data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the ordered triples $(a,b,c)$ of complex numbers that satisfy\n\\begin{align*}\na + bc &= 9, \\\\\nb + ac &= 15, \\\\\nc + ab &= 15.\n\\end{align*}\nbe $(a_1,b_1,c_1),$ $(a_2... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $r$ , $s$ be real numbers, find maximum $t$ so that if $a_1, a_2, \\ldots$ is a sequence of positive real numbers satisfying\n\\[ a_1^r + a_2^r + \\cdots + a_n^r \\le ... | math | {
"ground_truth": "t = 1 + \\frac{r}{s}",
"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 convex equilateral pentagon with side length $2$ has two right angles. The greatest possible area of the pentagon is $m+\\sqrt{n}$ , where $m$ and $n$ are positive integ... | math | {
"ground_truth": "407",
"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": "Natural numbers \\( x \\) and \\( y \\) satisfy the equation\n\n\\[ x^2 - 3x = 25y^2 - 15y \\]\n\nBy what factor is the number \\( x \\) greater than the number \\( y \\)?",
... | math | {
"ground_truth": "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": "How many sequences of $0$s and $1$s of length $21$ are there that begin with a $0$, end with a $0$, contain no two consecutive $0$s, and contain no three consecutive $1$s?\n**A)*... | math | {
"ground_truth": "**C)** 114",
"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 a disk with a radius of 8 cm rolls counter-clockwise around a circular clock face with a radius of 24 cm, at what point on the clock face will the disk be tangent when its a... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $\\left(\\dfrac{1+i}{2}\\right)^8 + \\left(\\dfrac{1-i}{2}\\right)^8.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{8}",
"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 six geometric means are inserted between $16$ and $11664$, calculate the sixth term in the geometric series.",
"role": "user"
}
] | math | {
"ground_truth": "3888",
"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 a right triangle \\(ABC\\) with a right angle at \\(B\\) and \\(\\angle A = 30^\\circ\\), a height \\(BD\\) is drawn. Then, in triangle \\(BDC\\), a median \\(DE\\) is drawn, ... | math | {
"ground_truth": "\\frac{1}{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": "A student was determining the interval $D$ where the root $x_0$ of the equation $x^3 = -x + 1$ lies. They set the function $f(x) = x^3 + x - 1$, calculated $f(-1) < 0$, and $f(1)... | math | {
"ground_truth": "(0.5, 0.75)",
"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 an arithmetic-geometric sequence $\\{a\\_n\\}$ that satisfies $2(a\\_3 + a\\_4) = 2 - a\\_1 - a\\_2$, find the minimum value of the sum of the first 6 terms of the sequence... | math | {
"ground_truth": "\\sqrt{3}",
"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 diagonals of a regular octagon also have different possible lengths. Determine the ratio of a shorter diagonal (connecting vertices one unit apart) to a longer diagonal (conn... | math | {
"ground_truth": "\\frac{1}{\\sqrt{2+\\sqrt{2}}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Before the World Cup, Coach $F$ of country $F$ plans to have players $A_{1}, A_{2}, \\cdots, A_{7}$ participate in three practice matches (each lasting 90 minutes). Suppose at an... | math | {
"ground_truth": "27352",
"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": "Determine all pairs of polynomials $f,g\\in\\mathbb{C}[x]$ with complex coefficients such that the following equalities hold for all $x\\in\\mathbb{C}$ : $f(f(x))-g(g(x))=1+i$... | math | {
"ground_truth": "f(x) = ix + 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": "Given that Albert's number is one more than twice Bob's, Bob's number is one more than twice Charlie's, and Charlie's number is two more than twice Albert's, determine the value ... | math | {
"ground_truth": "-\\frac{11}{7}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P$ be the plane passing through the origin with normal vector $\\begin{pmatrix} 2 \\\\ -1 \\\\ 2 \\end{pmatrix}.$ Find the matrix $\\mathbf{P}$ such that for any vector $\\m... | math | {
