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": "Let \\(d_1 = a^2 + 3^a + a \\cdot 3^{(a+1)/2}\\) and \\(d_2 = a^2 + 3^a - a \\cdot 3^{(a+1)/2}\\). If \\(1 \\le a \\le 251\\), how many integral values of \\(a\\) are there such ... | 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": "Given two sets $M = \\{1, 2, 3, m\\}$ and $N = \\{4, 7, n^4, n^2 + 3n\\}$ where $m, n \\in \\mathbb{N}$, the mapping $f: y \\mapsto 3x + 1$ is a function from $M$ to $N$. Determi... | 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": "What is the $y$-coordinate of the point on the $y$-axis that is equidistant from points $C(3, 0)$ and $D(5, 6)$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From the 8 English letters \\( A, B, C, D, E, X, Y, Z \\), select 5 letters (with repetition allowed) to form a \"word.\" Arrange all possible \"words\" in \"lexicographic order\... | math | {
"ground_truth": "9590",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the sequence $00$ , $01$ , $02$ , $03$ , $\\cdots$ , $99$ the terms are rearranged so that each term is obtained from the previous one by increasing or decreasing one o... | math | {
"ground_truth": "50",
"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": "Two dice each with 8 sides are rolled. What is the probability that the sum rolled is a perfect square?",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{3}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $f(-2)$ if $f(x) = x^3 - 3x^2 + x$?",
"role": "user"
}
] | math | {
"ground_truth": "-22",
"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 positive integers $n$ for which the equation $$ (x^2 + y^2)^n = (xy)^{2016} $$ has positive integer solutions.",
"role": "user"
}
] | math | {
"ground_truth": "n \\in \\{1344, 1728, 1792, 1920, 1984\\}",
"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 $\\angle A=76^{\\circ}$, calculate the measure of the complement of $\\angle A$.",
"role": "user"
}
] | math | {
"ground_truth": "14^{\\circ}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\sqrt[3]{1.51}=1.147$, $\\sqrt[3]{15.1}=2.472$, and $\\sqrt[3]{0.151}=0.5325$, calculate the value of $\\sqrt[3]{1510}$.",
"role": "user"
}
] | math | {
"ground_truth": "11.47",
"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 San Antonio-bound bus traveling from San Antonio to Austin departs every hour and the journey takes 7 hours. If buses from Austin to San Antonio leave every half hour, find the... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $14x + 5 - 21x^2 = -2$, then $6x^2 - 4x + 5 =$ ?",
"role": "user"
}
] | 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 functions $f(x) = x^2$ and $g(x) = \\log_{10}x$, if $f(a) = g(b)$, determine the range of $b$.",
"role": "user"
}
] | math | {
"ground_truth": "[1, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of distinct integers that can be expressed as the sum of two special fractions, where a special fraction is a fraction a/b, with positive integers a and b whose s... | math | {
"ground_truth": "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": "The surface area of a cube with edge length 1 cm is to be calculated.",
"role": "user"
}
] | math | {
"ground_truth": "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 that $i$ is the imaginary unit, find the value of ${\\left( \\frac{1+i}{1-i}\\right)}^{2016}$.",
"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": "What is the condition for a triangle, constructed from the medians of a right triangle as its sides, to also be a right triangle?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{The ratio of the legs of the right triangle must be \\(1: \\sqrt{2}\\)}",
"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": "Cleo the camel takes 36 equal steps to walk between consecutive telephone poles on a desert track. Zoe the zebra can cover the same distance in 9 equal jumps. The telephone poles... | math | {
"ground_truth": "\\textbf{(B) }14.7",
"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": "Schools A and B organize some teachers and students to go to an outdoor base for expansion training. They depart from two locations that are $240$ kilometers and $270$ kilometers... | math | {
"ground_truth": "\\text{The average speed of the bus for School A is 60 km/h, and for School B is 90 km/h.}",
"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 $3 \\in \\{1, a, a-2\\}$, determine the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alex writes down the smallest positive multiple of 12 that is both a perfect square and a perfect cube. Next, Alex writes down all the positive multiples of 12 up to this number.... | math | {
"ground_truth": "144",
"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": "Two candles, initially the same length, burn down at different consistent rates. One candle burns completely in $5$ hours, and the other in $6$ hours. At what time should the can... | math | {
