data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An engineer is designing an engine. Each cycle, it ignites a negligible amount of fuel, releasing $ 2000 \\, \\text{J} $ of energy into the cubic decimeter of air, which we ass... | math | {
"ground_truth": "0.33",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\(\\sin 2\\alpha + \\sin 2\\beta + \\sin 2\\gamma = 4 \\sin \\alpha \\sin \\beta \\sin \\gamma\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\sin 2\\alpha + \\sin 2\\beta + \\sin 2\\gamma = 4 \\sin \\alpha \\sin \\beta \\sin \\gamma",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The circle inscribed in a right-angled triangle with legs of lengths 6 and 8 touches the hypotenuse at point \\( M \\). Find the distance from point \\( M \\) to the vertex of th... | math | {
"ground_truth": "2 \\sqrt{\\frac{29}{5}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the complex number $z$ satisfies $z\\cdot(3-4i)=1$, determine the imaginary part of $z$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{4}{25}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a quadrilateral inscribed in the unit circle such that $\\angle BAD$ is $30$ degrees. Let $m$ denote the minimum value of $CP + PQ + CQ$ , where $P$ and ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The suggested retail price of a jacket was $120. The actual selling price was marked at 40% less than the suggested retail price during a store clearance event. During the final ... | math | {
"ground_truth": "C) 48%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of $8$ -tuples $(\\epsilon_1, \\epsilon_2,...,\\epsilon_8)$ such that $\\epsilon_1, \\epsilon_2, ..., 8 \\in \\{1,-1\\}$ and $\\epsilon_1 + 2\\epsilon_... | math | {
"ground_truth": "88",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A subscriber forgot the last digit of a phone number and therefore dials it randomly. What is the probability that they will have to dial the number no more than three times?",
... | math | {
"ground_truth": "0.3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\{a_n\\}$ satisfies $a_1=0$, $a_{n+1}=a_n+2n$, find the value of $a_{2012}$.",
"role": "user"
}
] | math | {
"ground_truth": "2011 \\times 2012",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular hexagon \\( A B C D E F \\) with side length \\( 10 \\sqrt[4]{27} \\), find the area of the union of triangles \\( ACE \\) and \\( BDF \\).",
"role": "user"
... | math | {
"ground_truth": "900",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the rectangle shown, find the value of \\(a - b\\).",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A jeweler can get an alloy that is $40\\%$ gold for $200$ dollars per ounce, an alloy that is $60\\%$ gold for $300$ dollar per ounce, and an alloy that is $90\\%$ gold... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of the expression: $\\frac{1}{1 + \\frac{1}{3 + \\frac{1}{4}}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{17}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $D = a^2 + b^2 + c^2$, where $b = a+2$, and $c = a(b-1)$. Compute $\\sqrt{D}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{D} = x^2 + 2x + 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, $\\overline{AB}$ and $\\overline{CD}$ are diameters of a circle with center $O$, with $\\overline{AB} \\perp \\overline{CD}$. Chord $\\overline{DF}$ intersects $\... | math | {
"ground_truth": "48\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the sum of the nine smallest distinct even positive integer multiples of 7?",
"role": "user"
}
] | math | {
"ground_truth": "630",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the area of triangle $XYZ$ is $100$ square units, and the geometric mean between sides $XY$ and $XZ$ is $15$ units, find $\\sin X$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five fair six-sided dice are rolled. What is the probability that at least four of the five dice show the same value?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{648}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, $AB = 13$, $BC = 15$, and $CA = 14$. Let $E$ be a point on the interior of $\\overline{BC}$. Let points $I_B$ and $I_C$ denote the incenters of triangles $ABE$... | math | {
"ground_truth": "171.75",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Carina baked a cake and cut it into ten equal pieces. She ate one piece and then arranged the remaining pieces evenly. What is the size of the angle at the center of the cake bet... | math | {
"ground_truth": "B \\; 4^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the random variable $\\xi \\sim N(0, \\sigma ^{2})$, and $P(\\xi \\geq 1) = 0.4$, find $P(-1 \\leq \\xi \\leq 0)$.",