"ground_truth": "\\begin{pmatrix} \\frac{5}{9} & \\frac{4}{9} & -\\frac{4}{9} \\\\ \\frac{4}{9} & \\frac{11}{9} & \\frac{4}{9} \\\\ -\\frac{4}{9} & \\frac{4}{9} & \\frac{5}{9} \\end{pmatrix}",
"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": "Each of $n$ boys and $n$ girls chooses a random number from the set $\\{ 1, 2, 3, 4, 5 \\}$ , uniformly and independently. Let $p_n$ be the probability that every boy cho... | math | {
"ground_truth": "\\frac{6}{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": "4 kilograms = grams 3 meters - 2 decimeters = decimeters \n8 meters = decimeters 1600 grams - 600 grams = kilograms．",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are approximately 0.4536 kilograms in a pound. To the nearest whole pound, how many pounds does a bus that weighs 350 kg weigh?",
"role": "user"
}
] | math | {
"ground_truth": "772\\text{ pounds}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,$ $b,$ and $c$ be positive real numbers. Find the minimum value of\n\\[\\frac{a + b + 1}{c} + \\frac{a + c + 1}{b} + \\frac{b + c + 1}{a}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There is a unique angle $\\theta$ between $0^{\\circ}$ and $90^{\\circ}$ such that for nonnegative integers $n$, the value of $\\tan{\\left(2^{n}\\theta\\right)}$ is positive whe... | math | {
"ground_truth": "235",
"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 $a = 7$ and $b = 4$, calculate the value of $\\frac{5}{(a-b)^2}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{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": "Given that 3/8 of the students travel home by bus, 2/5 go home by car, 1/8 go home by bicycle, and 5% of the students use skateboards, find the fractional part of the students wh... | math | {
"ground_truth": "\\frac{1}{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": "Calculate the sum $1i + 2i^2 + 3i^3 + 4i^4 + 5i^5 + 6i^6 + ... + 2500i^{2500}$.\nA) -1251 + 1251i\nB) -1252 + 1252i\nC) -1253 + 1253i\nD) -1254 + 1254i",
"role": "user"
}
] | math | {
"ground_truth": "\\text{(B) }-1252 + 1252i",
"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 sum of all prime numbers between 1 and 200 that are simultaneously 1 greater than a multiple of 5 and 1 less than a multiple of 7.\nA) 41\nB) 181\nC) 222\nD) 139",
"... | math | {
"ground_truth": "C) \\ 222",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $EFG$, the sides are in the ratio $3:4:5$. Segment $FH$ is the angle bisector of $\\angle F$, dividing side $EG$ into segments $EH$ and $HG$. If the length of side $E... | math | {
"ground_truth": "\\frac{15}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$N$ friends simultaneously learned $N$ pieces of news, with each friend knowing one distinct piece of news. They start calling each other to exchange the news. Each conversation ... | math | {
"ground_truth": "7\\ \\text{hours}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are 800 students split into four groups of equal size, and a computer randomly assigns each student to one of the four lunch groups, determine the probability th... | math | {
"ground_truth": "\\frac{1}{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": "Let $ABC$ be a triangle with $AB = 5$ , $AC = 8$ , and $BC = 7$ . Let $D$ be on side $AC$ such that $AD = 5$ and $CD = 3$ . Let $I$ be the incenter of triangle $AB... | math | {
"ground_truth": "13",
"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": "Convert the quadratic equation $3x^{2}+1=6x$ to general form, the coefficient of the quadratic term is $3$, then the coefficient of the linear term is ______.",
"role": "user... | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, $AB = 7$, $BC = 24$, and the area of triangle $ABC$ is 84 square units. Given that the length of median $AM$ from $A$ to $BC$ is 12.5, find $AC$.",
"role":... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real polynomials \\( p(x) \\) such that \\( p(x^2 + x + 1) = p(x) p(x + 1) \\).",
"role": "user"
}
] | math | {
"ground_truth": "0, 1, (x^2 + 1)^n \\text{ for } n = 1, 2, 3, \\ldots",
"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": "Volume $ A$ equals one fourth of the sum of the volumes $ B$ and $ C$ , while volume $ B$ equals one sixth of the sum of the volumes $ C$ and $ A$ .\r\nFind the ratio o... | math | {