"ground_truth": "1:00 \\text{ P.M.}",
"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 function $f(x)$ is defined by $f(x) = x^2 - 2x + 1$. What is the value of $f(4)$?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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": "$\\sqrt{(-9)^{2}}=$____.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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 the triangle \\( \\triangle ABC \\), it is known that \\( \\sin A = \\frac{4}{5} \\), \\( \\cos B = \\frac{12}{13} \\). Calculate \\( \\cos C \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\cos C = -\\frac{16}{65} \\text{ or } \\cos C = \\frac{56}{65}",
"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 two-digit number \\( ab \\) be \\( 10a + b \\), where \\( a \\) and \\( b \\) are digits such that \\( 1 \\leq a \\leq 9 \\) and \\( 0 \\leq b \\leq 9 \\). The difference b... | math | {
"ground_truth": "D) 99",
"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 odd function \\( f(x) \\) is increasing on the interval \\( (-\\infty, 0) \\), and that \\( f(-2) = -1 \\), \\( f(1) = 0 \\). When \\( x_{1} > 0 \\) and \\( x_{2} ... | math | {
"ground_truth": "(-4, -2) \\cup (-2, -1) \\cup \\left( \\frac{1}{4}, \\frac{1}{2} \\right) \\cup \\left(\\frac{1}{2}, 1 \\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": "Given that point P moves on the circle $x^2+y^2=1$, and DP is perpendicular to the y-axis with the foot of the perpendicular being point D. Point M is on line segment DP, and $\\... | math | {
"ground_truth": "(-1, -\\frac{1}{2}) \\cup (\\frac{1}{2}, 1)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four friends came to the skating rink, each with her brother. They paired up and started skating. It turned out that in each pair, the \"gentleman\" is taller than the \"lady\" a... | math | {
"ground_truth": "\\text{1. Люся Егорова с Юрой Воробьевым, 2. Оля Петрова с Андреем Егоровым, 3. Инна Кры́мова с Сергеем Петровым, 4. Аня Воробьева с Димой Кры́мовым.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the number $2^{1000}$ is divided by $17$, what is the remainder?\nA) 0\nB) 1\nC) 2\nD) 3\nE) 4",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(A) }0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If one minus twice the reciprocal of $(1+x)$ equals the reciprocal of $(1+x)$, find $x$.\nA) 1/3 \nB) 2 \nC) -2 \nD) -1 \nE) 3",
"role": "user"
}
] | math | {
"ground_truth": "B) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a larger checkerboard composed of 10 × 10 = 100 unit squares, calculate the probability that a randomly chosen unit square does not touch the outer edge of the board.",
"r... | math | {
"ground_truth": "\\frac{16}{25}",
"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": "Evaluate the expression $\\frac{(0.5)^{3.5}}{(0.05)^3}$.\nA) $158.11\\sqrt{5}$\nB) $316.23\\sqrt{5}$\nC) $632.46\\sqrt{5}$\nD) $948.69\\sqrt{5}$\nE) $500\\sqrt{5}$",
"role": ... | math | {
"ground_truth": "316.23\\sqrt{5}",
"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": "$(3^1 - 2 + 6^2 - 1)^{-2} \\times 3$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{432}",
"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 area of the $MNRK$ trapezoid with the lateral side $RK = 3$ if the distances from the vertices $M$ and $N$ to the line $RK$ are $5$ and $7$ , respectively.... | math | {
"ground_truth": "18",
"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": "<details><summary>R stands for Ramanujan , P stands for Pascal</summary>they had two problem sets under those two names</details> \n\n<u>Set 1</u>**R1.1 / P1.1** Find $291 + 50... | math | {
"ground_truth": "241",
"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": "This year's gift idea from BabyMath consists of a series of nine colored plastic containers of decreasing size, alternating in shape like a cube and a sphere. All containers can ... | math | {
"ground_truth": "\\frac{s_1}{9}",
"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 an integral solution of the equation \n\\[ \\left \\lfloor \\frac{x}{1!} \\right \\rfloor + \\left \\lfloor \\frac{x}{2!} \\right \\rfloor + \\left \\lfloor \\frac{x}{3!} \\... | math | {
"ground_truth": "1176",
"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 pairs of positive integers \\((a, b)\\) such that \\(2^{a}+3^{b}\\) is the square of an integer.",
"role": "user"
}
] | math | {
"ground_truth": "(4, 2)",
"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": "What is the degree measure of the supplement of the complement of a 65-degree angle?",
"role": "user"
}
] | math | {
"ground_truth": "155^\\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": "A club with $x$ members is organized into four committees in accordance with these two rules: each member belongs to two and only two committees, and each pair of committees has ... | math | {
"ground_truth": "6",
