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": "Find all integers \\( n \\) such that \\( n^5 + 3 \\) is divisible by \\( n^2 + 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "-3, -1, 0, 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": "Consider the sequence defined by the nth term as $(-1)^n \\cdot (n+1)$. What is the average of the first $150$ terms of this sequence?\nA) -0.5\nB) 0\nC) 0.5\nD) 1\nE) -1",
"... | math | {
"ground_truth": "C) 0.5",
"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 area of the region enclosed by the graph of $|x-50|+|y|=\\left|\\frac{x}{3}\\right|.$",
"role": "user"
}
] | math | {
"ground_truth": "1250",
"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 expression $\\frac{a^{-2}b^{-2}}{a^{-4} + b^{-4}}$, find the equivalent simplified form.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a^2b^2}{a^4 + b^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": "A student walks down a hall with a row of 512 closed lockers, numbered from 1 to 512. He starts by opening every second locker. On his return journey, he toggles (opens if closed... | math | {
"ground_truth": "509",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a cube $ABCD\\_\\\\(A\\_1\\\\)B\\_\\\\(A\\_1\\\\)C\\_\\\\(A\\_1\\\\)D\\_\\\\(A\\_1\\\\)$, where edges $AB$, $AD$, and $AA\\_1$ lie on the axes of a three-dimensional Cartes... | math | {
"ground_truth": "\\\\left(\\\\begin{matrix} \\\\begin{matrix}1, 1, \\\\frac{1}{2} \\\\end{matrix}\\\\end{matrix}\\\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given propositions $p$ and $q$:\n- Proposition $p$: The quadratic equation $x^{2}+2x+m=0$ has no real roots.\n- Proposition $q$: The domain of the function $f(x)=\\lg (mx^{2}-x+ ... | math | {
"ground_truth": "1 < m \\leq 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": "In the Cartesian coordinate system xOy, the equation of circle C is $x^2+y^2+8x+15=0$. If there exists at least one point on the line $y=kx$ such that a circle with this point as... | math | {
"ground_truth": "[-\\frac {4}{3}, \\frac { \\sqrt {3}}{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": "Given the values $1256, 2561, 5612, 6125$, calculate the sum.",
"role": "user"
}
] | math | {
"ground_truth": "15554",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\frac{3x^5 + 4y^3 + z^2}{7}$ if $x = 2$, $y = 5$, and $z = 3$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{605}{7}",
"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 that the two asymptotes of the hyperbola \\\\( \\dfrac {x^{2}}{a^{2}}- \\dfrac {y^{2}}{b^{2}}=1(a > 0,b > 0)\\\\) are perpendicular to each other, then the eccentricity of ... | math | {
"ground_truth": "\\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": "The values of $x$ and $y$ are always positive, and $x^3$ and $y$ vary inversely. If $y$ is 8 when $x$ is 2, find $x$ when $y$ is 64.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that\n\\[\n\\frac{1}{x}+\\frac{1}{y}=5 \\quad \\text{and} \\quad xy+x+y=11,\n\\]\ncompute \\(x^2+y^2\\).",
"role": "user"
}
] | math | {
"ground_truth": "x^2+y^2 = \\frac{2893}{36}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a graph with $n$ ( $n\\ge 4$ ) vertices . It is known that for any two vertices $A$ and $B$ there exists a vertex which is connected by edges both with $A$ and $B$... | math | {
"ground_truth": "\\frac{3(n-1)}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( n \\geq 3 \\) be an integer and \\( x_{2}, \\ldots, x_{n} \\) be positive real numbers such that \\( x_{2} \\times \\cdots \\times x_{n} = 1 \\). Show the following inequ... | math | {
"ground_truth": "\\left(1 + x_2\\right)^2 \\times \\left(1 + x_3\\right)^3 \\times \\cdots \\times \\left(1 + x_n\\right)^n > n^n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a 4-digit number has exactly the four digits of 2023 and is odd, calculate the total count of such numbers.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimum value of \n\\[x^2 + 12x + \\frac{108}{x^4}\\]\nfor \\(x > 0\\).",
"role": "user"
}
] | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find a necessary and sufficient condition on the positive integer $n$ that the equation \\[x^n + (2 + x)^n + (2 - x)^n = 0\\] have a rational root.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that triangle $ABC$ has $AC=3$, $BC=4$, and $AB=5$, with point $D$ on $\\overline{AB}$ and $\\overline{CD}$ bisecting the right angle, find the ratio of the radii of the in... | math | {
"ground_truth": "\\frac{3}{28}\\left(10-\\sqrt{2}\\right)",