"role": "user"
}
] | math | {
"ground_truth": "0.1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given circle $O: x^2+y^2=4$ and its intersection point with the positive y-axis is $M$, point $M$ moves clockwise along circle $O$ for an arc length of $\\frac{\\pi}{2}$ to reach... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ be a function piecewise defined as\n\\[\nf(x) = \\left\\{\n\\begin{array}{cl}\n2x & x\\le 0, \\\\\n3x - 52 & x>0.\n\\end{array}\n\\right.\n\\]\nIf $a$ is negative, fin... | math | {
"ground_truth": "a = -19",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many integers $x$ satisfy the equation $(x^2-x-1)^{x+2}=1$?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rancher has $1300 to spend on purchasing steers and cows. Each steer costs $30 and each cow costs $33. If the number of steers $s$ and the number of cows $c$ are both positive ... | math | {
"ground_truth": "B) 30 cows",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The motion equation of an object is $s=3+t^2$. Find the average velocity of the object during the time interval $[2, 2.1]$.",
"role": "user"
}
] | math | {
"ground_truth": "4.1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four positive integers $p,$ $q,$ $r,$ $s$ satisfy\n\\[ p \\times q \\times r \\times s = 9! \\]\nFind the smallest possible value of $p + q + r + s.$",
"role": "user"
}
] | math | {
"ground_truth": "133",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all functions $f:\\mathbb{Z} \\rightarrow \\mathbb{Z}$ which satisfy the following equations:\na)\t $f(f(n))=4n+3$ $\\forall$ $n \\in \\mathbb{Z}$ ;\nb)\t $f(f(n)... | math | {
"ground_truth": "f(n) = 2n + 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ A$ be an integer not equal to $ 0$ . Solve the following system of equations in $ \\mathbb{Z}^3$ .\r $ x \\plus{} y^2 \\plus{} z^3 \\equal{} A$ \r $ \\frac {1}{x} \\plu... | math | {
"ground_truth": "(x, y, z) = (-k^{12}, \\pm k^3, -k^2) \\quad \\text{or} \\quad (x, y, z) = (-k^3, \\pm k^3, -k^4)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a + 2 = b + 3 = c + 4 = d + 5 = a + b + c + d + 15$. What is $a + b + c + d$?\nA) $-\\frac{14}{3}$\nB) $-\\frac{46}{3}$\nC) $-\\frac{50}{3}$\nD) $-\\frac{42}{3}$",
"role... | math | {
"ground_truth": "\\text{(B)}\\ -\\frac{46}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. $S_1, S_2, \\ldots, S_n$ are pairwise non-intersecting sets, and $S_k $ has exactly $k$ elements $(k = 1, 2, \\ldots, n)$ . Define $S = S... | math | {
"ground_truth": "\\frac{(n+1)!n^2(n-1)}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x,y$ be real numbers with $x \\geqslant \\sqrt{2021}$ such that\n\\[ \\sqrt[3]{x+\\sqrt{2021}}+\\sqrt[3]{x-\\sqrt{2021}} = \\sqrt[3]{y}\\]\nDetermine the set of all poss... | math | {
"ground_truth": "\\frac{y}{x} \\in [2, 8)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a function \\( y = f(x) \\) such that shifting its graph 30 units to the right results in the identical graph \\( y = f(x) \\). Determine the smallest positive \\( b \\)... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ be an odd function defined on $\\mathbb{R}$, and it satisfies $f(x) = f(x+4)$, $f(1) = 1$. Calculate $f(-1) + f(8)$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cubic block with dimensions $n$ by $n$ by $n$ is made up of a collection of $1$ by $1$ by $1$ unit cubes. What is the smallest value of $n$ so that if the outer t... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In rectangle $ABCD$, $AB = 8$ cm, $BC = 10$ cm, and $DF = 2 \\times DE$. The area of triangle $DEF$ is one-fourth the area of rectangle $ABCD$. What is the length in centimeters ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a 90-minute lecture attended by 200 people, 30% of the audience listened to the entire lecture, while 5% slept through it. Of the remaining audience, 40% heard half of the lec... | math | {
"ground_truth": "B) 47.5 minutes",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which values of \\(a\\) does the system \n\\[\n\\begin{cases}\n(x-7 \\cos a)^{2}+(y-7 \\sin a)^{2}=1 \\\\\n|x|+|y|=8\n\\end{cases}\n\\]\nhave a unique solution?",
"role":... | math | {
"ground_truth": "a= \\pm \\arcsin \\left(\\frac{4\\sqrt{2} + 1}{7} \\right) + \\frac{(2k-1) \\pi}{4}, k \\in \\mathbb{Z}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sequence of natural numbers $c_1, c_2,\\dots$ is called *perfect* if every natural\nnumber $m$ with $1\\le m \\le c_1 +\\dots+ c_n$ can be represented as $m =\\frac{c_1}{... | math | {