"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 $P(x)$ be a polynomial with integer coefficients and roots $1997$ and $2010$ . Suppose further that $|P(2005)|<10$ . Determine what integer values $P(2005)$ can get."... | math | {
"ground_truth": "P(2005) = 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": "If the inequality $|2x-m| \\leq |3x+6|$ always holds, then the range of the real number $m$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\{m | m = -4\\}",
"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 a list of five positive integers has a mean of 15 and a range of 24, and the mode and median are both 10, calculate the number of possible different values for the sec... | 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": "Trapezoid $EFGH$ has sides $EF=84$, $FG=58$, $GH=27$, and $HE=64$, with $EF$ parallel to $GH$. A circle with center $Q$ on $EF$ is drawn tangent to $FG$ and $HE$. Find the length... | math | {
"ground_truth": "54",
"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": "Mr. Rose, Mr. Stein, and Mr. Schwartz start at the same point around a circular track and run clockwise. Mr. Stein completes each lap in $6$ minutes, Mr. Rose in $10$ minutes... | math | {
"ground_truth": "90",
"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": "John drives from his home to a business meeting location. He drives 40 miles in the first hour but realizes that he will be 1.5 hours late if he continues at this speed. He incre... | math | {
"ground_truth": "420",
"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": "There are two trains, each 125 meters and 115 meters long respectively, with speeds of 22 meters per second and 18 meters per second respectively. They are moving towards each ot... | math | {
"ground_truth": "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": "A certain type of bacteria starts with four cells. Each cell divides into two cells every two days. If this process continues unhindered for a total of 10 days, how many cells wi... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively, and $\\frac{\\cos B}{\\cos C} =- \\frac{b}{2a+c}$.\n\n1. Find the measure ... | math | {
"ground_truth": "\\sqrt{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": "Every edge of a cube is coloured either red or green, and every face of the cube has at least one red edge. Determine the smallest number of red edges.",
"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": "Let $m\\geq 4$ and $n\\geq 4$ . An integer is written on each cell of a $m \\times n$ board. If each cell has a number equal to the arithmetic mean of some pair of numbers w... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $78$ is divided into three parts which are proportional to $1, \\frac13, \\frac16$, calculate the value of the middle part.",
"role": "user"
}
] | math | {
"ground_truth": "17\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A parking lot has 20 spaces in a row. Fourteen cars arrive, each of which requires one parking space, and their drivers choose spaces at random from among the available spaces. A... | math | {
"ground_truth": "\\textbf{(B)} \\; \\frac {850}{922}",
"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 smallest real number \\(\\lambda\\) such that the inequality\n$$\n5(ab + ac + ad + bc + bd + cd) \\leq \\lambda abcd + 12\n$$\nholds for all positive real numbers \\(a, ... | 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": "A thin diverging lens, with an optical power \\( D_p = -6 \\) diopters, is illuminated by a light beam with a diameter of \\( d_1 = 5 \\) cm. On a screen parallel to the lens, a ... | math | {
"ground_truth": "10 \\text{ diopters}",
"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 $\\log_3(\\log_4(\\log_5 x))=\\log_4(\\log_5(\\log_3 y))=\\log_5(\\log_3(\\log_4 z))=0$, determine the value of the sum $x+y+z$.",
"role": "user"
}
] | math | {
"ground_truth": "932",
"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": "An \"$n$-pointed star\" is created as follows: in a convex polygon with sides numbered $1, 2, \\ldots, n$ (where \\(n \\geq 6\\)), each side $k$ is non-parallel to side $k+3$, an... | math | {
"ground_truth": "180^\\circ (n - 2)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Some of the digits in the following correct addition have been replaced by the letters \\( P, Q, R, \\) and \\( S \\), as shown.\nWhat is the value of \\( P+Q+R+S \\)?\n\\[\n\\be... | math | {
"ground_truth": "15",
"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 coefficient of the term containing $x^2$ in the expansion of the binomial $(x- \\frac {2}{x})^{8}$ needs to be calculated.",
"role": "user"
}
] | math | {
"ground_truth": "-448",
"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": "Ms. Garcia teaches a class of 17 students with an average grade of 87 after grading two additional students. The average grade of the first 15 students is 85. Find the combined t... | math | {
