C \\) lies on arc \\( AD \\)... | math | {
"ground_truth": "20^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find real roots $x_1$ , $x_2$ of equation $x^5-55x+21=0$ , if we know $x_1\\cdot x_2=1$",
"role": "user"
}
] | math | {
"ground_truth": "\\left\\{\\frac{3 + \\sqrt{5}}{2}, \\frac{3 - \\sqrt{5}}{2}\\right\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\tan \\theta=2$, evaluate $\\sin \\left(2\\theta+ \\frac{\\pi}{4}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{2}}{10}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( a > 1 \\) be a natural number. Find all numbers that are divisors of at least one of the numbers\n\n\\[ \na_{n} = \\sum_{k=0}^{n} a^{k}, \\quad n \\in \\mathbf{N}. \n\\]"... | math | {
"ground_truth": "m \\in \\mathbb{N} \\mid \\gcd(m, a) = 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A group of $n$ numbers has the original sum $s$. If each number of the group is increased by $10$, then multiplied by $3$, and finally decreased by $15$, find the sum of the new ... | math | {
"ground_truth": "\\textbf{B)}\\ 3s + 15n",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( Q(x) = x^2 + 2x + 3 \\), and suppose that \\( P(x) \\) is a polynomial such that\n\\[ P(Q(x)) = x^6 + 6x^5 + 18x^4 + 32x^3 + 35x^2 + 22x + 8. \\]\n\nCompute \\( P(2) \\).... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the quadratic equation $x^2 - 7x + 10 = 0$. Determine the absolute value of the difference between the roots of this equation.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n\\geq 2$ be an integer. Alice and Bob play a game concerning a country made of $n$ islands. Exactly two of those $n$ islands have a factory. Initially there is no bri... | math | {
"ground_truth": "n \\equiv 3 \\pmod 4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a= \\frac {2}{\\pi } \\int _{ -1 }^{ 1 }( \\sqrt {1-x^{2}}+\\sin x)dx$, find the constant term in the expansion of the binomial $((x- \\frac {a}{x^{2}})^{9})$.",
"role... | math | {
"ground_truth": "-84",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that line $l_1$: $x+2y-1=0$ is parallel to line $l_2$: $mx-y=0$, find the value of the real number $m$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Xiaoming brought 24 homemade souvenirs to sell at the London Olympics. In the morning, he sold each souvenir for 7 pounds, but the number of souvenirs sold was less than half of ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the track has a width of 6 meters, find Keiko's speed in meters per second, knowing it takes her 36 seconds longer to walk around the outside edge of the track than around ... | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a class, the students are playing a game with 960 tokens. At the start, each student received the same number of tokens. When the teacher joins the students, each student give... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence {a<sub>n</sub>} with the sum of the first n terms denoted as S<sub>n</sub>, if $$a_{n+1}=a_{n}+1 (n∈N^{*})$$ and S<sub>3</sub>\\=12:\n\n(Ⅰ) Find the general ter... | math | {
"ground_truth": "T_n = \\frac{n}{3n + 9}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. A child builds a wall along a line with $n$ identical cubes. He lays the first cube on the line and at each subsequent step, he lays the next c... | math | {
"ground_truth": "2^{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest difference between two factors of the number $1950$ when it is expressed as a product of two positive integers.\nA) 10\nB) 11\nC) 13\nD) 15\nE) 17",
"r... | math | {
"ground_truth": "B\\text{) }11",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, $EF$ and $GH$ are straight parallel lines. Line $IJ$ intersects $EF$ at point $K$ and $GH$ at point $L$, forming a $70^\\circ$ angle at $K$ and a $55^\\circ$ angl... | math | {
"ground_truth": "85^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a box initially containing 3 red, 3 green, and 3 yellow marbles, determine the probability that Cheryl takes 3 marbles of the same color after Carol takes 3 marbles at rand... | math | {
"ground_truth": "\\frac{1}{28}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest positive integer that is not the sum of a positive integral multiple of 42 and a positive composite integer?",
"role": "user"
}
] | math | {