"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": "What is the quadrant in which the point $(-2,3)$ is located?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find $\\int \\frac{\\sin ^{3} x}{\\cos ^{5} x} \\, dx$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{4 \\cos^4 x} - \\frac{1}{2 \\cos^2 x} + C",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In space, $n$ planes are drawn. Each plane intersects with exactly 1999 others. Find all possible values of $n$.",
"role": "user"
}
] | math | {
"ground_truth": "3998",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In parallelogram $ABCD$, $\\overline{DE}$ is the altitude to the base $\\overline{AB}$ and $\\overline{DF}$ is the altitude to the base $\\overline{BC}$. If $AB = 15$, $DC = 15$,... | math | {
"ground_truth": "8",
"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 \\( p, q > 0 \\) and the triangle in the first quadrant bounded by the coordinate axes and the graph of \\( px+qy=24 \\) has an area of 48, calculate \\( pq \\).",
"rol... | math | {
"ground_truth": "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": "Given that x and y are inversely proportional positive quantities, determine the percent by which y decreases when x increases by q%.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{100q}{100+q}\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the 42nd number in the row of Pascal’s triangle that contains 45 numbers?",
"role": "user"
}
] | math | {
"ground_truth": "13254",
"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 sequence \\(\\{x_{n}\\}\\) is defined by the conditions \\(x_{1}=20\\), \\(x_{2}=17\\), and \\(x_{n+1}=x_{n}-x_{n-1}\\) for \\(n \\geq 2\\). Find \\(x_{2018}\\).",
"role"... | math | {
"ground_truth": "17",
"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 $f : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[f(f(x) + y) = f(x^2 - y) + 6f(x)y\\]\nfor all real numbers $x$ and $y.$ Determine the number of possible values... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the radius of curvature of the cycloid $x = a(t - \\sin t), y = a(1 - \\cos t)$ at an arbitrary point.",
"role": "user"
}
] | math | {
"ground_truth": "R = 4a \\left| \\sin \\frac{t}{2} \\right|",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Plot the solution set of the system of equations \\(\\left\\{\\begin{array}{l} x - 2y = 1 \\\\ x^{3} - 6xy - 8y^{3} = 1 \\end{array}\\right.\\) on the coordinate plane.",
"ro... | math | {
"ground_truth": "y = \\frac{x-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": "For how many positive integer values of $n$ is not only $\\frac{n}{4}$ a three-digit whole number, but also $4n$ a four-digit whole number?\n**A)** 525 **B)** 530 **C)** 1048 **D... | math | {
"ground_truth": "**A) 525**",
"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 rectangle has positive integer side lengths and an area of 24. Express the perimeter of the rectangle in terms of its side lengths, and identify the perimeter values that the r... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, if $\\frac{\\cos A + 2 \\cos C}{\\cos A + 2 \\cos B} = \\frac{\\sin B}{\\sin C}$, determine the shape of $\\triangle ABC$.",
"role": "user"
}
] | math | {
"ground_truth": "A = 90^\\circ \\text{ or } B = C",
"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": "Suppose that \\(\\log _{a} 125 = \\log _{5} 3\\) and \\(\\log _{b} 16 = \\log _{4} 7\\). Find the value of \\(a^{\\left(\\log _{5} 3\\right)^{2}} - b^{\\left(\\log _{4} 7\\right)... | math | {
"ground_truth": "-22",
"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 regular 15-gon is inscribed in a circle. Three segments are chosen at random among all possible segments connecting pairs of its vertices. What is the probability that these th... | math | {
"ground_truth": "\\frac{321}{455}",
"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": "Regular polygons with $4, 5, 6,$ and $7$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. D... | math | {
"ground_truth": "56",
"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 the form \\(3 p^{2}\\), where \\(p\\) is a prime number not equal to 3, if the sum of all its divisors is 124.",
"role": "user"
}
] | math | {
"ground_truth": "75",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the range of the real number $m$ such that the equation $x^3 - 3x - m = 0$ has a real root in the interval $[0, 1]$.",
"role": "user"
}
] | math | {
"ground_truth": "[-2, 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": "All four friends visited Daphne yesterday. Determine how many days of the next 400-day period will exactly two friends visit her.",
"role": "user"
}
] | math | {
"ground_truth": "142",
"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": "Points $A$ , $B$ , $C$ , $D$ , and $E$ are on the same plane such that $A,E,C$ lie on a line in that order, $B,E,D$ lie on a line in that order, $AE = 1$ , $BE = 4$ ,... | math | {
"ground_truth": "967",
