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 $X = \\{-5,-4,-3,-2,-1,0,1,2,3,4,5\\}$ and $S = \\{(a,b)\\in X\\times X:x^2+ax+b \\text{ and }x^3+bx+a \\text{ have at least a common real zero .}\\}$ How many elements a... | math | {
"ground_truth": "21",
"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 $a$ and $b$ are opposite numbers, and $c$ and $d$ are reciprocals, then $\\frac{5a+5b-7cd}{(-cd)^{3}}=$____.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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": "How many ways can we arrange 4 history books and 6 science books on a shelf if all the history books must stay together and all the science books must also stay together? (Each b... | math | {
"ground_truth": "34560",
"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": "Calculate $300,000$ times $300,000$ times $3$.",
"role": "user"
}
] | math | {
"ground_truth": "270,000,000,000",
"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 box contains $30$ red balls, $23$ green balls, $21$ yellow balls, $17$ blue balls, $14$ white balls, and $12$ black balls. Calculate the minimum number of balls that must be dr... | math | {
"ground_truth": "95",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = x^5 + 3x^4 - 5x^3 + 7x^2 - 9x + 11$ when $x = 4$.",
"role": "user"
}
] | math | {
"ground_truth": "1559",
"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 hyperbola $C:\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$ with an eccentricity of $4$, find the equations of its asymptotes.\n\nA) $y = \\pm \\sqrt{15}x$... | math | {
"ground_truth": "y = \\pm \\sqrt{15}x",
"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": "At the beginning of the year, a stock was purchased for 5000 rubles. At the end of the year, it was sold, and the profit from the transaction amounted to 400 rubles. Determine th... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $\\log_8 \\sqrt[3]{8}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac13",
"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 $ABCD$ be a quadrilateral such that $m(\\widehat{A}) = m(\\widehat{D}) = 90^\\circ$. Let $M$ be the midpoint of $[DC]$. If $AC\\perp BM$, $|DC|=12$, and $|AB|=9$, calculate $... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given 5 points on a plane where no 3 points are collinear and no 4 points are concyclic. A circle passing through any 3 of these points with one of the remaining two points insid... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of the coefficients in the polynomial $2(4x^{8} - 5x^5 + 9x^3 - 6) + 8(x^6 - 4x^3 + 6)$ when it is fully simplified.",
"role": "user"
}
] | math | {
"ground_truth": "28",
"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": "Determine all real numbers \\( b \\) such that the inequality \\( |x^2 + 3bx + 4b| \\leq 3 \\) has exactly one solution in \\( x \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{3}, 1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the total volume and the total surface area in square feet of three cubic boxes if their edge lengths are 3 feet, 5 feet, and 6 feet, respectively?",
"role": "user"
... | math | {
"ground_truth": "420",
"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": "Determine the least positive integer $n$ such that the sum of all its positive divisors is 12600.",
"role": "user"
}
] | math | {
"ground_truth": "n = 1200",
"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 are 2 dimes of Chinese currency, how many ways can they be exchanged into coins (1 cent, 2 cents, and 5 cents)?",
"role": "user"
}
] | math | {
"ground_truth": "46",
"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 cube with a side length of 2 units is sliced along a diagonal plane that intersects three major vertices, A, B, and D, forming a tetrahedral piece removed from the original cub... | math | {
"ground_truth": "\\frac{1}{6}",
"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 \\( \\frac{5}{4} (p + q + r + s) = 20 \\), what is the average of \\( p, q, r, \\) and \\( s \\)?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the area of the region defined by the inequality $|4x - 24| + |3y + 10| \\le 4$?\nA) $2$\nB) $\\frac{5}{3}$\nC) $\\frac{2}{3}$\nD) $\\frac{4}{3}$\nE) $1$",