"ground_truth": "215",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation in terms of $x$: $\\frac{3x-m}{2}-\\frac{x+m}{3}=\\frac{5}{6}$. \n$(1)$ If $m=-1$, find the solution to the equation. \n$(2)$ If $x=5$ is a solution to the e... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Anumber of schools took part in a tennis tournament. No two players from the same school played against each other. Every two players from different schools played exactly one ma... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The notation $[x]$ represents the greatest integer less than or equal to $x$ (for example, $[\\sqrt{5}] = 2$). Let $n$ be a natural number, and let $I = (n+1)^2 + n - [\\sqrt{(n+... | math | {
"ground_truth": "I > 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If one root of the quadratic equation $x^{2}+kx-2=0$ with respect to $x$ is $x=1$, then the other root of this quadratic equation is ____.",
"role": "user"
}
] | math | {
"ground_truth": "x=-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Paula initially had enough paint for 40 identically sized rooms and had reduced capacity to just enough paint for 30 rooms after losing 5 cans of paint, calculate the ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A function is given by the following expression, where $x$ is the variable, and $a$ and $b$ are constants, neither of which equals 1. What could be the domain of the function? Wh... | math | {
"ground_truth": "x \\in \\mathbb{R} \\setminus \\{ 1, a, b \\}, \\ f(x) = \\frac{a + b - ab}{(1-a)(1-b)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From $n$ positive integers $1$, $2$, $...$, $n$, if the probability of randomly selecting two different numbers such that their sum equals $5$ is $\\frac{1}{14}$, then $n=$ \\_\\... | math | {
"ground_truth": "n = 8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given on hypotenuse $AB$ of a right triangle $ABC$, another right triangle $ABD$ is constructed with $AB$ as the hypotenuse, and $\\overline{BC}=1$, $\\overline{AC}=3$, $\\overli... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What value of $x$ will give the minimum value of $3x^2 - 18x + 7$?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let two natural number $n > 1$ and $m$ be given. Find the least positive integer $k$ which has the following property: Among $k$ arbitrary integers $a_1, a_2, \\ldots, a... | math | {
"ground_truth": "d \\cdot \\left\\lfloor \\frac{n}{2d} \\right\\rfloor",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum to infinity of the terms of an infinite geometric progression is $9$. The sum of the first two terms is $7$. The first term of the progression is:\nA) $9$ or $9\\sqrt{2}$... | math | {
"ground_truth": "3(3+\\sqrt{2})",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let x, y, and z be the three numbers. If x + y + z = 30, x = 5y, and y = 9z, calculate the product of x, y, and z.",
"role": "user"
}
] | math | {
"ground_truth": "56.25",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a function $f(x) = ax - a + 1$, where $(a > 0 \\text{ and } a \\neq 1)$ always passes through the fixed point $(3,2)$,\n1. Find the real number $a$.\n2. Under the condition... | math | {
"ground_truth": "m \\geq 5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The lines \\( x = \\frac{1}{3}y + a \\) and \\( y = \\frac{1}{3}x + b \\) intersect at the point \\( (3,6) \\). Calculate \\( a + b \\).",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the rectangular coordinate system $xOy$, it is known that the eccentricity of the ellipse $(C\\_1)$: $\\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1 (a > b \\geqslant 1)$ is ... | math | {
"ground_truth": "\\frac{\\sqrt{65}}{8}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**Q11.** Let be given a sequense $a_1=5, \\; a_2=8$ and $a_{n+1}=a_n+3a_{n-1}, \\qquad n=1,2,3,...$ Calculate the greatest common divisor of $a_{2011}$ and $a_{2012}$ .",
... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A permutation of $\\{1, \\ldots, n\\}$ is drawn at random. How many fixed points does it have on average?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \"There exists $x \\in \\mathbb{R}$, such that $x + ax + a = 0$\" is a true statement, then the range of values for the real number $a$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 0] \\cup [4, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $ABC$ is inscribed in circle $\\omega$ with $AB=6$, $BC=8$, and $AC=5$. The median from vertex $A$ meets side $\\overline{BC}$ at $D$ and circle $\\omega$ at another poi... | math | {
"ground_truth": "72.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using the digits 3, 4, 7, and 8, form two two-digit numbers (each digit can only be used once and must be used) such that their product is maximized. What is the maximum product?... | math | {