"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": "Solve the system of equations\n$$\n\\left\\{\\begin{array}{l}\nx y^{2}-2 y+3 x^{2}=0, \\\\\ny^{2}+x^{2} y+2 x=0 .\n\\end{array}\\right.\n$$",
"role": "user"
}
] | math | {
"ground_truth": "(-1, 1), \\left( -\\frac{2}{\\sqrt[3]{3}}, -2 \\sqrt[3]{3} \\right), (0, 0)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the set of all points $(x,y)$ in the coordinate plane for which one of the coordinates is either twice the other or equal to the other. If we were to plot all such point... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Expand $(2x + 5)(3y + 4z + 15)$.",
"role": "user"
}
] | math | {
"ground_truth": "6xy + 8xz + 30x + 15y + 20z + 75",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using the digits $0$, $1$, $2$, $3$, $4$, $5$, how many different five-digit even numbers greater than $20000$ can be formed without repeating any digit?",
"role": "user"
}... | math | {
"ground_truth": "240",
"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": "Person A and Person B each choose 2 courses out of 4 courses. The number of ways in which at least one course chosen by Person A and Person B is different is.",
"role": "user... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The standard equation of a circle with center P(-1, 2) and radius 2.",
"role": "user"
}
] | math | {
"ground_truth": "(x+1)^2+(y-2)^2=4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In our standard number system, the base is ten. If the base were changed to eight, computing numbers would follow as $\\{1,2,3,4,5,6,7,10,11,12,13,14,15,16,17,20,\\ldots\\}$. Det... | math | {
"ground_truth": "24_8",
"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": "Hexagon ABCDEF has a horizontal line of symmetry. What is the $x$-coordinate of vertex C so that the area of the hexagon is 30 square units, given that vertices A, B, D, E, and F... | math | {
"ground_truth": "x = 22",
"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,b,c are positives with 21ab+2bc+8ca \\leq 12 . Find the least possoble value of the expresion 1/a + 2/b + 3/c.\r\nThanks",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{15}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the universal set $U=\\mathbb{R}$, and the sets $A=\\{x\\mid -1 < x < 3\\}$, $B=\\{x\\mid 0 < x\\leqslant 4\\}$, $C=\\{x\\mid a < x < a+1\\}$.\n\n1. Find $A\\cup B$ and $(A... | math | {
"ground_truth": "[0,2]",
"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": "The greatest common divisor of two integers $1908$ and $4187$ is to be determined.",
"role": "user"
}
] | math | {
"ground_truth": "53",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of significant digits in the measurement of the side of a square whose computed area is $2.4896$ square inches to the nearest ten-thousandth of a square inch.",
"r... | math | {
"ground_truth": "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": "Simplify the fraction $\\frac{75}{100}$ and find the sum of the numerator and the denominator of the fraction in its simplest form.",
"role": "user"
}
] | math | {
"ground_truth": "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": "The squares in a $7\\times7$ grid are colored one of two colors: green and purple. The coloring has the property that no green square is directly above or to the right of a pur... | math | {
"ground_truth": "3432",
"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": "Three times Dick's age plus Tom's age equals twice Harry's age, and double the cube of Harry's age is equal to three times the cube of Dick's age added to the cube of Tom's age. ... | math | {
"ground_truth": "42",
"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": "(a) Find all positive integers $n$ for which the equation $(a^a)^n = b^b$ has a solution\nin positive integers $a,b$ greater than $1$ .\n(b) Find all positive integers $a... | math | {
"ground_truth": "(a, b) = (4^4, 4^5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $v$ and $w$ be distinct, randomly chosen roots of the equation $z^{1997}-1=0.$ Let $m/n$ be the probability that $\\sqrt{2+\\sqrt{3}}\\le |v+w|,$ where $m$ and ... | math | {
"ground_truth": "2312047",
"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 $T$ denote the value of the sum\n\\[\\sum_{n = 2}^{5000} \\frac{1}{\\sqrt{n + \\sqrt{n^2 - 4}}}\\]\n$T$ can be expressed as $a + b \\sqrt{c}$, where $a, b,$ and $c$ are posit... | math | {
"ground_truth": "99",
"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 $180(180-12)-(180\\cdot180-12)$?",
"role": "user"
}
] | math | {
"ground_truth": "-2148",
"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 a map with a scale of 1:300,000, there is a shaped area with an approximate area of 24 cm². What is the actual area of this region in square kilometers?",
"role": "user"
... | math | {
