data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Factorization: $-2x^{2}+2x-\\frac{1}{2}=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "-2(x-\\frac{1}{2})^{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the area of a polygon whose vertices are given as $(0,0)$, $(4,3)$, $(7,3)$, and $(3,0)$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the interval(s) where the function $f(x)=\\tan (2x-\\frac{{ }\\,!\\!\\pi\\!\\!{ }}{3})$ is strictly increasing.",
"role": "user"
}
] | math | {
"ground_truth": "(\\frac{k\\pi}{2}-\\frac{\\pi}{12},\\frac{k\\pi}{2}+\\frac{5\\pi}{12}), k \\in \\mathbb{Z}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the function\n\\[f(x) = \\max \\{-7x - 25, x^2 - 1, 5x + 7\\}\\]\ndefined for all real $x.$ Let $p(x)$ be a quadratic polynomial tangent to the graph of $f$ at three dis... | math | {
"ground_truth": "-\\frac{16}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An infinite sequence $ \\,x_{0},x_{1},x_{2},\\ldots \\,$ of real numbers is said to be **bounded** if there is a constant $ \\,C\\,$ such that $ \\, \\vert x_{i} \\vert \\le... | math | {
"ground_truth": "a = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The area bounded by the larger circle with radius \\( R \\) is twice the area of the region outside the smaller circle and inside the larger circle.",
"role": "user"
}
] | math | {
"ground_truth": "5\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Chongqing hotpot, also known as tripe hotpot or spicy hotpot, is one of the traditional ways of eating in China. It originated on the banks of the Jialing River in Chongqing at t... | math | {
"ground_truth": "675",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "My recipe for apple crumble uses 100 grams of flour, 50 grams of butter, and 50 grams of sugar to make the crumble topping. When my family comes for a meal, I have to use two and... | math | {
"ground_truth": "\\text{A } 0.5 \\, \\text{kg}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The roots of the equation $x(x-1)=0$ are ____.",
"role": "user"
}
] | math | {
"ground_truth": "x_{1}=0, x_{2}=1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John's truck can travel 25 miles on a gallon of gas, and the current price of gas is $5 per gallon. Calculate the number of miles John can drive on $30 worth of gas.",
"role"... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the molar mass of $\\ce{NaHCO3}$ is 84 g/mol and 25.0 mL of 0.125 M $\\ce{H2SO4}$ is present, calculate the mass of $\\ce{NaHCO3}$ required to completely neutralize th... | math | {
"ground_truth": "0.525",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The three sides of a right triangle have integral lengths which form an arithmetic progression. Express the length of the longest side in terms of the common difference between t... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A servant is sent to a spring with two vessels of 7 pints and 11 pints capacity. She needs to bring back exactly 2 pints of water.\n\nWhat is the minimum number of operations req... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mr. and Mrs. Gamma wish to name their baby such that its monogram (first, middle, and last initials) contains their last initial 'G' as the middle initial, and the other initials... | math | {
"ground_truth": "The correct answer is (C) 108.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions $f:\\mathbb{Z}_{>0}\\rightarrow\\mathbb{Z}_{>0}$ that satisfy the following two conditions:\n[list] $\\bullet\\ f(n)$ is a perfect square for all $n\\in\\m... | math | {
"ground_truth": "f(n) = n^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest positive integer $n$ less than $10, 000$ such that in base $4$ , $n$ and $3n$ have the same number of digits; in base $8$ , $n$ and $7n$ have th... | math | {
"ground_truth": "4369",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $12^{603} - 8^{402}$, determine the greatest power of $2$ that is a factor of this expression.",
"role": "user"
}
] | math | {
"ground_truth": "2^{1209}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the base-10 integers 350 and 1500 are expressed in base 2, and their binary forms are added, how many digits does the resulting binary sum have?",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of $\\log_{3}{0.54}$.\nA) -0.5603\nB) -1.5603\nC) 0.5603\nD) -0.4630",
"role": "user"
}
] | math | {
"ground_truth": "The answer is A) -0.5603.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smaller of the two distinct solutions to the equation $$x^2 - 9x + 20 = 0.$$",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $x_{1}$ and $x_{2}$ are two real roots of the equation $x^{2}-x-2023=0$, calculate the value of the algebraic expression $x_1^3-2023{x_1}+x_2^2$.",
"role": "user"
... | math | {
"ground_truth": "4047",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $(1+mx)^{6}=a_{0}+a_{1}x+a_{2}x^{2}+\\cdots +a_{6}x^{6}$, and $a_{1}-a_{2}+a_{3}-a_{4}+a_{5}-a_{6}=-63$, then the value of the real number $m$ is.",
"role": "user"