"ground_truth": "C_n = 4 \\times 3^{n-2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $N$ such that $N$ contains only the prime factors 2 and 5, and $N + 25$ is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "200 \\text{ and } 2000",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find $\\tan B$ in a right triangle with sides as follows:\n\n[asy]\npair A,B,C;\nA = (0,0);\nB = (12,0);\nC = (0,5);\n\ndraw(C--B--A--C);\ndraw(rightanglemark(C,A,B,20));\n\nlabe... | math | {
"ground_truth": "\\frac{5}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Jack needs to bike a total of eight blocks, with each block traveled east or north, and avoiding two specific intersections, determine the number of possible routes to... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $12\\cdot\\left(\\tfrac{1}{3}+\\tfrac{1}{4}+\\tfrac{1}{6}\\right)^{-1}$.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A collection of $2000$ congruent circles is given on the plane such that no \r\ntwo circles are tangent and each circle meets at least two other circles. \r\nLet $N$ be the n... | math | {
"ground_truth": "3997",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the area of the smallest region enclosed by $y = |x|$ and $x^2 + y^2 = 9$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9\\pi}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any interval $\\mathcal{A}$ in the real number line not containing zero, define its *reciprocal* to be the set of numbers of the form $\\frac 1x$ where $x$ is an elemen... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that two pitchers, each containing $600$ mL of orange juice, are filled to different levels, one pitcher being $1/3$ full and the other being $2/5$ full, then calculate the... | math | {
"ground_truth": "\\frac{11}{30}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer that cannot be expressed in the form \\(\\frac{2^{a}-2^{b}}{2^{c}-2^{d}}\\), where \\(a, b, c, d\\) are non-negative integers.",
"role": "u... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute \\(\\dbinom{6}{2}\\).",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $\\begin{pmatrix} 4 & 2 \\\\ -1 & 5 \\end{pmatrix} \\begin{pmatrix} -2 \\\\ 3 \\end{pmatrix}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{pmatrix} -2 \\\\ 17 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The roots of the cubic equation $Ax^3 + Bx^2 + Cx + D = 0$ are $u$, $v$, and $w$. If the quadratic equation $x^2 + px + q = 0$ has roots $u^2$, $v^2$, then find the value of $p$ ... | math | {
"ground_truth": "\\textbf{(A)}\\ \\frac{B^2 - 2C}{A^2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real numbers $x$ such that \\[2 \\le \\frac{x}{3x-5} < 9.\\](Give your answer in interval notation.)",
"role": "user"
}
] | math | {
"ground_truth": "(\\frac{45}{26}, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( A \\) represent the set of integer solutions \\(\\left(x_{1}, x_{2}, \\cdots, x_{2n}\\right)\\) to the equation \\( x_{1}+x_{2}+\\cdots+x_{2n}=n \\) that satisfy the cons... | math | {
"ground_truth": "\\frac{1}{n} C_{2n-2}^{n-1}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bill is tasked with purchasing exactly eight donuts from a shop offering six different kinds. He must buy at least two of each of three specific kinds but has no restrictions on ... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $T = TNFTPP$ . Triangle $ABC$ has integer side lengths, including $BC = 100T - 4$ , and a right angle, $\\angle ABC$ . Let $r$ and $s$ denote... | math | {
"ground_truth": "1624",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define the determinant $D_1$ = $|1|$ , the determinant $D_2$ =\f \f \f \f \f \f $|1 1|$ $|1 3|$ \f \f \f \f \f \f\n, and the determinant $D_3=$ \f \f \f \f \f \f \f \f \f... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the four digits 2, 3, 5, and 8, how many different positive three-digit integers can be formed using these digits if a digit may not be repeated in an integer?",
"role"... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cube has faces numbered with consecutive integers, including negative numbers. The sum of the numbers on each pair of opposite faces is the same. If the smallest number is -3, ... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the hyperbola given by the equation \\[\\frac{(y-1)^2}{16} - \\frac{(x+2)^2}{9} = 1.\\] This hyperbola has asymptotes of the form $y - 1 = \\pm mx + 2m$. Find the value ... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A school holds a speech contest with 10 participants: 3 from Class 1, 2 from Class 2, and 5 from other classes. The speaking order is determined by drawing lots. Calculate the pr... | math | {