"ground_truth": "204",
"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": "Penniless Pete's piggy bank has 100 coins, all nickels, dimes, and quarters, with a total value of $8.35. Determine the difference between the largest and smallest number of dime... | math | {
"ground_truth": "64",
"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": "4. k pieces are placed in k squares of an n x n (n ≥ 2) grid (with exactly one piece in each square), and in each 2 x 2 subgrid, there are exactly two pieces. Find all possible v... | math | {
"ground_truth": "k \\in \\left\\{0, \\frac{n^2}{2}\\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": "If the integers $m,n,k$ hold the equation $221m+247n+323k=2001$, find the smallest possible value of $k$ greater than 100.",
"role": "user"
}
] | math | {
"ground_truth": "111",
"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 $ABCD$, $AEFB$, and $AGHD$ be three adjacent square faces of a cube, where $AD = 10$. Let $P$ be the eighth vertex of the cube. Let $L$, $M$, and $N$ be the points on $\\over... | math | {
"ground_truth": "597",
"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": "Seventy percent of a ship's passengers are women, and fifteen percent of these women are in first class. What is the number of women in first class if the ship is carrying 300 pa... | math | {
"ground_truth": "31",
"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": "Jerry and Sylvia plan to walk from the southwest corner of a square plaza to the northeast corner. Jerry walks east first and then north to reach the destination, while Sylvia he... | math | {
"ground_truth": "30\\%",
"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": "Paul owes Paula $45$ cents and has a pocket full of $5$-cent coins, $10$-cent coins, and $25$-cent coins that he can use to pay her. Find the difference between the largest and 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": "Find $x$ such that $\\log_{10}(5x + 10) = 3$.",
"role": "user"
}
] | math | {
"ground_truth": "198",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A number 198 is multiplied by 53. The product is then required to be expressed in base-8. Before finding the product, subtract 3 from 198 and add 7 to 53. What is the unit's digi... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\{a_n\\}$ be a geometric sequence with the sum of the first $n$ terms denoted by $S_n = 2^n + a$, and $\\{b_n\\}$ be an arithmetic sequence with the sum of the first $n$ te... | math | {
"ground_truth": "0",
"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": "Isosceles triangles \\(ABC (AB = BC)\\) and \\(A_1B_1C_1 (A_1B_1 = B_1C_1)\\) are similar and \\(AB : A_1B_1 = 2 : 1\\).\n\nVertices \\(A_1, B_1\\), and \\(C_1\\) are located on ... | math | {
"ground_truth": "\\arccos \\left( \\frac{1}{8} \\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": "A geometric sequence starts with $32$, $-48$, $72$, $-108$, $162$. Verify the common ratio of the sequence and ensure it remains consistent across the terms provided.",
"role... | math | {
"ground_truth": "-\\frac{3}{2}",
"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 which values of \\(a\\) and \\(b\\) do the equations\n\n\\[ \n19 x^{2} + 19 y^{2} + a x + b y + 98 = 0 \n\\]\n\nand \n\n\\[ \n98 x^{2} + 98 y^{2} + a x + b y + 19 = 0 \n\\]\n... | math | {
"ground_truth": "a^2 + b^2 \\geq 13689",
"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 point $P$ is outside a circle and is $15$ inches from the center. A secant from $P$ cuts the circle at $Q$ and $R$ so that the external segment of the secant $PQ$ is $11$ inche... | math | {
"ground_truth": "2 \\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": "The sequence \\(\\{a_n\\}\\) is defined by the recurrence relation:\n\\[ a_1 = 1, \\quad a_{n+1} = a_n + \\frac{1}{a_n}, \\quad n \\geq 1. \\]\n\nFind all \\( n \\) such that \\(... | math | {
"ground_truth": "n > 191",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the limit of the function\n\n$$\n\\lim _{x \\rightarrow 1}\\left(\\frac{2 x-1}{x}\\right)^{\\ln (3+2 x) / \\ln (2-x)}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "Let \\[f(x) = \\left\\{\n\\begin{array}{cl} \n2ax+6, & \\text{ if } x > 2, \\\\\n3x-2 & \\text{ if } -2 \\leq x \\leq 2, \\\\\n4x+2c & \\text{ if } x < -2.\n\\end{array} \n\\righ... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many real numbers $x$ satisfy the equation $2^{4x} - 5(2^{2x+1}) + 4 = 0$.\nA) 0 \nB) 1 \nC) 2 \nD) 3 \nE) 4",
"role": "user"
}
] | math | {
"ground_truth": "C) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using digits $ 1, 2, 3, 4, 5, 6$ , without repetition, $ 3$ two-digit numbers are formed. The numbers are then added together. Through this procedure, how many different sums ... | math | {
"ground_truth": "100",