}
] | math | {
"ground_truth": "3 \\text{ or } -1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $$f(x)= \\begin{cases} -2x-3, & \\text{if } x<2 \\\\ 2^{-x}, & \\text{if } x\\geq2 \\end{cases}$$, then the value of $f[f(-3)]$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Write the canonical equations of the line.\n\n$$\n\\begin{aligned}\n& 4x + y + z + 2 = 0 \\\\\n& 2x - y - 3z - 8 = 0\n\\end{aligned}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x-1}{-2} = \\frac{y+6}{14} = \\frac{z}{-6}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using only the digits 6, 7, and 8, how many positive nine-digit integers can be created that are palindromes?",
"role": "user"
}
] | math | {
"ground_truth": "243",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a, b \\in \\mathbb{R}^+$, and the line $ax+by-6=0$ is parallel to the line $2x+(b-3)y+5=0$, find the minimum value of $2a+3b$.",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "One of the boxes that Joshua and Wendy unpack has Joshua's collection of board games. Michael, Wendy, Alexis, and Joshua decide to play one of them, a game called $\\textit{Ris... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The target below is made up of concentric circles with diameters $4$ , $8$ , $12$ , $16$ , and $20$ . The area of the dark region is $n\\pi$ . Find $n$ .\n\n[asy]\nsize(15... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation of ellipse C is $$\\frac {x^{2}}{a^{2}}+ \\frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$), and its left and right foci are $F_{1}$ and $F_{2}$ respectively. If the su... | math | {
"ground_truth": "(-2, -\\frac { \\sqrt {3}}{2})\\cup(\\frac { \\sqrt {3}}{2}, 2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the values of the algebraic expressions $4y+8$ and $8y-7$ are opposite, then the value of $y$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A natural number that can be expressed as the difference of squares of two other natural numbers is called a \"wise number\". For example, \\( 16 = 5^{2} - 3^{2} \\), so \\( 16 \... | math | {
"ground_truth": "2659",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On the sides $ AB $ and $ AC $ of the triangle $ ABC $ consider the points $ D, $ respectively, $ E, $ such that $$ \\overrightarrow{DA} +\\overrightarrow{DB} +\\over... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow{a}=(6,-2,6)$ and $\\overrightarrow{b}=(-3,1,x)$, find the value of $x$ that satisfies $\\overrightarrow{a}$ ∥ $\\overrightarrow{b}$.",
"role":... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular region is bounded by the graphs of the equations \\(y = 2a\\), \\(y = -b\\), \\(x = -2c\\), and \\(x = d\\), where \\(a, b, c,\\) and \\(d\\) are all positive numbe... | math | {
"ground_truth": "A) \\((2a + b)(d + 2c) - \\frac{1}{2} (d + 2c + b + a)(a + b + 2c)\\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the $1500^{\\text{th}}$ digit past the decimal point in the decimal expansion of \\(\\frac{7}{22}\\).",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of triples (a, b, c) of positive integers which satisfy the simultaneous equations ab+bc = 44 and ac+bc=23.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $$f(x)=\\frac{{{2}^{x}}+3}{{{2}^{x}}+1}$$, determine the range of the function y=[f(x)].",
"role": "user"
}
] | math | {
"ground_truth": "\\{1, 2\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On each move, you can choose a natural number \\( x \\) and cross out all natural numbers \\( y \\) such that \\( |x-y| \\) is a natural composite number. Already crossed out num... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the volumes of eight cubes are 1, 8, 27, 64, 125, 216, 343, and 512 cubic units. The structure features seven cubes stacked vertically in decreasing order of volume, while ... | math | {
"ground_truth": "890",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the sum of the first 10 terms of a geometric sequence $\\{a_n\\}$ is 32 and the sum of the first 20 terms is 56, find the sum of the first 30 terms.",
"role": "use... | math | {
"ground_truth": "74",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ be a triangle with $AB = 7$ , $AC = 8$ , and $BC = 3$ . Let $P_1$ and $P_2$ be two distinct points on line $AC$ ( $A, P_1, C, P_2$ appear in that... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $\\frac{17!}{8!9!}$.",
"role": "user"
}
] | math | {
"ground_truth": "130",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which integer $a$ does $x^2 - x + a$ divide $x^{13} + x + 180$?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The tens digit of the original three-digit number is $x$, the hundreds digit is $x+3$, and the units digit is $x-3$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For what smallest value of the parameter \\( a \\) will the coefficient of \\( x^{4} \\) in the expansion of the polynomial \\( \\left(1-3 x+a x^{2}\\right)^{8} \\) be equal to 7... | math | {
