data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the hyperbola $\\dfrac{y^{2}}{4}-x^{2}=1$, find its equation of asymptote.",
"role": "user"
}
] | math | {
"ground_truth": "y = \\pm 2x",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Fix an integer $ b \\geq 2$ . Let $ f(1) \\equal{} 1$ , $ f(2) \\equal{} 2$ , and for each $ n \\geq 3$ , define $ f(n) \\equal{} n f(d)$ , where $ d$ is the number of bas... | math | {
"ground_truth": "b = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\(ABC\\) with side \\(BC\\) equal to 9, an incircle is drawn, touching side \\(BC\\) at point \\(D\\). It is known that \\(AD = DC\\) and the cosine of angle \\(BCA\... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which $n>3$ can a set of weights with masses $1, 2, 3, \\ldots, n$ grams be divided into three piles of equal mass?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{All } n > 3 \\text{ that are of the form } 3k \\text{ for } k \\geq 1 \\text{ or } 3k + 2 \\text{ for } k \\geq 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Diana rolls an 8-sided die and Apollo rolls a standard 6-sided die, each obtaining a number at random from 1 to their respective maximum numbers. What is the probability that Dia... | math | {
"ground_truth": "\\dfrac{9}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The fi\fgure below shows a $9\\times7$ arrangement of $2\\times2$ squares. Alternate squares of the grid are split into two triangles with one of the triangles shaded. Find t... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fair 10-sided die is rolled twice. Calculate the probability that the first number that comes up is strictly greater than the second number.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{20}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive integers \\( a \\) for which the equation\n\n$$\n\\left(1+\\frac{1}{x}\\right) \\cdot\\left(1+\\frac{1}{x+1}\\right) \\cdots \\left(1+\\frac{1}{x+a}\\right... | math | {
"ground_truth": "a = 7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that four circles with radii $1,3,5,$ and $7$ are tangent to line $\\ell$ at the same point $A$, but they may be on either side of $\\ell$, determine the maximum possible a... | math | {
"ground_truth": "65\\pi",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find, with proof, all solutions of the equation $\\frac 1x +\\frac 2y- \\frac 3z = 1$ in positive integers $x, y, z.$",
"role": "user"
}
] | math | {
"ground_truth": "S_{(x, y, z)} = \\{ (2, 1, 2), (k, 2, 3k), (2, 3, 18), (1, 2k, 3k), (2, 2, 6) \\mid k \\in \\mathbb{N} \\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $A(3,5,-7)$, $B(-1,3,3)$, and $\\overrightarrow{AB}=2\\overrightarrow{CB}$, find the coordinates of point $C$.",
"role": "user"
}
] | math | {
"ground_truth": "(1,4,-2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the real number line, paint red all points that correspond to integers of the form $81x+100y$ , where $x$ and $y$ are positive integers. Paint the remaining integer point... | math | {
"ground_truth": "3960",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each face of a cube has stripes painted from the midpoint of one edge to the midpoint of the opposite edge. On any two opposing faces (like top and bottom), exactly one face's st... | math | {
"ground_truth": "\\mathrm{(C)}\\, \\frac{3}{32}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the coefficient of the term that does not contain $x$ in the binomial expansion of $\\left(xy-\\frac{1}{x}\\right)^{8}$.",
"role": "user"
}
] | math | {
"ground_truth": "70",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the game show $\\text{\\emph{Wheel of Fortune II}}$, the following spinner is displayed. Assuming each region is of equal area, what is the probability of earning exactly $\\$... | math | {
"ground_truth": "\\frac{12}{125}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The length of the interval of solutions of the inequality $a \\le 2x + 3 \\le b$ is $10$. Calculate $b - a$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For real numbers $x$ , $y$ and $z$ , solve the system of equations: $$ x^3+y^3=3y+3z+4 $$ $$ y^3+z^3=3z+3x+4 $$ $$ x^3+z^3=3x+3y+4 $$",
"role": "user"
}
] | math | {
"ground_truth": "x = y = z = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given points \\( A \\) and \\( B \\). Determine the locus of points \\( C \\) such that \\( C \\), the midpoints of segments \\( AC \\) and \\( BC \\), and the centroid of the tr... | math | {
"ground_truth": "\\text{Circle with center at midpoint of } AB \\text{ and radius } \\frac{\\sqrt{3}}{2} AB \\text{ excluding intersection with } AB \\text{.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ with the following property: there does not exist an arithmetic progression of $1999$ real numbers containing exactly $n$ integers.",... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_1, a_2, \\ldots$ and $b_1, b_2, \\ldots$ be sequences such that $a_ib_i - a_i - b_i = 0$ and $a_{i+1} = \\frac{2-a_ib_i}{1-b_i}$ for all $i \\ge 1$ . If $a_1 = ... | math | {