"role": "u... | math | {
"ground_truth": "\\frac{4}{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": "Jerry starts at 0 on the real number line and tosses a fair coin 10 times. When he gets heads, he moves one unit in the positive direction; when he gets tails, he moves one unit ... | math | {
"ground_truth": "C) 271",
"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 vectors $\\mathbf{a}, \\mathbf{b},$ and $\\mathbf{c}$ be given. Consider $\\mathbf{p}$ such that \\[\\|\\mathbf{p} - \\mathbf{b}\\| = 3 \\|\\mathbf{p} - \\mathbf{a}\\|.\\] Am... | math | {
"ground_truth": "\\left(\\frac{9}{2}, \\frac{1}{4}, 0\\right)",
"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": "In triangle $\\triangle ABC$, where $A B = 16$, $B C = 5 \\sqrt{5}$, and $C A = 9$. What is the area of the plane region covered by the set of points outside $\\triangle ABC$ suc... | math | {
"ground_truth": "54\\pi + \\frac{5\\sqrt{95}}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the group of equations: \\[\\begin{cases} (x + y)^3 = z (y + z)^3 = x (z + x)^3 = y \\end{cases}\\]",
"role": "user"
}
] | math | {
"ground_truth": "(x, y, z) \\in \\{(0, 0, 0), (\\frac{\\sqrt{2}}{4}, \\frac{\\sqrt{2}}{4}, \\frac{\\sqrt{2}}{4}), (-\\frac{\\sqrt{2}}{4}, -\\frac{\\sqrt{2}}{4}, -\\frac{\\sqrt{2}}{4})\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right triangle \\(ABC\\) is inscribed in a circle. A chord \\(CM\\) is drawn from the vertex \\(C\\) of the right angle, intersecting the hypotenuse at point \\(K\\). Find the ... | math | {
"ground_truth": "\\frac{9}{19} \\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": "Treasure was buried in a single cell of an $M\\times N$ ( $2\\le M$ , $N$ ) grid. Detectors were brought to find the cell with the treasure. For each detector, you can set it ... | math | {
"ground_truth": "\\lceil \\frac{m}{2} \\rceil + \\lceil \\frac{n}{2} \\rceil",
"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 $g(x)=3x^5 + 2x^4 - x^3 + x^2 - 4x + s$. For what value of $s$ is $g(-1)=0$?",
"role": "user"
}
] | math | {
"ground_truth": "-5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Divide $120$ into three parts that are proportional to $\\frac{1}{2}, \\frac{1}{4}, \\text{and } \\frac{1}{8}$. What is the value of the middle part?",
"role": "user"
}
] | math | {
"ground_truth": "34.2857",
"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": "On the picture, several circles are drawn connected by segments. Kostya chooses a natural number \\( n \\) and places different natural numbers in the circles so that the followi... | 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": "The vertex of the parabola $y = 2x^2 - 10x + c$ will be a point on the $x$-axis. Determine the value of $c$ for which this condition holds.",
"role": "user"
}
] | math | {
"ground_truth": "12.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x$ is such that $\\frac{1}{x}<3$ and $\\frac{1}{x}>-2$, then determine the range of possible values for $x$.\nA) $x > \\frac{1}{3} \\text{ or } x < -\\frac{1}{2}$ \\\\\nB) $x... | math | {
"ground_truth": "x > \\frac{1}{3} \\text{ or } x < -\\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": "Suppose that \\( x - y = 1 \\). Find the value of \\( x^4 - xy^3 - x^3 y - 3x^2 y + 3xy^2 + y^4 \\).",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $q<50$ be a prime number. Call a sequence of polynomials $P_0(x), P_1(x), P_2(x), ..., P_{q^2}(x)$ *tasty* if it satisfies the following conditions: \n\n\n\n- $P_i$ has ... | math | {
"ground_truth": "30416",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest natural number that has exactly the following numbers of divisors: $2, 3, 4, 5, 6, 8, 10, 16, 36, 64, 100, 216, 1000, 1000000$. (The divisors include both ... | math | {
"ground_truth": "N_{1000000}",
"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": "Define the operation $a*b$ as:\n$$\na * b = \\begin{cases}\na, & \\text{if } a \\leq b \\\\\nb, & \\text{if } a > b\n\\end{cases},\n$$\nfor instance, $1 * 2 = 1$. Determine the r... | math | {
"ground_truth": "(0,1]",