"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 $AB$ be a diameter of a circle and let $C$ be a point on the segement $AB$ such that $AC : CB = 6 : 7$ . Let $D$ be a point on the circle such that $DC$ is perpen... | 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": "Find all polynomials $P\\in\\mathbb{Z}[x]$ such that $$ |P(x)-x|\\leq x^2+1 $$ for all real numbers $x$ .",
"role": "user"
}
] | math | {
"ground_truth": "P(x) = ax^2 + (b + 1)x + c",
"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": "Mark and William are playing a game with a stored value. On his turn, a player may either multiply the stored value by $2$ and add $1$ or he may multiply the stored value by ... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Denis kept chameleons that can change color only to red and brown. At first, the number of red chameleons was five times greater than the number of brown chameleons. After two br... | math | {
"ground_truth": "36",
"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": "Caroline can make eleven lassis using two mangoes. How many lassis can she make if she has ten mangoes?",
"role": "user"
}
] | math | {
"ground_truth": "55",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the probability that Alex wins each round is $\\frac{3}{7}$ and Mel is three times as likely to win as Chelsea, find the probability that Alex wins four rounds, Mel wi... | math | {
"ground_truth": "\\frac{76545}{823543}",
"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 $XYZ$ be a triangle with $ \\angle X = 60^\\circ $ and $ \\angle Y = 45^\\circ $ . A circle with center $P$ passes through points $A$ and $B$ on side $XY$ , $C$ ... | math | {
"ground_truth": "52.5^\\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": "Given that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ in $\\triangle ABC$, respectively, and $\\cos 2A= -\\frac{1}{3}$, $c= \\sqrt{3}$, $\\cos 2A=6\\cos... | math | {
"ground_truth": "\\frac{5\\sqrt{2}}{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 sequence \\\\(\\{a_n\\}\\\\) with the sum of the first \\\\(n\\\\) terms being \\\\(S_n\\\\), and it satisfies: \\\\(a_1=1\\\\), \\\\(a_2=2\\\\), \\\\(S_n+1=a_{n+2}-a_{n+... | math | {
"ground_truth": "\\lambda > 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": "Compute the domain of the function $$f(x)=\\frac{1}{\\lfloor x^2 - 9x + 20 \\rfloor}.$$",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, \\frac{9 - \\sqrt{5}}{2}) \\cup (\\frac{9 + \\sqrt{5}}{2}, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a calculator that alternately squares and reciprocates the displayed entry a number of times, $n$, find the formula for the final result, $y$, in terms of the initial numbe... | math | {
"ground_truth": "x^{((-2)^n)}",
"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": "Let $k$ be a positive integer. Find the smallest positive integer $n$ for which there exists $k$ nonzero vectors $v_1,v_2,…,v_k$ in $\\mathbb{R}^n$ such that for every ... | math | {
"ground_truth": "\\left\\lceil \\frac{k}{2} \\right\\rceil",
"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 convex polygons $P_1$ and $P_2$ are drawn in the same plane with $n_1$ and $n_2$ sides, respectively, with $n_1\\le n_2$. If $P_1$ and $P_2$ do not have any line segment in... | math | {
"ground_truth": "n_1n_2",
"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": "The equation of the hyperbola with asymptotes $y=\\pm x$ and passing through the point $(2,0)$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x^2}{4}-\\frac{y^2}{4}=1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a polynomial $p(x)$, which satisfies the conditions: \\( p(0) = 2 \\) and \\( p(2) = 6 \\), find the remainder polynomial \\( r(x) \\) when \\( p(x) \\) is divided by \\( (... | math | {
"ground_truth": "B) \\( 2x + 2 \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ such that the number $2^n + 2^8 + 2^{11}$ is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a $k$ -player tournament for $k > 1$ , every player plays every other player exactly once. Find with proof the smallest value of $k$ such that it is possible that for any ... | math | {
"ground_truth": "k = 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": "The interval in which the function $x=\\log x^2$ is monotonically decreasing is __________.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For real numbers $a$ and $b$, the definition of $\\min \\{a,b\\}$ is as follows: when $a \\lt b$, $\\min \\{a,b\\}=a$; when $a \\gt b$, $\\min \\{a,b\\}=b$. For example, $\\min \... | math | {
"ground_truth": "4",
"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 sequence $a_n=\\begin{cases}n-1, & \\text{if } n \\text{ is odd}, \\\\ n, & \\text{if } n \\text{ is even},\\end{cases}$ then $S_{100}=$ ______.",
"role": "user"
... | math | {
"ground_truth": "5000",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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