"ground_truth": "\\frac{23}{12}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $20\\%$ of the students are juniors and $80\\%$ are seniors with an overall average score of $86$, and the average score of the seniors is $85$, calculate the score re... | math | {
"ground_truth": "90",
"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 privateer discovers a merchantman $12$ miles to the leeward at 10:00 a.m. and pursues her at $10$ mph, while the merchantman moves at $7$ mph. If, after three hours of pursuit,... | math | {
"ground_truth": "E) 6:08 p.m.",
"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 all pairs of positive integers $m, n \\ge 3$ for which there exist infinitely many positive integers $a$ such that \\[\\frac{a^{m}+a-1}{a^{n}+a^{2}-1}\\] is itself an in... | math | {
"ground_truth": "(m, n) = (5, 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": "Find the sum of the roots of $\\tan^2x-6\\tan x+2=0$ that are between $x=0$ and $x=2\\pi$ radians.",
"role": "user"
}
] | math | {
"ground_truth": "3\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the curve $y=e^{x}$, its tangent line at point $(0,1)$ is perpendicular to the tangent line of the curve $y= \\frac{1}{x}$ (where $x > 0$) at point $P$. Determine the coord... | math | {
"ground_truth": "(1,1)",
"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": "In triangle $XYZ$, $XY = 12$, $XZ = 15$, and $YZ = 23$. The medians $XM$, $YN$, and $ZO$ of triangle $XYZ$ intersect at the centroid $G$. Let $Q$ be the foot of the altitude from... | math | {
"ground_truth": "\\frac{40}{23}",
"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": "For how many integers $n$ between 1 and 14 (inclusive) is $\\frac{n}{18}$ a repeating decimal?",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function defined on the interval $0 \\le x < 1$:\n\n\\[ \nf_{1}(x) = \\begin{cases} \n1, & \\text{if } 0.5 \\le x < 0.6 \\\\ \n0, & \\text{otherwise} \n\\end{cases} \n\... | math | {
"ground_truth": "\\frac{1}{10 - 9q}",
"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": "As shown in the diagram, \\( F \\) is a fixed point, \\( l \\) is a fixed line, and the distance from point \\( F \\) to line \\( l \\) is \\( p \\). Point \\( M \\) slides along... | math | {
"ground_truth": "\\begin{array}{ll}\n \\text{When } e = \\frac{1}{p} > 1, & \\text{Hyperbola, right of } l' \\\\\n \\text{When } e = \\frac{1}{p} = 1, & \\text{Parabola, right of } l' \\\\\n \\text{When } 0 < e = \\frac{1}{p} < 1, & \\text{Ellipse, right of } l'\n \\end{array}",
"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 centers of two circles are $50$ inches apart. One circle has a radius of $7$ inches, while the other has a radius of $10$ inches. Calculate the length of the common internal ... | math | {
"ground_truth": "\\sqrt{2211} \\, \\text{inches}",
"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 that $b>1$, $x>0$, and $(4x)^{\\log_b 2} - (5x)^{\\log_b 3}=0$, determine the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{4}{5}\\right)^{\\log_{\\frac{3}{2}} b}",
"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 the set \\( S = \\{1, 2, \\ldots, 30\\} \\). There are 10 subsets, \\( A_1, A_2, \\ldots, A_{10} \\), each containing 3 elements, where any two subsets \\( A_i \\) and \... | math | {
"ground_truth": "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": "For reals $x\\ge3$ , let $f(x)$ denote the function\n\\[f(x) = \\frac {-x + x\\sqrt{4x-3} } { 2} .\\]Let $a_1, a_2, \\ldots$ , be the sequence satisfying $a_1 > 3$ , $a_{20... | math | {
"ground_truth": "4025",
"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 function $f(x)= \\sqrt {|x+5|-|x-1|+t}$ with a domain of $R$.\n(1) Find the range of values for the real number $t$;\n(2) If the minimum value of $t$ is $s$, and positi... | math | {
"ground_truth": "\\frac {3}{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": "Eight trees are equally spaced along one side of a straight road. The distance from the first tree to the fifth is 100 feet. Calculate the distance in feet between the first and ... | math | {
"ground_truth": "175",