"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": "If the function $f(x)$ satisfies $f'(x_0)=-3$, then $\\lim\\limits_{h \\to 0} \\frac{f(x_0+h)-f(x_0-ah)}{h}$ equals \\_\\_\\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "-12",
"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 ellipse centered at the origin with its major axis on the $x$-axis and an eccentricity of $e$, if the maximum distance between a point on the circle $C: x^{2}+\\left(y-\... | math | {
"ground_truth": "\\begin{cases}\nx = 2 \\cos \\theta \\\\\ny = \\sin \\theta\n\\end{cases}",
"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": "[list=1]\n[*] If $a$ , $b$ , $c$ , $d > 0$ , show inequality: $$ \\left(\\tan^{-1}\\left(\\frac{ad-bc}{ac+bd}\\right)\\right)^2\\geq 2\\left(1-\\frac{ac+bd}{\\sqrt{\\left(a^... | 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": "In triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, satisfying $\\left(c-2a\\right)\\cos B+b\\cos C=0$. Find:<br/>\n$... | math | {
"ground_truth": "S_{\\triangle ABC} = \\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": "Let $k$ be a fixed integer. In the town of Ivanland, there are at least $k+1$ citizens standing on a plane such that the distances between any two citizens are distinct. An e... | math | {
"ground_truth": "5k",
"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": "Alex paid $250 for a set of four tires with a deal that included a fourth tire for $10. What was the regular price of one tire?",
"role": "user"
}
] | math | {
"ground_truth": "80",
"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": "Solve the following equations (systems): \n$(1)\\left\\{\\begin{array}{l}{x+2y=3}\\\\{2x-y=1}\\end{array}\\right.$; \n$(2)\\frac{1}{x-1}+2=\\frac{5}{1-x}$.",
"role": "user"... | math | {
"ground_truth": "x = -2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $ABC$ with vertices $A(-2, 0)$, $B(1, 4)$, and $C(-3, 2)$ is reflected over both the $y$-axis and the $x$-axis to form triangle $A'B'C'$. What is the length of a segment... | math | {
"ground_truth": "2\\sqrt{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": "In triangle $ABC$, point $F$ divides side $AC$ in the ratio $2:3$. Let $H$ be the midpoint of $CF$. Point $E$ is defined as the intersection of side $BC$ and line $BH$. Determine... | math | {
"ground_truth": "\\frac{4}{7}",
"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 $\\begin{tabular}{r|l}a&b \\\\ \\hline c&d\\end{tabular} = \\text{a}\\cdot \\text{d} - \\text{b}\\cdot \\text{c}$, find the value of $\\begin{tabular}{r|l}3&4 \\\\ \\hline ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, if $(\\sin A+\\sin B):(\\sin A+\\sin C):(\\sin B+\\sin C)=4:5:6$, and the area of the triangle is $15\\sqrt{3}$, then the length of the longest side of $\\tr... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all naturals $k$ such that $3^k+5^k$ is the power of a natural number with the exponent $\\ge 2$ .",
"role": "user"
}
] | math | {
"ground_truth": "k = 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": "Cagney can frost a cupcake every 15 seconds and Lacey can frost a cupcake every 25 seconds. If they start working together but Lacey takes a 1-minute break after the first 2 minu... | math | {
"ground_truth": "62",
"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": "Which function grows faster on the interval $(1, +\\infty)$, $y=x^2$ or $y=x\\ln x$?",
"role": "user"
}
] | math | {
"ground_truth": "y=x^2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $$f(x)= \\begin{cases} \\overset{x+2,x<a}{x^{2},x\\geq a}\\end{cases}$$, find the range of values for the real number $a$ such that the function $f(x)$ is mono... | math | {
"ground_truth": "a \\in [2, +\\infty) \\text{ and } a \\in (-\\infty, -2]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the complex number $z$ satisfies the equation $$\\frac{z}{1+i}$$=-3i, where $i$ is the imaginary unit, find the modulus of the complex number $z$.",
"role": "user"... | math | {
"ground_truth": "3\\sqrt{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": "What is the largest possible result of Ahn's operation, given that he selects a three-digit integer, adds it to 200, and triples the result?",
"role": "user"
}
] | math | {
"ground_truth": "3597",