"ground_truth": "6142",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S_n$ be the sum of the first $n$ terms of the geometric sequence $\\{a_n\\}$. If $S_3$, $S_9$, and $S_6$ form an arithmetic sequence, and $a_2 + a_5 = 2a_m$, then $m = \\box... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( P(x) = x^4 + ax^3 + bx^2 + cx + d \\), where \\( a, b, c, d \\) are constants. Given \\( P(1) = 1993 \\), \\( P(2) = 3986 \\), and \\( P(3) = 5979 \\), compute \\( \\frac... | math | {
"ground_truth": "4693",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two trains start simultaneously from two places 536 kilometers apart and move towards each other. They meet after 4 hours. If the slower train travels at 60 kilometers per hour, ... | math | {
"ground_truth": "74 \\text{ km/h}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( g(x) = \\frac{4}{16^x + 4} \\). Find the sum:\n\\[ g\\left( \\frac{1}{2002} \\right) + g\\left( \\frac{2}{2002} \\right) + g\\left( \\frac{3}{2002} \\right) + \\dots + g\... | math | {
"ground_truth": "1000.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression \\(2 + 22 + 222 + \\ldots + \\underbrace{222 \\ldots 2}_{2021}\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{20 \\cdot (10^{2021} - 1)}{81} - \\frac{2 \\cdot 2021}{9} = \\frac{2 \\cdot 10^{2022} - 36398}{81}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given tickets to a concert cost $x$ dollars, and a whole number, where a group of 11th graders buys tickets costing a total of $72$, a group of 12th graders buys tickets costing ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When $\\left ( 1 - \\frac{1}{a} \\right ) ^6$ is expanded, calculate the sum of the last three coefficients.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\( a=\\underset{2016 \\uparrow}{55 \\cdots 5} \\), determine the remainder when \\( a \\) is divided by 84.",
"role": "user"
}
] | math | {
"ground_truth": "63",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a graph with $8$ vertices that contains no cycle of length $4$ , at most how many edges can there be?",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For an integer $n$ , let $f_9(n)$ denote the number of positive integers $d\\leq 9$ dividing $n$ . Suppose that $m$ is a positive integer and $b_1,b_2,\\ldots,b_m$ are... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\log_2 x^2 + \\log_{1/2} x = 7,$ compute $x.$",
"role": "user"
}
] | math | {
"ground_truth": "128",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Provide an example of a function that is equal to zero for any values of \\( x \\) that are equal to any of the numbers \\( a_{1}, a_{2}, a_{3}, \\ldots, a_{n} \\), and as \\( x ... | math | {
"ground_truth": "\\frac{(x - a_1)(x - a_2)\\ldots(x - a_n)}{(x - b_1)(x - b_2)\\ldots(x - b_n)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The line $kx - y + 1 - 3k = 0$, as $k$ varies, always passes through a fixed point, find the coordinates of this fixed point.",
"role": "user"
}
] | math | {
"ground_truth": "(3, 1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the set $A=\\{1,2, \\cdots, 366\\}$. If a two-element subset $B=\\{a, b\\}$ of $A$ satisfies $17 \\mid(a+b)$, then $B$ is said to have property $P$.\n(1) Find the number of t... | math | {
"ground_truth": "179",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a rectangle in which $AB + BC + CD = 20$ and $AE = 9$ where $E$ is the midpoint of the side $BC$ . Find the area of the rectangle.",
"role": "user"
}... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of sets $M$ that satisfy $\\{1, 2\\} \\subsetneq M \\subseteq \\{1, 2, 3, 4, 5, 6\\}$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cylinder with a volume of 21 is inscribed in a cone. The plane of the upper base of this cylinder cuts off a truncated cone with a volume of 91 from the original cone. Find the... | math | {
"ground_truth": "94.5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( a + b + 1 \\) is a prime number, then one of the numbers \\( a!b! + 1 \\) and \\( a!b! - 1 \\) is divisible by \\( a + b + 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Therefore, one of the numbers } a! b! + 1 \\text{ or } a! b! - 1 \\text{ is divisible by } a + b + 1.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "All the edges of the regular tetrahedron \\(P-ABC\\) have length \\(1\\). Let \\( L, M, N \\) be the midpoints of the edges \\( PA, PB, PC \\) respectively. Find the area of the ... | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest value and the second greatest value among the numbers \\(4^{1/4}, 5^{1/5}, 7^{1/7}, 12^{1/12}\\).\nA) $4^{1/4}, 5^{1/5}$ \nB) $5^{1/5}, 7^{1/7}$ \nC) $7^{1/7}... | math | {