"ground_truth": "257",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the angle between the planes:\n$$\n\\begin{aligned}\n& 3x - 2y + 3z + 23 = 0 \\\\\n& y + z + 5 = 0\n\\end{aligned}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "81^\\circ 19' 45''",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $g(n)$ be the sum of all the divisors of a positive integer $n$. If $g(g(n)) = n+3$, define $n$ as hyperdeficient. Determine how many hyperdeficient positive integers there a... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "All numbers from 1 to 10,000,000,000 are written in a row. Which numbers will be more - those that contain the digit 1 in their notation, or those that do not contain the digit 1... | math | {
"ground_truth": "\\text{Numbers containing the digit 1 are more frequent.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using the four numbers 8, 8, 8, and 10, form an expression using addition, subtraction, multiplication, and division (parentheses can be added) to make the result equal to 24.",
... | math | {
"ground_truth": "(10 - 8) \\times 8 + 8 = 24",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A four-inch wooden cube is fully painted blue and then cut into one-inch cubes. How many of the one-inch cubes have blue paint on at least three faces?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many positive integer values of N is the expression $\\dfrac{48}{N+3}$ an integer?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If for every \\\\(α∈\\left[ \\frac{π}{6}, \\frac{2π}{3} \\right]\\\\), there exists \\\\(β∈\\left[ \\frac{π}{6}, \\frac{2π}{3} \\right]\\\\) such that \\\\(\\cos α \\geqslant \\s... | math | {
"ground_truth": "a \\leqslant -1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\lg 2\\lg 50 + \\lg 25 - \\lg 5\\lg 20 = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A \"nearly regular\" triangle $H_{0}$ has angles of $59.5^\\circ$, $60^\\circ$, and $60.5^\\circ$. Consider the following sequence of triangles. Let $H_{1}$ be the pedal triangle... | math | {
"ground_truth": "H_6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the product $3^{1/5}3^{3/5}\\cdots3^{(2n+1)/5}$, where the exponents are generated by successive odd integers from 1 to $2n+1$, find the smallest positive odd integer $n$ s... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the sequence $x, 2x+2, 3x+3, \\dots$ are in geometric progression, calculate the value of the fourth term.",
"role": "user"
}
] | math | {
"ground_truth": "-13.5",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest quotient that can be formed using two numbers chosen from the set $\\{-24, -3, -2, 1, 2, 8\\}$, when the divisor is positive?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Point \\( O \\) is the center of the circle inscribed in triangle \\( ABC \\). It is known that \\( BC = a \\), \\( AC = b \\), \\(\\angle AOB = 120^{\\circ}\\). Find the side \\... | math | {
"ground_truth": "\\sqrt{a^2 + b^2 - ab}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be the largest integer such that $5^n$ divides $12^{2015}+13^{2015}$ . Compute the remainder when $\\frac{12^{2015}+13^{2015}}{5^n}$ is divided by $1000$ .",
... | math | {
"ground_truth": "625",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the equation of the normal to the given curve at the point with abscissa $x_{0}$.\n\n$y=2x^{2}+3x-1, \\, x_{0}=-2$",
"role": "user"
}
] | math | {
"ground_truth": "y = \\frac{1}{5} x + \\frac{7}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At which points are the tangents to the curve \\( y = \\frac{x^3}{3} - x^2 - x + 1 \\) parallel to the line \\( y = 2x - 1 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "(3, -2) \\text{ and } (-1, \\frac{2}{3})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression $\\sqrt{25\\sqrt{15\\sqrt{9}}}$.",
"role": "user"
}
] | math | {
"ground_truth": "5\\sqrt{15}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N{}$ be a fixed positive integer, $S{}$ be the set $\\{1, 2,\\ldots , N\\}$ and $\\mathcal{F}$ be the set of functions $f:S\\to S$ such that $f(i)\\geqslant i$ f... | math | {
"ground_truth": "\\frac{N+1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There is a very popular race course where runners frequently go for a daily run. Assume that all runners randomly select a start time, a starting position on the course, and a di... | math | {
"ground_truth": "225",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a design studio at various times during the day, the head designer hands over draft designs to an assistant for detailed drafting, stacking each new draft on top of the pile. ... | math | {