"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": "While doing her homework for a Momentum Learning class, Valencia draws two intersecting segments $AB = 10$ and $CD = 7$ on a plane. Across all possible configurations of tho... | math | {
"ground_truth": "35",
"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": "When \\( x = 3 \\), simplify the expression \n\n\\[\n\\frac{\\sqrt{x-2 \\sqrt{2}}}{\\sqrt{x^{2}-4 \\sqrt{2} x+8}}-\\frac{\\sqrt{x+2 \\sqrt{2}}}{\\sqrt{x^{2}+4 \\sqrt{2} x+8}}\n\\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bug walks all day and sleeps all night. On the first day, it starts at point $O$, faces east, and walks a distance of $5$ units due east. Each night the bug rotates $60^\\circ$... | math | {
"ground_truth": "103",
"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": "Find the conjugate of the complex number $(1 + 2i)^2$.",
"role": "user"
}
] | math | {
"ground_truth": "-3 - 4i",
"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": "Determine all positive integers in the form $a<b<c<d$ with the property that each of them divides the sum of the other three.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 2, 3, 6), (1, 2, 6, 9), (1, 3, 8, 12), (1, 4, 5, 10), (1, 6, 14, 21), (2, 3, 10, 15)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For $a, b \\in \\mathbb{R}$, let $\\max\\{a, b\\} = \\begin{cases} a, & \\text{if } a \\geq b \\\\ b, & \\text{if } a < b \\end{cases}$. The minimum value of the function $f(x) =... | math | {
"ground_truth": "\\frac{11}{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": "We are given 5771 weights weighing 1,2,3,...,5770,5771. We partition the weights into $n$ sets of equal weight. What is the maximal $n$ for which this is possible?",
"rol... | math | {
"ground_truth": "2886",
"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 $y = (x-a)^2 + (x-b)^2 + cx$, where $a, b, c$ are constants. Find the value of $x$ that minimizes $y$.\n**A)** $\\frac{a+b}{2}$ \n**B)** $\\frac{a+b-c}{2}$ \n**C)** $\\frac... | math | {
"ground_truth": "\\textbf{(E)}\\ \\frac{a+b-\\frac{c}{2}}{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": "Given a pyramid \\( S-ABCD \\) with a square base where each side measures 2, and \\( SD \\perp \\) plane \\( ABCD \\) and \\( SD = AB \\). Determine the surface area of the circ... | math | {
"ground_truth": "12\\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": "Given the expansion of \\(\\left(1+x+x^{2}\\right)^{1000}\\) as \\(a_{0}+a_{1} x+a_{2} x^{2}+\\cdots+a_{2000} x^{2000}\\), find the value of \\(a_{0}+a_{3}+a_{6}+\\cdots +a_{1998... | math | {
"ground_truth": "3^{999}",
"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 solution set of the inequality $$\\frac {2x+1}{x-3}$$ ≤ 0, find the interval of x.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|- \\frac {1}{2}≤x＜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": "*Version 1*. Let $n$ be a positive integer, and set $N=2^{n}$ . Determine the smallest real number $a_{n}$ such that, for all real $x$ ,\n\\[\n\\sqrt[N]{\\frac{x^{2 N}+1}{2... | math | {
"ground_truth": "2^{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, side lengths are $AB = 3$, $BC = 4$, and $CA = 5$. Points $G$ and $H$ are on ray $AB$ such that $AB < AG < AH$. Another point $I \\neq C$ is the point of inter... | math | {
"ground_truth": "79",
"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 trigonometric expression $\\cos(\\alpha-35^\\circ)\\cos(25^\\circ+\\alpha)+\\sin(\\alpha-35^\\circ)\\sin(25^\\circ+\\alpha)$, simplify the expression using trigonometri... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which natural numbers $n \\geq 2$ does the inequality $x_{1}^{2}+x_{2}^{2}+\\ldots+x_{n}^{2} \\geq p\\left(x_{1} x_{2}+x_{2} x_{3}+\\ldots+x_{n-1} x_{n}\\right)$ hold for any... | math | {
"ground_truth": "c) n \\leq 4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be the least positive integer greater than $1000$ for which $\\gcd(63, n+120) =21$ and $\\gcd(n+63, 120)=60$. Calculate the sum of the digits of $n$.",
"role": "user"... | math | {
"ground_truth": "18",
"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 that $A$, $B$, and $C$ are playing in a backgammon tournament, and each player has an equal chance to win a game, calculate the probability that $C$ wins the tournament.",