"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 all real solutions to the equation\n\n\\[\nx^{2}+2x\\sin(xy)+1=0\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "(x, y) = (\\pm 1, -\\frac{\\pi}{2} + k\\pi)",
"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 all primes $p \\ge 3$ such that $p- \\lfloor p/q \\rfloor q$ is a square-free integer for any prime $q<p$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\{3, 5, 7, 13\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a geometric sequence of real numbers, the sum of the first $3$ terms is $13$, and the sum of the first $7$ terms is $183$. Find the sum of the first $5$ terms.\nA) 33\nB) 35\n... | math | {
"ground_truth": "C) 37",
"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 $ABC$ be an acute triangle and $AD$ a height. The angle bissector of $\\angle DAC$ intersects $DC$ at $E$ . Let $F$ be a point on $AE$ such that $BF$ is perpen... | math | {
"ground_truth": "135^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sphere is inscribed in a cube that has a surface area of 24 square meters. A second cube is then inscribed within the sphere. Calculate the surface area in square meters of the... | math | {
"ground_truth": "8",
"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": "Consider a regular tetrahedron with vertices A, B, C, and D where each edge measures 1 unit. Let P be a point on edge AB and Q be a point on edge BC. Determine the least possible... | 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": "Equilateral triangle $ABC$ has point $P$ inside and point $Q$ on side $BC$ such that $PB=PQ=QC$ and $\\angle PBC=20^o$ . Find the measure of $\\angle AQP$ .",
... | math | {
"ground_truth": "40^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a < 0$, then the solution set of the inequality $(x-1)(ax-4) < 0$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|x > 1 \\text{ or } x < \\frac{4}{a}\\}",
"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": "On the sides $AB$, $BC$, and $AC$ of triangle $ABC$, whose area is 75, points $M$, $N$, and $K$ are respectively located. It is known that $M$ is the midpoint of $AB$, the area o... | 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": "Positive real numbers $x$ and $y$ satisfy $$ \\Biggl|\\biggl|\\cdots\\Bigl|\\bigl||x|-y\\bigr|-x\\Bigr|\\cdots -y\\biggr|-x\\Biggr|\\ =\\ \\Biggl|\\biggl|\\cdots\\Bigl|\\big... | 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": "Select the dimensions of a regular tetrahedral pyramid such that the ratio of the radii of the circumscribed and inscribed spheres is minimized.",
"role": "user"
}
] | math | {
"ground_truth": "1 + \\sqrt{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Natural numbers are placed in an infinite grid. Such that the number in each cell is equal to the number of its adjacent cells having the same number. Find the most distinct numb... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the following expressions:\n1. $(1)(2a^{\\frac{2}{3}}b^{\\frac{1}{2}})(-6a^{\\frac{1}{2}}b^{\\frac{1}{3}}) \\div (-3a^{\\frac{1}{6}}b^{\\frac{5}{6}}) (a > 0, b > 0)$\n2... | math | {
"ground_truth": "1 + \\frac{1}{2}\\lg{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": "You have four shirts and five pairs of pants. How many outfits consisting of one shirt, one pair of pants, and one hat can you make if you have three hats available?",
"role"... | math | {
"ground_truth": "60",
"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 $\\log_3(\\log_3(\\log_3(x)))=3$, find the number of digits in the base-ten representation of $x$.",
"role": "user"
}
] | 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": "If 20 bahs are equal to 30 rahs, and 12 rahs are equal in value to 20 yahs, how many bahs are equal in value to 500 yahs?",
"role": "user"
}
] | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A group of schoolchildren decided to buy pizza. Each pizza is cut into 12 slices. They calculated that if each boy eats 7 slices and each girl eats 2 slices, three pizzas will no... | math | {
"ground_truth": "1 \\text{ girl and 5 boys.}",
"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 $\\triangle ABC$, the sides opposite to angles A, B, and C are denoted as $a$, $b$, and $c$ respectively. Given that $a= \\sqrt{2}$, $b=2$, and $\\sin B - \\cos B = \\sqrt{2}$... | math | {