"ground_truth": "1554",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assume that the differential equation $$ y'''+p(x)y''+q(x)y'+r(x)y=0 $$ has solutions $y_1(x)$ , $y_2(x)$ , $y_3(x)$ on the real line such that $$ y_1(x)^2+y_2(x)^2+y_3(x)... | math | {
"ground_truth": "A = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Divide 96 into three parts that are proportional to 1, 1/4, 1/8. What is the middle part?",
"role": "user"
}
] | math | {
"ground_truth": "17\\frac{21}{44}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all ordered triples \\((a, b, c)\\) of positive reals that satisfy: \n\\[\n\\lfloor a\\rfloor bc = 3, \\quad a\\lfloor b\\rfloor c = 4, \\quad \\text{and} \\quad ab\\lfloor ... | math | {
"ground_truth": "\\left(\\frac{\\sqrt{30}}{3}, \\frac{\\sqrt{30}}{4}, \\frac{2 \\sqrt{30}}{5}\\right), \\left(\\frac{\\sqrt{30}}{3}, \\frac{\\sqrt{30}}{2}, \\frac{\\sqrt{30}}{5}\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An unfair coin is flipped 10 times. The coin has a $\\frac{1}{3}$ probability of coming up heads and a $\\frac{2}{3}$ probability of coming up tails. What is the probability that... | math | {
"ground_truth": "\\frac{512}{6561}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The water tank in the diagram is an inverted right circular cone. The radius of its base is 16 feet, and its height is 120 feet. The water in the tank is $30\\%$ of the tank's ca... | math | {
"ground_truth": "66",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate:<br/>$(1)-30-18-\\left(-29\\right)+\\left(-24\\right)$;<br/>$(2)-\\frac{1}{3}×54+(-\\frac{3}{4})÷|-0.25|$;<br/>$(3)-1^{2023}+(-\\frac{3}{2})^3×\\frac{4}{9}-5$;<br/>$(4)... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the hyperbola $E: \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1 (a > 0, b > 0),$ find the eccentricity of $E$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a function $f(x) = xe^{1-x} + ax^{3} - x$ where $a \\in \\mathbb{R}$.<br/>$(1)$ If $a = \\frac{1}{3}$, determine the monotonicity of $f(x)$ on $(-\\infty, 0]$;<br/>$(2)$ If... | math | {
"ground_truth": "[\\frac{2}{3}, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 2 girls and 6 boys playing a game. Determine the number of additional girls that must join the game so that $\\frac{5}{8}$ of the players are girls.",
"role": "user... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $a$ and $b$ are complex numbers such that $a^2 + b^2 = 5$ and $a^3 + b^3 = 7$ , then their sum, $a + b$ , is real. The greatest possible value for the sum $a + b$ is... | math | {
"ground_truth": "57",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all polynomials \\( P \\) such that the identity\n\n\\[ P(x+1) = P(x) + 2x + 1 \\]\n\nis satisfied.",
"role": "user"
}
] | math | {
"ground_truth": "P(x) = x^2 + c",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In how many different ways can we rearrange the twelve integers 1 to 12 on the face of a clock so that the sum of any three adjacent integers after the rearrangement is divisible... | math | {
"ground_truth": "82944",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the left focus of the ellipse $\\frac{x^2}{2}+y^2=1$ is $F_{1}$, and the line $l:y=x-1$ intersects the ellipse $C$ at points $A$ and $B$. \n$(1)$ Find the length of s... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice sells an item at $15$ less than the list price and receives $15\\%$ of her selling price as her commission. \nBob sells the same item at $25$ less than the list price and r... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $a + b = 40$, where $a$ and $b$ are positive integers and $a \\geq 5$, how many distinct ordered-pair solutions $(a, b)$ exist?",
"role": "user"
}
] | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers $n\\geq 3$ satisfying one can cut a convex $n$ -gon into different triangles along some of the diagonals (None of these diagonals intersects others at... | math | {
"ground_truth": "3 \\mid n",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the square's sides are each $5$ km long and Charlyn can see exactly $1$ km horizontally in all directions, calculate the area of the region consisting of all points Ch... | math | {
"ground_truth": "43",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $-2^2+\\sqrt{8}-3+\\frac{1}{3}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{20}{3} + 2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We call an isosceles trapezoid $PQRS$ *interesting*, if it is inscribed in the unit square $ABCD$ in such a way, that on every side of the square lies exactly one vertex of t... | math | {
"ground_truth": "1 - 2a",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression $\\sqrt{\\left(5-3\\sqrt{5}\\right)^2} - \\sqrt{\\left(5+3\\sqrt{5}\\right)^2}$.",
"role": "user"
}
] | math | {
"ground_truth": "-10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A family has 3 children. It is equally likely that a child is a boy as it is that a child is a girl. Determine the probability that the 3 children are all girls.",