... | math | {
"ground_truth": "\\frac{3}{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": "Squares A, B, and C are constructed such that the perimeter of square A is 16 and the perimeter of square B is 28. The side length of square C is determined as the absolute diffe... | math | {
"ground_truth": "A) 12",
"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 circular disk is divided by $3n$ equally spaced radii and two secant lines that do not intersect each other. Determine the maximum number of non-overlapping areas into which th... | math | {
"ground_truth": "9n",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the year 2022, the sum of the year's digits is $6$. What is the first year after 2022 in which the sum of the digits is $5$?",
"role": "user"
}
] | math | {
"ground_truth": "2030",
"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 $b$ be a real number randomly sepected from the interval $[-17,17]$ . Then, $m$ and $n$ are two relatively prime positive integers such that $m/n$ is the probabilit... | math | {
"ground_truth": "63",
"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 $52$ cards in a deck are numbered $1, 2, \\cdots, 52$. Alex, Blair, Corey, and Dylan each picks a card from the deck without replacement and with each card being equally like... | math | {
"ground_truth": "143",
"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": "An arithmetic sequence has its sum of the first fifteen terms as three times the sum of the first eight terms. Find the ratio of the first term to the common difference.\nA) 2:1\... | math | {
"ground_truth": "C) 7:3",
"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": "Evaluate the expression \\[(5^{1001} + 6^{1002})^2 - (5^{1001} - 6^{1002})^2\\] and express it in the form \\(k \\cdot 30^{1001}\\) for some integer \\(k\\).",
"role": "user"... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The average cost of a long-distance call in the USA in $1985$ was $41$ cents per minute, and the average cost of a long-distance call in the USA in $2005$ was $7$ cents per minut... | math | {
"ground_truth": "80\\%",
"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": "On equilateral $\\triangle{ABC}$ point D lies on BC a distance 1 from B, point E lies on AC a distance 1 from C, and point F lies on AB a distance 1 from A. Segments AD, BE, an... | math | {
"ground_truth": "30",
"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 the sum of the coefficients in the expansion of $(x + x^{-1})^n$ is 128, the coefficient of $x^5$ in the expansion is ______.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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 smallest positive integer $b$ for which $x^2 + bx + 2304$ factors into a product of two polynomials, each having integer coefficients.",
"role": "user"
}
] | math | {
"ground_truth": "96",
"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": "Determine all positive integers $n > 2$ , such that \\[ \\frac{1}{2} \\varphi(n) \\equiv 1 ( \\bmod 6) \\]",
"role": "user"
}
] | math | {
"ground_truth": "n = 3, 4, 6, p^{2k}, 2p^{2k} \\text{ for } k \\equiv 11 \\pmod{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 twelve points are spaced evenly around the perimeter of a 3 x 3 square, with each placed at the corners and the midpoints of each side, find the probability that two of the... | math | {
"ground_truth": "\\frac{2}{11}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find two different natural numbers whose sum of cubes is equal to the square of their sum.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 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": "The tangent lines to the circle $(x-2)^2+(y+1)^2=1$ passing through the point $(3,3)$, the equation of the tangent line is $\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "x=3 \\text{ or } 15x-8y-21=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": "An inverted cone with base radius $8 \\mathrm{cm}$ and height $12 \\mathrm{cm}$ is full of water. This water is poured into a cylindrical container with a horizontal base radius ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What percent of the numbers $1, 2, 3, ... 1000$ are divisible by exactly one of the numbers $4$ and $5?$",