"ground_truth": "\\frac{\\pi}{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integers $a$ and $b$ are such that $a < 6$ and $b \\leq 7$. Calculate the smallest possible value for $2 \\cdot a - a \\cdot b$.",
"role": "user"
}
] | math | {
"ground_truth": "-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": "Let $A, B, C, D$ be points, in order, on a straight line such that $AB=BC=CD$ . Let $E$ be a point closer to $B$ than $D$ such that $BE=EC=CD$ and let $F$ be the mid... | math | {
"ground_truth": "250",
"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 slope of the tangent line to the curve $y = \\frac{1}{3}x^{3}-2$ at the point $x=-1$ is equal to what value?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of $f'( \\frac{\\pi}{2} )$ where $f(x) = x \\cdot \\cos{x}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{\\pi}{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 the set $A=\\{x|mx=1\\}=\\phi$, the value of $m$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "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": "For any positive integer $N$, the notation $N!$ denotes the product of integers $1$ through $N$. What is the largest integer $n$ for which $5^n$ is a factor of the sum $97! + 98!... | math | {
"ground_truth": "The correct choice is C) 22.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In △ABC, the sides opposite to angles A, B, and C are a, b, and c, respectively. If sinA=2sinB, c= $\\sqrt {2}$, and cosC= $\\frac {3}{4}$, then the area of triangle ABC is _____... | math | {
"ground_truth": "\\frac { \\sqrt {7}}{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": "For a real number $x,$ find the maximum value of \n\\[\n\\frac{x^6}{x^{10} + 3x^8 - 6x^6 + 12x^4 + 32}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $n=3 \\int _{ - \\frac {\\pi}{2} }^{ \\frac {\\pi}{2} }(\\sin x+\\cos x)dx$, then the constant term in the expansion of $(y+ \\dfrac {2}{y})^{n}$ is \\_\\_\\_\\_\\_.",
"ro... | math | {
"ground_truth": "160",
"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": "Factorize: $4m^{3}n-16mn^{3}=$____.",
"role": "user"
}
] | math | {
"ground_truth": "4mn(m+2n)(m-2n)",
"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 girl has three different types of coins in her wallet: $3$ nickels, $3$ dimes, and $2$ quarters. She also adds $2$ half-dollars. She randomly picks two coins, calculates the to... | math | {
"ground_truth": "10",
"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": "Xiaopang and Xiaoya are counting their storybooks. It is known that if Xiaopang gives 8 books to Xiaoya, they will have the same number of books. Moreover, if Xiaoya gives 4 book... | math | {
"ground_truth": "32 \\text{ books}",
"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 $X=\\{1,2,3,...,10\\}$ . Find the number of pairs of $\\{A,B\\}$ such that $A\\subseteq X, B\\subseteq X, A\\ne B$ and $A\\cap B=\\{5,7,8\\}$ .",
"role": "user"
}... | math | {
"ground_truth": "2186",
"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": "Observing the following expressions: $1\\times 3+1=2^{2}$, $2\\times 4+1=3^{2}$, $3\\times 5+1=4^{2}$, $4\\times 6+1=5^{2}$, $\\ldots $, \n$(1)$ Please write out the $6$th expre... | math | {
"ground_truth": "\\frac{99}{50}",
"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": "Express, as concisely as possible, the value of the product\n$$\n\\left(0^{3}-350\\right)\\left(1^{3}-349\\right)\\left(2^{3}-348\\right)\\left(3^{3}-347\\right)\\cdots\\left(349... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the radius of convergence of the power series\n\n$$\n\\sum_{n=0}^{\\infty} \\cos(i \\cdot n) \\cdot z^{n}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "e^{-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": "Given that $\\frac{2}{3}$ of the balloons are yellow and the rest are green, and the number of green balloons is tripled while the number of yellow balloons remains constant, det... | math | {