"role": "u... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the center of an ellipse is at the origin, and it passes through the point $(1, \\dfrac{3}{2})$ on the $x$-axis. The eccentricity of the ellipse is the reciprocal of t... | math | {
"ground_truth": "(-\\infty,- \\dfrac{\\sqrt{7}}{7}) \\cup ( \\dfrac{\\sqrt{7}}{7}, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with sides $AB=19$ , $BC=21$ , and $AC=20$ . Let $\\omega$ be the incircle of $ABC$ with center $I$ . Extend $BI$ so that it intersects $AC$ ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are two distinguishable flagpoles, and there are $ 19$ flags, of which $ 10$ are identical blue flags, and $ 9$ are identical green flags. Let $ N$ be the number of... | math | {
"ground_truth": "310",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the binary operations $\\diamondsuit$ and $\\heartsuit$ defined by $a \\, \\diamondsuit \\, b = a^{\\log_{7}(b)}$ and $a \\, \\heartsuit \\, b = a^{\\frac{1}{\\log_{7}(b)}... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the numbers $0.001$, $1.01$, and $0.11$, calculate their sum.",
"role": "user"
}
] | math | {
"ground_truth": "1.121",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the domain of the function $f(x)$ is $\\left[1,+\\infty \\right)$, determine the domain of the function $y=f(x-1)+f(4-x)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[2,3\\right]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the vertex coordinate of the quadratic function $f(x)$ is $(1,2)$, and its graph passes through the origin, the function $g(x)=\\log_a x$ has its graph passing through... | math | {
"ground_truth": "\\text{Range of } F(x): (-\\infty, 1]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An eight-sided die (numbered 1 through 8) is rolled, and $Q$ is the product of the seven numbers that are visible. What is the largest number that is certain to divide $Q$?",
... | math | {
"ground_truth": "960",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathbf{a} = \\begin{pmatrix} 2 \\\\ -3 \\\\ -6 \\end{pmatrix},$ $\\mathbf{b} = \\begin{pmatrix} \\sqrt{11} \\\\ 5 \\\\ -2 \\end{pmatrix},$ and $\\mathbf{c} = \\begin{pmatr... | math | {
"ground_truth": "90^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Liu Hui was one of the most outstanding mathematicians in ancient China. His most significant contribution to the history of Chinese arithmetic was his annotation of \"The Nine C... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( A B C \\), the angle bisectors of its interior angles intersect at point \\( S \\). The angle \\( \\angle B S C \\) measures \\( 130^\\circ \\), and the angle \\(... | math | {
"ground_truth": "\\alpha = 80^\\circ, \\beta = 60^\\circ, \\gamma = 40^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a small town with 100,000 people, a random survey of 2,000 people was conducted. Among them, 250 people watched the morning news on CCTV. If you ask a person in the town at ra... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A diagram of a pentagonal pyramid is given. Construct the image of the section of this pyramid by a plane, which is defined by a line $l$ that intersects the plane of the base bu... | math | {
"ground_truth": "\\begin{aligned}\n&1.\\ \\text{Identify points on pyramid edges intersecting plane.} \\\\\n&2.\\ \\text{Verify all intersection points accurately.} \\\\\n&3.\\ \\text{Construct and outline sectional shape correctly. }\n\\end{aligned}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagram consists of a 4x4 grid of circles and rhombuses. If a 9x9 grid is formed following the same pattern, how many circles are there in the outermost ring?",
"role": "... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $f(x)= \\begin{cases} 2x-1, & (x\\geqslant 2) \\\\ f[f(x+1)]+1, & (x < 2) \\end{cases}$, find $f(1)$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a directed graph with $2013$ vertices, there is exactly one edge between any two vertices and for every vertex there exists an edge outwards this vertex. We know that whatev... | math | {
"ground_truth": "k = 2012",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ and $y$ be two-digit positive integers with a mean of $55$. Find the maximum value of the ratio $\\frac{x}{y}$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let be $f: (0,+\\infty)\\rightarrow \\mathbb{R}$ monoton-decreasing . \n\nIf $f(2a^2+a+1)<f(3a^2-4a+1)$ find interval of $a$ .",
"role": "user"
}
] | math | {
"ground_truth": "a \\in (0, \\frac{1}{3}) \\cup (1, 5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ be a positive real number and $a > 0$. Find the maximum possible value of $$\\frac{x^2+2-\\sqrt{x^4+a}}{x}.$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{2(\\sqrt{2} + \\sqrt{a})}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given four numbers, the sum of three of these numbers are 21, 28, 29, and 30, respectively. Find these four numbers.",