"role": "user"
}
] | math | {
"ground_truth": "35\\%",
"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 \\( F_{1}, F_{2} \\) be the foci of the ellipse \\(\\frac{x^{2}}{9} + \\frac{y^{2}}{4} = 1\\). Point \\( P \\) lies on the ellipse, and the ratio \\(\\left|P F_{1}\\right| : ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a square divided into a composition of different geometric shapes: Triangle I, Circle II, and a smaller Square III, each splitting the square differently. Triangle I occ... | math | {
"ground_truth": "\\frac{1}{2}, \\frac{\\pi}{4}, \\frac{1}{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": "Joe bikes $x$ miles East at $20$ mph to his friend’s house. He then turns South and bikes $x$ miles at $20$ mph to the store. Then, Joe turns East again and goes to his g... | math | {
"ground_truth": "10",
"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 the triangle \\(ABC\\), another triangle \\(A_1B_1C_1\\) is inscribed and a third triangle \\(A_2B_2C_2\\) is circumscribed such that \\(A_1B_1 \\parallel A_2B_2\\), \\(A_1C_1... | math | {
"ground_truth": "\\sqrt{t_1 \\cdot t_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": "At what point does the line $2y + 5x = 15$ intersect the $x$-axis? Express your answer as an ordered pair.",
"role": "user"
}
] | math | {
"ground_truth": "(3,0)",
"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 light ray begins at point $A$ in a plane, and reflects multiple times between two lines, $PQ$ and $RS$, before hitting a target point $B$ such that it strikes $B$ perpendicular... | math | {
"ground_truth": "C) 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 a hyperbola shares the same foci with the ellipse $x^2+4y^2=64$, and one of its asymptotes is given by the equation $x- \\sqrt {3}y=0$, find the equation of the hyperb... | math | {
"ground_truth": "\\frac {x^{2}}{36}- \\frac {y^{2}}{12}=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": "How many ways are there to rearrange the letters of the word \"GEOMETRY\" so that no two consonant letters are next to each other?",
"role": "user"
}
] | math | {
"ground_truth": "21600",
"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 $\\tan \\alpha=-\\frac{4}{3} $, find:\n\n(1) $\\sin \\alpha+\\cos \\alpha $\n\n(2) $\\frac{\\sin (π-\\alpha)+2\\cos \\left(π+\\alpha\\right)}{\\sin ( \\frac{3}{2}π-\\alpha)... | math | {
"ground_truth": "-10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the equation of the line $l$ that is parallel to the line $2x+5y-1=0$ and forms a triangle with the coordinate axes that has an area of 5.",
"role": "user"
}
] | math | {
"ground_truth": "2x+5y-10=0 \\text{ or } 2x+5y+10=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": "Simplify the expression first, then evaluate it: \\\\(5(3a^{2}b-ab^{2})-(ab^{2}+3a^{2}b)\\\\), where \\\\(a= \\frac {1}{2}\\\\), \\\\(b= \\frac {1}{3}\\\\).",
"role": "user"
... | math | {
"ground_truth": "\\frac {2}{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": "If $p$ is a positive integer, then $\\frac{4p + 11}{2p - 7}$ can be a positive integer, if and only if $p$ is:\nA) At least 4 \nB) At least 4 and no more than 9 \nC) No more th... | math | {
"ground_truth": "D) Equal to 4 or 5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of all $\\text{permutations}$ of $\\left \\{ 1,2,\\cdots ,n \\right \\}$ like $p$ such that there exists a unique $i \\in \\left \\{ 1,2,\\cdots ,n \\right... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sequence $a_0,a_1,a_2,\\cdots,a_n,\\cdots$ satisfies that $a_0=3$ , and $(3-a_{n-1})(6+a_n)=18$ , then the value of $\\sum_{i=0}^{n}\\frac{1}{a_i}$ is________.",
"rol... | math | {
"ground_truth": "\\frac{2^{n+2} - n - 3}{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": "Let $A$ be an $n$-element set, and let $A_{1}, A_{2}, \\cdots, A_{m}$ be subsets of $A$ that are pairwise disjoint. Determine the maximum value of $m$.",
"role": "user"
}
] | math | {
"ground_truth": "\\binom{n}{\\lfloor \\frac{n}{2} \\rfloor}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.