"ground_truth": "216 \\, \\text{km}^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 median for the seven-number set $\\{x, 2x, 3x, 5, 4, 7, 1\\}$ if $x$ can be any positive integer?",
"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": "The product of three consecutive positive integers is $8$ times their sum.",
"role": "user"
}
] | math | {
"ground_truth": "77",
"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": "During a camping trip, Emily, Felipe, George, and Hannah are debating how far they are from the nearest village. Emily claims, \"We are at least 8 miles away,\" Felipe argues, \"... | math | {
"ground_truth": "(7,8)",
"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": "With what minimum force must you press on a cube with a volume of 10 cm³, floating in water, so that it is completely submerged? The density of the cube's material is 600 kg/m³, ... | math | {
"ground_truth": "0.04 \\, \\text{N}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A coat, a hat, and a pair of shoes originally sold for $150$, $50$, and $100$ dollars respectively. During a sale, Alice bought the $150$ dollar coat at a $35\\%$ discount, the $... | math | {
"ground_truth": "C) 45.83%",
"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 the sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$ is $S_n=2^n-a$, find the sum $a_1^2+a_2^2+\\cdots+a_n^2$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{3}(4^n-1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all prime numbers \\( p \\) for which there exist integers \\( m \\) and \\( n \\) such that \\( p = m^2 + n^2 \\) and \\( p \\mid m^3 + n^3 - 4 \\).",
"role": "user"
... | math | {
"ground_truth": "2, 5, 13",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of different complex numbers $z$ with the properties that $|z|=1$ and $z^{5!}-z^{4!}$ is a real number.",
"role": "user"
}
] | math | {
"ground_truth": "1149",
"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 $8 \\div 0.\\overline{3}$?",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $g(x) = \\sqrt{x-5}$, what is the smallest real number $x$ in the domain of $g(g(x))$?",
"role": "user"
}
] | math | {
"ground_truth": "30",
"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 Michael walks at the rate of $4$ feet per second on a long straight path, and the garbage truck travels at $8$ feet per second in the same direction as Michael, calculate t... | 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": "Find the functions $f: \\mathbb{R} \\to (0, \\infty)$ which satisfy $$ 2^{-x-y} \\le \\frac{f(x)f(y)}{(x^2+1)(y^2+1)} \\le \\frac{f(x+y)}{(x+y)^2+1}, $$ for all $x,y \\in ... | math | {
"ground_truth": "f(x) = \\frac{x^2 + 1}{2^x}",
"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 $ n$ be a positive integer. Consider\r\n\\[ S \\equal{} \\left\\{ (x,y,z) \\mid x,y,z \\in \\{ 0, 1, \\ldots, n\\}, x \\plus{} y \\plus{} z > 0 \\right \\}\r\n\\]\r\nas a s... | math | {
"ground_truth": "3n",
"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 expression \\((5 \\times 5) + (5 \\times 5) + (5 \\times 5) + (5 \\times 5) + (5 \\times 5)\\) can be simplified by calculating the product of 5 and 5, and then adding the re... | math | {
"ground_truth": "125",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In right triangle $DEF$ with $\\angle D = 90^\\circ$, let $DE = 8$ and $EF = 17$. Find $\\cos F$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{15}{17}",
"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": "Convert the point \\( (3, -3) \\) in rectangular coordinates to polar coordinates. Enter your answer in the form \\((r, \\theta)\\), where \\( r > 0 \\) and \\( 0 \\le \\theta < ... | math | {
"ground_truth": "\\left(3 \\sqrt{2}, \\frac{7 \\pi}{4}\\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": "Let \\( x, y, z \\) be non-negative numbers such that \\( x^{2} + y^{2} + z^{2} + x + 2y + 3z = \\frac{13}{4} \\). Find the minimum value of \\( x + y + z \\).",
"role": "use... | math | {
"ground_truth": "\\frac{-3 + \\sqrt{22}}{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": "Find the flux of the vector field **a** = (x - 2z)i + (x + 3y + z)j + (5x + y)k through the upper side of the triangle ABC with vertices at points A(1,0,0), B(0,1,0), C(0,0,1).",... | math | {
"ground_truth": "\\frac{5}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow {a} = (4,-2,-4)$ and $\\overrightarrow {b} = (6,-3,2)$, calculate the dot product of $(2\\overrightarrow {a}-3\\overrightarrow {b})$ and $(\\overr... | math | {
"ground_truth": "-200",
"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": "When flipping a fair coin, what is the probability that you get three heads in a row? Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = ax + 19$, and $f(3) = 7$, if $f(t) = 15$, then $t = \\ $.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five positive consecutive integers starting with a have an average of b. Calculate the average of 5 consecutive integers that start with b.",