"ground_truth": "\\text{In a box of balloons, $\\frac{2}{3}$ of the balloons are yellow and the rest are green. If the number of green balloons is tripled while the number of yellow balloons remains constant, what fraction of the balloons will be green?}",
"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 that a line with slope \\( k \\) passes through a focus of the ellipse \\( x^2 + 2y^2 = 3 \\) and intersects the ellipse at points \\( A \\) and \\( B \\). If \\( AB = 2 \\... | math | {
"ground_truth": "\\sqrt{1 + \\sqrt{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": "Given the following propositions:\n1. If $k > 0$, then the equation $x^2 + 2x - k = 0$ has real roots;\n2. The negation of \"If $a > b$, then $a + c > b + c$\";\n3. The converse ... | math | {
"ground_truth": "1, 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": "What is the area of the polygon with vertices at $(2,1)$, $(4,3)$, $(6,1)$, and $(4,6)$?",
"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": "The average age of 7 people in a room is 28 years. A 22-year-old person leaves the room, and immediately after, a new person aged 30 years enters. Find the new average age of the... | math | {
"ground_truth": "29",
"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 $P$ be the set of all $2012$ tuples $(x_1, x_2, \\dots, x_{2012})$ , where $x_i \\in \\{1,2,\\dots 20\\}$ for each $1\\leq i \\leq 2012$ . The set $A \\subset P$ is... | math | {
"ground_truth": "\\frac{1}{20^{2012}}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ P,\\ Q,\\ R$ be the points such that $ BP: PC=CQ: QA=AR: RB=t: 1-t\\ (0<t<1)$ for a triangle $ ABC$ .\r\nDenote $ K$ by the area of the triangle with segments $ AP,... | math | {
"ground_truth": "(1-t+t^2)^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": "Let $p$ and $q$ be the solutions of the equation $3x^2 - 9x - 15 = 0$. Calculate the value of $(3p-5)(6q-10)$.",
"role": "user"
}
] | math | {
"ground_truth": "-130",
"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 two points $(2, -2)$ and $(6, 6)$, find the $x$-intercept of the straight line joining them.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a tournament with $55$ participants, one match is played at a time, with the loser dropping out. In each match, the numbers of wins so far of the two participants differ by ... | math | {
"ground_truth": "8",
"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 all pairs $(x, y)$ of positive integers such that $(x + y)(x^2 + 9y)$ is the cube of a prime number.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of a plane with intercepts on the x, y, and z axes of a, b, and c (abc ≠ 0) respectively is represented by the equation.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x}{a} + \\frac{y}{b} + \\frac{z}{c} = 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 the power function $f(x)=({m}^{2}-\\frac{7}{2}m+\\frac{5}{2}){x}^{m}$ passes through the third quadrant.<br/>$(1)$ Find the value of $m$;<br/>$(2)$ Solve the inequality in ... | math | {
"ground_truth": "(0,+\\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": "Given two real numbers $a, b$ with $a \\neq 0$ , find all polynomials $P(x)$ which satisfy\n\\[xP(x - a) = (x - b)P(x).\\]",
"role": "user"
}
] | math | {
"ground_truth": "P(x) = Ax(x - a)(x - 2a) \\cdots (x - (k - 1)a)",
"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 $\\overrightarrow{a}=(4,3)$, $\\overrightarrow{b}=(-1,2)$. \n$(1)$ Find $|\\overrightarrow{b}|$; \n$(2)$ Find the cosine of the angle between $\\overrightarrow{a}$ and $\... | math | {
"ground_truth": "\\dfrac{2\\sqrt{5}}{25}",
"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": "Factorize: $x+x^2-y-y^2$.",
"role": "user"
}
] | math | {
"ground_truth": "(x+y+1)(x-y)",
"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 $a > 0, b > 0, a+b=2$, the minimum value of $y=\\frac{1}{a}+\\frac{4}{b}$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{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": "Let $A$ and $B$ be points with $AB=12$ . A point $P$ in the plane of $A$ and $B$ is $\\textit{special}$ if there exist points $X, Y$ such that\n\n\n- $P$ lies on ... | math | {
"ground_truth": "1331",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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