"ground_truth": "\\frac{1}{20}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of $k$ if $3 \\cdot 2^{2001} - 3 \\cdot 2^{2000} - 2^{1999} + 2^{1998} = k \\cdot 2^{1998}$.\nA) 9 \nB) 10 \nC) 11 \nD) 13 \nE) 14",
"role": "user"
}
] | math | {
"ground_truth": "C) 11",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Convert the number $529_{10}$ to a base-7 number and count the number of even digits.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\sqrt[3]{x+6}=3$, calculate the value of $(x+6)^3$.",
"role": "user"
}
] | math | {
"ground_truth": "(x+6)^3 = 19683",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If two lines $l$ and $m$ have equations $y = -2x + 8$, and $y = -3x + 9$, what is the probability that a point randomly selected in the 1st quadrant and below $l$ will fall betwe... | math | {
"ground_truth": "0.16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $f(x) = a\\ln x + \\frac{1}{2}x^2$ ($a > 0$), if for any two different positive real numbers $x_1$, $x_2$, it always holds that $\\frac{f(x_1) - f(x_2)}{x_1 - x_2} \\geq 2$... | math | {
"ground_truth": "[1, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The volume of the parallelepiped generated by $\\begin{pmatrix} 3 \\\\ 3 \\\\ 4 \\end{pmatrix},$ $\\begin{pmatrix} 1 \\\\ k \\\\ 3 \\end{pmatrix},$ and $\\begin{pmatrix} 2 \\\\ 2... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "During chemistry labs, we oftentimes fold a disk-shaped filter paper twice, and then open up a flap of the quartercircle to form a cone shape, as in the diagram. What is the angl... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive integers $n$ such that it is possible to fill the $n \\times n$ table with numbers $1, 2$ and $-3$ so that the sum of the numbers in each row and e... | math | {
"ground_truth": "n \\geq 3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the cartesian coordinate plane $(xOy)$, two circles $C\\_1$ and $C\\_2$ are given, where $C\\_1: (x+3)^2+(y-1)^2=4$ and $C\\_2: (x-4)^2+(y-5)^2=1$.\n\n(I) If a line $l$ passes... | math | {
"ground_truth": "k \\in (-\\infty, -2\\sqrt{30}] \\cup [2\\sqrt{30}, \\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangle $ABC$ , consider the semicircle with diameter $\\overline{EF}$ on $\\overline{BC}$ tangent to $\\overline{AB}$ and $\\overline{AC}$ . If $BE=1$ , $EF=2... | math | {
"ground_truth": "175",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Sally has 150 coins consisting only of nickels, dimes, and quarters, totaling $20.00, and the collection contains coins of all three types, determine the difference be... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a parliament with 30 members, where every two members are either friends or enemies, and each member has exactly 6 enemies. A committee of three members is formed. If all t... | math | {
"ground_truth": "1990",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When $126$ is added to its reversal, $621,$ the sum is $126 + 621 = 747.$ Find the greatest integer which when added to its reversal yields $1211.$",
"role": "user"
... | math | {
"ground_truth": "952",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $x^3y = k$ for a positive constant $k$, find the percentage decrease in $y$ when $x$ increases by $20\\%$.",
"role": "user"
}
] | math | {
"ground_truth": "42.13\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine $\\left[\\frac{(2^3}{4^2}\\right] \\odot 6] - \\left[2 \\odot \\frac{(4^3}{6^2}\\right]$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{81}{32}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $F$ be the family of all sets of positive integers with $2010$ elements that satisfy the following condition:\nThe difference between any two of its elements is never the... | math | {
"ground_truth": "4040100",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We divide a given segment into 3 parts by selecting two random points. What is the probability that a triangle can be constructed from these 3 segments? Solve the problem using a... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the two sides of angle $\\angle A$ are parallel to the two sides of angle $\\angle B$, and that the measure of angle $\\angle A$ is $20^\\circ$ less than three times t... | math | {
"ground_truth": "10^\\circ \\text{ or } 130^\\circ",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sixteen dots are arranged in a four by four grid as shown. The distance between any two dots in the grid is the minimum number of horizontal and vertical steps along the grid lin... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain swimming pool offers two payment methods for swimming in the summer. Method one: first purchase a membership card for $120$ yuan, which can only be used by the cardhold... | math | {