"role": "user"
}
] | math | {
"ground_truth": "(a+2), (a+3), (a+4), (a+5), (a+6)",
"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 the graph of $y = mx + 3$ passes through no lattice point with $0 < x \\le 50$ for all $m$ such that $\\frac{1}{3} < m < b$, find the maximum possible value of $b$.",
"... | math | {
"ground_truth": "\\frac{17}{50}",
"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": "Compute $\\begin{pmatrix} 3 & -1 \\\\ 5 & 2 \\end{pmatrix} \\begin{pmatrix} 2 & 6 \\\\ -1 & 3 \\end{pmatrix}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{pmatrix} 7 & 15 \\\\ 8 & 36 \\end{pmatrix}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any positive integer $n$ , let $S_n$ denote the set of positive integers which cannot be written in the form $an+2017b$ for nonnegative integers $a$ and $b$ . Let $A... | math | {
"ground_truth": "840",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola $x^{2}=y$, points $A$ and $B$ are on the parabola and located on both sides of the $y$-axis, and the line $AB$ intersects the $y$-axis at point $(0,a)$. If $\\... | math | {
"ground_truth": "(1,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given points A(3, 2, 0), B(2, -1, 2), and a point M located on the x-axis such that its distances to points A and B are equal, find the coordinates of point M.",
"role": "use... | math | {
"ground_truth": "M(2, 0, 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": "Given the new operation $x \\otimes y = x^2 - y^2$, calculate the value of $(a \\otimes a) \\otimes (a \\otimes a)$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 square with sides of length $\\frac{2}{\\pi}$, find the perimeter of the region bounded by the semicircular arcs constructed on the sides of the square.",
"role": "us... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a number $\\overline{abcd}$ , where $a$ , $b$ , $c$ , and $d$ , represent the digits of $\\overline{abcd}$ , find the minimum value of\n\\[\\frac{\\overline{abcd}}{a+... | math | {
"ground_truth": "60.5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation is given $x^2-(m+3)x+m+2=0$ .\nIf $x_1$ and $x_2$ are its solutions find all $m$ such that $\\frac{x_1}{x_1+1}+\\frac{x_2}{x_2+1}=\\frac{13}{10}$ .",
"rol... | math | {
"ground_truth": "m = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a $4 \\times 4$ array filled with numbers from 1 to 16, where entries in every row and column are in increasing order, determine the number of such arrays.",
"role": "u... | math | {
"ground_truth": "120",
"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 cube is given. Three planes, parallel to its faces, divide it into 8 parallelepipeds. These parallelepipeds were painted in a checkerboard pattern. The volumes of the black par... | math | {
"ground_truth": "2, 3, 4, 24",
"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 $A$ and $B$ be sets such that there are exactly $144$ sets which are subsets of either $A$ or $B$ . Determine the number of elements $A \\cup B$ has.",
"role":... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a fraction $\\frac{a}{b}$, not necessarily in the simplest form, where $a$ and $b$ are positive integers whose sum is $18$, calculate the number of distinct integers that c... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Elmer's new car gives $50\\%$ percent better fuel efficiency than his old car, but uses diesel fuel that is $20\\%$ more expensive per liter than the gasoline his old ... | math | {
"ground_truth": "20\\%",
"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 all positive integers $a$ such that for any positive integer $n\\ge 5$ we have $2^n-n^2\\mid a^n-n^a$ .",
"role": "user"
}
] | math | {
"ground_truth": "a = 2 \\text{ or } a = 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": "Determine the smallest positive integer $ n$ such that there exists positive integers $ a_1,a_2,\\cdots,a_n$ , that smaller than or equal to $ 15$ and are not necessarily di... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P (x) = x^{3}-3x+1.$ Find the polynomial $Q$ whose roots are the fifth powers of the roots of $P$ .",
"role": "user"
}
] | math | {
"ground_truth": "y^3 + 15y^2 - 198y + 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": "Miki uses her juicer to obtain 10 ounces of pear juice from 4 pears and 12 ounces of orange juice from 3 oranges. She decides to make a juice blend using an equal number of pears... | math | {
"ground_truth": "38\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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