"ground_truth": "4^{1/4}, 5^{1/5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two lines $l_1: x+y-3m=0$ and $l_2: 2x-y+2m-1=0$, their intersection point is $M$. If the y-intercept of line $l_1$ is 3, \n(Ⅰ) Find the coordinates of point $M$; \n(Ⅱ) F... | math | {
"ground_truth": "3x+6y-16=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The volume of the region consisting of all points in three-dimensional space within $4$ units of line segment $\\overline{CD}$ is $432 \\pi$. Determine the length of $\\overline{... | math | {
"ground_truth": "\\frac{50}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The imaginary part of the complex number $z = \\frac{2 + i}{i}$, where $i$ is the imaginary unit, find the imaginary part of $z$.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all solutions of $a^2 + b^2 = n!$ for positive integers $a$ , $b$ , $n$ with $a \\le b$ and $n < 14$ .",
"role": "user"
}
] | math | {
"ground_truth": "(a, b, n) = (1, 0, 1), (1, 1, 2), (12, 24, 6)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x^{2}+2\\left(m-1\\right)x+4$ is a perfect square trinomial, then $m=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "3 \\text{ or } -1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a circular table with 80 chairs, there are N people seated at the table where the next person seated must sit next to someone already seated, find the smallest possible val... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the product of all real roots of the equation $x^{\\log_{2}{x}}=32$.\nA) \\( 1 \\)\nB) \\( 2 \\)\nC) \\( 2^5 \\)\nD) \\( 2^{-5} \\)",
"role": "user"
}
] | math | {
"ground_truth": "The correct answer is A) \\( 1 \\).",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For the quadratic equation $6x^2 + ax + 12x + 16 = 0$, determine the sum of the values of $a$ that make the equation have exactly one solution for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "-24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $(2^x - 4^x) + (2^{-x} - 4^{-x}) = 3$ , find the numerical value of the expression $$ (8^x + 3\\cdot 2^x) + (8^{-x} + 3\\cdot 2^{-x}). $$",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using any number of coins with denominations of 1, 2, 5, and 10 rubles, as well as (free) brackets and signs of the four arithmetic operations, create an expression with a value ... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of \\(k\\) so that the line \\(4x + 6y + k = 0\\) is tangent to the parabola \\(y^2 = 32x\\).",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Chloe chooses a real number uniformly at random from the interval $[0, 3500]$. Independently, Laurent chooses a real number uniformly at random from the interval $[0, 7000]$. Lau... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the three lines \\(4y - 3x = 2\\), \\(2x + 3y = 9\\) and \\(x - y = 1\\) are drawn in the plane, how many points will lie at the intersection of at least two of the three line... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What fraction of $\\frac{2}{3}$ is $\\frac{3}{8}$, and what is the result when this fraction is then tripled?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{27}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using only digits 1, 2, 3, 4, and 5, a sequence is created as follows: one 1, two 2's, three 3's, four 4's, five 5's, six 1's, seven 2's, and so on. What is the value of the 100t... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a fixed positive integer and let $x, y$ be positive integers such that $xy = nx+ny$ . \nDetermine the minimum and the maximum of $x$ in terms of $n$ .",
"... | math | {
"ground_truth": "n + 1 \\leq x \\leq n(n + 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the real number \\(a\\) ensures that the inequality \\( |x - 2a| + |2x - a| \\geq a^2 \\) holds for any real number \\(x\\), then what is the range of values for the real numb... | math | {
"ground_truth": "\\left[-\\frac{3}{2}, \\frac{3}{2}\\right]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $v$ and $w$ be distinct, randomly chosen roots of the equation $z^{2027}-1=0$. Find the probability that $\\sqrt{3} \\le \\left|v+w\\right|$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{225}{675}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $U=\\frac{1}{4-\\sqrt{9}}+\\frac{1}{\\sqrt{9}-\\sqrt{8}}-\\frac{1}{\\sqrt{8}-\\sqrt{7}}+\\frac{1}{\\sqrt{7}-\\sqrt{6}}-\\frac{1}{\\sqrt{6}-3}$, evaluate the value of $U$.",
... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive four-digit integers less than 5000 have at least two digits that are the same?",
"role": "user"
}
] | math | {
"ground_truth": "1984",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We define the bulldozer of triangle $ABC$ as the segment between points $P$ and $Q$ , distinct points in the plane of $ABC$ such that $PA\\cdot BC=PB\\cdot CA=PC\\cdot AB... | math | {
"ground_truth": "129",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) Given that $a < 0$, the terminal side of angle $\\alpha$ passes through point $P(-3a, 4a)$. Find the value of $\\sin\\alpha + 2\\cos\\alpha$.\n(2) Given that $\\tan\\beta = 2... | math | {
"ground_truth": "\\frac{8}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five coins are picked from a piggy bank containing pennies, nickels, dimes, and half-dollars. Which of the following could not be the sum of these five coins, in cents?\nA) 30 \... | math | {
"ground_truth": "E) 95",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a cube where its diagonal is equal to the perimeter of a square, what is the ratio of the area of the square to the volume of the cube?\n**A)** $\\frac{1}{16}$ \n**B)** $\... | math | {
"ground_truth": "\\frac{3}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice is choosing between two internet plans for her home office. Plan X charges no initial fee but costs 20 cents per gigabyte of data used. Plan Y has a one-time fee of $30 and... | math | {
"ground_truth": "301",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest value of positive integer $ x$ , such that the number \r\n\r\n $ A\\equal{} 2^{182} \\plus{} 4^x \\plus{} 8^{700}$ \r\n\r\n is a perfect square .",
"ro... | math | {
"ground_truth": "2008",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $\\frac {1}{3 - \\frac {1}{3 + \\frac {1}{3 - \\frac {1}{3}}}}$.\nA) $\\frac{24}{73}$\nB) $\\frac{27}{73}$\nC) $\\frac{27}{81}$\nD) $\\frac{27}{67}$\nE) $\... | math | {
"ground_truth": "\\frac{27}{73}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $2a^{2}-3a=1$, calculate the value of the algebraic expression $9a+7-6a^{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 11 members in total from two units, A and B, with unit A having 7 members and unit B having 4 members. A group of 5 people is to be formed from these members. \n\n1. Ho... | math | {
"ground_truth": "378",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a cube $ABCD-A_{1}B_{1}C_{1}D_{1}$ with edge length of $4$, where sphere $O$ is the inscribed sphere of the cube, $MN$ is the diameter of sphere $O$, and point $G$ is a mov... | math | {
"ground_truth": "\\left[0,8\\right]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a$ and $b$ are real numbers, the equation $3x-5+a=bx+1$ has a unique solution $x$ when the coefficient of $x$ in the equation is nonzero.",
"role": "user"
}
] | math | {
"ground_truth": "b \\neq 3",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n \\ge 4$ be an integer and let $T = \\{4,5,6,\\ldots,n\\}$. Find the smallest value of $n$ such that for every partition of $T$ into two subsets, at least one of the subset... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider 2 concentric circle radii $ R$ and $ r$ ( $ R > r$ ) with centre $ O.$ Fix $ P$ on the small circle and consider the variable chord $ PA$ of the small circle.... | math | {
"ground_truth": "6R^2 + 2r^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The base of a triangle is $30 \\text{ cm}$, and the other two sides are $26 \\text{ cm}$ and $28 \\text{ cm}$. The height of the triangle is divided in the ratio $2:3$ (counting ... | math | {
"ground_truth": "322.56 \\, \\text{cm}^2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A line with slope 4 intersects a line with slope -3 at the point $(8,20)$. What is the distance between the $x$-intercepts of these two lines?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{35}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Hazel, Leo, and Mia went shopping for art supplies and each bought a set number of colored pencils that can only be packaged in boxes containing the same number of pencils. Hazel... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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