"ground_truth": "\\text{Method one is less expensive for Zhang when swimming at least 40 times.}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Distribute some books to several students. If each person receives 3 books, there will be 6 books left over. If each of the previous students receives 5 books, then the last pers... | math | {
"ground_truth": "21, 5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The fourth-degree equation $x^4-x-504=0$ has $4$ roots $r_1$ , $r_2$ , $r_3$ , $r_4$ . If $S_x$ denotes the value of ${r_1}^4+{r_2}^4+{r_3}^4+{r_4}^4$ , compute $S_4$... | math | {
"ground_truth": "2016",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the operation \\( \\star \\) is defined as \\( a \\star b = a + \\frac{a}{b} \\), and \\( \\circ \\) is defined such that \\( x \\circ y = x \\star y \\times y \\), what is th... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$ is denoted as $S_n$. If $S_3 + 3S_2 = 0$, then the common ratio $q=$ .",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given four numbers \\(a, b, c, d\\). Each pair of these numbers is summed, resulting in 6 sums: \\(a+b, b+c, c+d, a+c, b+d, a+d\\). The four smallest of these sums are \\(7, 15, ... | math | {
"ground_truth": "56.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( A, B, C \\) be points in a line in this order, with \\( AB = BC \\). A car travels from \\( A \\) to \\( B \\) at 40 kilometers per hour and then from \\( B \\) to \\( C ... | math | {
"ground_truth": "48 \\text{ kilometers per hour}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $X=\\{1,2,3,...,10\\}$ . Find the number of pairs of $\\{A,B\\}$ such that $A\\subseteq X, B\\subseteq X, A\\ne B$ and $A\\cap B=\\{2,3,5,7\\}$ .",
"role": "user"
... | math | {
"ground_truth": "1330",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the remainders when \\(a^{4}\\) is divided by 5 for all possible integer values of \\(a\\).",
"role": "user"
}
] | math | {
"ground_truth": "0 \\text{ and } 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$B$ needs 6 more days to complete a task than $A$, and $C$ needs 3 more days than $B$. If $A$ works for 3 days and $B$ works for 4 days together, they complete the same amount of... | math | {
"ground_truth": "18 \\text{, } 24 \\text{, } 27",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rationalize the denominator of $\\displaystyle\\frac{50 + \\sqrt{8}}{\\sqrt{50} + \\sqrt{8}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{50(\\sqrt{50} - \\sqrt{8}) + 12}{42}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are the following four statements:\n① Two lines perpendicular to the same line are parallel;\n② Two planes perpendicular to the same line are parallel;\n③ Two lines perpend... | math | {
"ground_truth": "\\text{②③}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( \\triangle ABC \\), the angles are \\( \\angle B = 30^\\circ \\) and \\( \\angle A = 90^\\circ \\). Point \\( K \\) is marked on side \\( AC \\), and points \\( L... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a \"Modulo $m$ graph paper\" where $m=7$. Graph the congruence $$ 2x \\equiv 3y + 1 \\pmod 7 $$. Determine the single $x$-intercept $(x_0, 0)$ and single $y$-intercept $... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the result of $\\left(-1\\right)^{2019}$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a certain natural number $n$, $n^2$ gives a remainder of 9 when divided by 11, and $n^3$ gives a remainder of 5 when divided by 11. What remainder does $n$ give when divided ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the unit vectors $e_{1}$ and $e_{2}$ have an angle of $α$ between them, and $\\cos α= \\frac{1}{3}$, the angle between vector $a=3e_{1}-2e_{2}$ and $b=3e_{1}-e_{2}$ is... | math | {
"ground_truth": "\\frac{2\\sqrt{2}}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,b,c,x,y,$ and $z$ be complex numbers such that \\[a=\\dfrac{b+c}{x-2},\\qquad b=\\dfrac{c+a}{y-2},\\qquad c=\\dfrac{a+b}{z-2}.\\] If $xy+yz+xz=67$ and $x+y+z=2010$ ... | math | {
"ground_truth": "-5892",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The coefficient of $x^2$ in the expansion of $\\sqrt{x}(1-\\sqrt{x})^5$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "-10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of positive even divisors of 210 is.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A regular $2012$ -gon is inscribed in a circle. Find the maximal $k$ such that we can choose $k$ vertices from given $2012$ and construct a convex $k$ -gon without parall... | math | {
"ground_truth": "1509",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.