"role": "user"
}
] | math | {
"ground_truth": "6, 7, 8, 15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the edges \\(AC\\), \\(BC\\), \\(BS\\), \\(AS\\) of the regular triangular pyramid \\(SABC\\) with vertex \\(S\\), points \\(K\\), \\(L\\), \\(M\\), \\(N\\) are chosen, respec... | math | {
"ground_truth": "\\frac{52}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\{a_{n}\\}$ be an arithmetic sequence with a common difference $d=-2$, and $S_{n}$ be the sum of its first $n$ terms. If $S_{10}+110=2S_{11}$, then find the value of $a_{6}... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangle has an area of $16$ and a perimeter of $18$ ; determine the length of the diagonal of the rectangle.\n\n*2015 CCA Math Bonanza Individual Round #8*",
"role": "... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice and Mary were searching attic and found scale and box with weights. When they sorted weights by mass, they found out there exist $5$ different groups of weights. Playing ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "People use decibels ($dB$) to classify the level of sound. The level of sound $d(x)$ (unit: $dB$) is related to the sound intensity $x$ (unit: $W/m^{2}$) by the formula $d(x) = 9... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The radii of the inscribed and circumscribed circles of a right triangle are 2 and 5, respectively. Find the legs of the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "6 \\text{ and } 8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A box contains 13 balls, numbered from 1 through 13. If 7 balls are drawn simultaneously at random, what is the probability that the sum of the numbers on the balls drawn is odd?... | math | {
"ground_truth": "\\frac{847}{1716}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a complex number $z=(2m^{2}-7m+6)+(m^{2}-m-2)i\\left(m\\in R\\right)$.<br/>$(1)$ If the complex number $z$ is purely imaginary, find the value of the real number $m$;<br/>$... | math | {
"ground_truth": "(-1, \\frac{3}{2})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$2014$ points are placed on a circumference. On each of the segments with end points on two of the $2014$ points is written a non-negative real number. For any convex polygon ... | math | {
"ground_truth": "\\frac{n^2}{8}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the line $y=kx$ is tangent to the curve $y=x+e^{-x}$, then $k=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "1-e",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A set of integers \\( T \\) is called \"orensano\" if there exist integers \\( a < b < c \\) such that \\( a \\) and \\( c \\) are in \\( T \\) and \\( b \\) is not in \\( T \\).... | math | {
"ground_truth": "2^{2019} - 2039191",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A *domino* is a $2 \\times 1$ or $1 \\times 2$ tile. Determine in how many ways exactly $n^2$ dominoes can be placed without overlapping on a $2n \\times 2n$ chessboard... | math | {
"ground_truth": "\\binom{2n}{n}^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An express train from Basltown to Ironchester travels at a speed of 60 km/h, while an express train from Ironchester to Basltown, which departs at the same time, travels at a spe... | math | {
"ground_truth": "100 \\, \\text{km}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If 1 pint of paint is needed to paint a statue 8 ft. high, then the number of pints it will take to paint (to the same thickness) 400 statues similar to the original but only 2 f... | math | {
"ground_truth": "\\text{B) 25 pints}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S = \\{(x,y) | x = 1, 2, \\ldots, 1993, y = 1, 2, 3, 4\\}$ . If $T \\subset S$ and there aren't any squares in $T.$ Find the maximum possible value of $|T|.$ The squa... | math | {
"ground_truth": "5183",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Cyclic quadrilateral $ABCD$ satisfies $\\angle ADC = 2 \\cdot \\angle BAD = 80^\\circ$ and $\\overline{BC} = \\overline{CD}$ . Let the angle bisector of $\\angle BCD$ meet... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of the fractions $\\frac{2}{20} + \\frac{4}{40} + \\frac{9}{90}$.",
"role": "user"
}
] | math | {
"ground_truth": "0.3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimal positive integer $m$ , so that there exist positive integers $n>k>1$ , which satisfy $11...1=11...1.m$ , where the first number has $n$ digits $1$ , and the... | math | {
"ground_truth": "101",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the length of segment $GH$ if $JK \\parallel LM \\parallel GH$?\n\n[asy]\nsize(4cm,4cm);\npair J,K,L,M,G,H,Y;\n\nJ=(0,1.2);\nK=(1.2,1.2);\nL=(1.2,0);\nY=(0,0);\nM=(1/3)*L... | math | {
"ground_truth": "72 \\text{ cm}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
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