"ground_truth": "-50",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The set $\\{-1, 0, 1\\}$ has a total of ____ subsets.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $f(x) = -\\dfrac{2}{x},$ what is $f(f(f(f(f(3)))))$?",
"role": "user"
}
] | math | {
"ground_truth": "-\\dfrac{2}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) If $f(x+1)=2x^{2}+1$, find the expression for $f(x)$;\n(2) If the function $f(x)= \\frac {x}{ax+b}$, $f(2)=1$, and the equation $f(x)=x$ has a unique solution, find the expre... | math | {
"ground_truth": "\\frac {2x}{x+2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and $\\cos A = \\frac{1}{3}$.\n(1) Find the value of $\\sin^2 \\frac{B+C}... | math | {
"ground_truth": "\\frac{3\\sqrt{2}}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\log_2(\\log_3(\\log_2(x)))=2$, then how many digits are in the base-ten representation for $x$?\nA) 23\nB) 24\nC) 25\nD) 26\nE) 27",
"role": "user"
}
] | math | {
"ground_truth": "C) 25",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $c$ and $d$ are nonzero real numbers, and the equation $x^2 + cx + d = 0$ has solutions $c$ and $d$. Find the ordered pair $(c, d)$.",
"role": "user"
}
] | math | {
"ground_truth": "(1, -2)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a pentagon is inscribed in a circle, calculate the sum of the angles that are inscribed into each of the five segments outside the pentagon, each segment being the region o... | math | {
"ground_truth": "720^{\\circ}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a cell phone plan with a base cost of $25 per month and an additional rate of $0.15 per minute beyond 25 hours of talk time, and an additional cost of $0.08 per text messag... | math | {
"ground_truth": "64.00",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What three-digit number with units digit 4 and hundreds digit 6 is divisible by 7?",
"role": "user"
}
] | math | {
"ground_truth": "658",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x$ varies as the cube of $y$, and $y$ varies as the fifth root of $z$, then determine the value of the exponent $n$ in the relationship $x$ varies as the $z^n$.",
"role":... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Is there a number that is divisible by 737 and whose decimal representation consists of ones and zeros?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Yes, there exists a number that is divisible by 737 and whose decimal representation consists of the digits 0 and 1.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\sin(3x+3\\varphi)-2\\sin(x+\\varphi)\\cos(2x+2\\varphi)$, where $|\\varphi| < \\pi$, if $f(x)$ is monotonically decreasing in the interval $\\left( \\f... | math | {
"ground_truth": "\\frac{5\\pi}{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\angle \\alpha = 60^\\circ$, then its supplementary angle equals to ____.",
"role": "user"
}
] | math | {
"ground_truth": "120^\\circ",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the altitudes of triangle \\( \\triangle ABC \\), which has a perimeter of 1, can form a new triangle, what is the range of values for \\( \\min \\{AB, BC, CA\\} \\)?",
"r... | math | {
"ground_truth": "\\left( \\frac{3 - \\sqrt{5}}{4}, \\frac{1}{3} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(For this question, full score is 10 points) Elective 4-4: Coordinate System and Parametric Equations: \nIt is known that the parametric equation of circle C is (φ is the parame... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "To ensure that Xiaoxiao's school's soccer team secures at least the top two positions in a forthcoming friendly round-robin tournament (where each of the 4 teams plays against on... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of distinct pairs \\((x,y)\\) of real numbers satisfying both of the following equations:\n\\[x = x^2 + 2y^2\\]\n\\[y = 3xy\\]\n**A)** 0 \n**B)** 1 \n**C)** 2 \n**D... | math | {
"ground_truth": "\\textbf{(E)} \\ 4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the expression $\\left(\\sum_{k=1}^{20} \\log_{5^k} 3^{k^2}\\right)\\cdot\\left(\\sum_{k=1}^{100} \\log_{9^k} 25^k\\right)$, calculate the value.",
"role": "user"
}
] | math | {
"ground_truth": "21000",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a right circular cone with base radius $5$ and height $12$, find the radius $r$ of three congruent spheres that are tangent to each other and to the base and side of the co... | math | {
"ground_truth": "\\frac{90-40\\sqrt{3}}{11}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(\\frac{P_{n}}{Q_{n}}\\) be \\([ \\underbrace{1 ; 1, \\ldots, 1}_{n} ]\\). What are \\(P_{n}\\) and \\(Q_{n}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "P_{n} = F_{n+1}, Q_{n} = F_{n}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all pairs $ (n,p)$ of positive integers, where $ p$ is prime, such that $ 3^p\\minus{}np\\equal{}n\\plus{}p$ .",
"role": "user"
}
] | math | {
"ground_truth": "(n, p) = (6, 3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\triangle ABC$ be a triangle with sides $a$, $b$, and $c$ such that $a \\geq b \\geq c$, find the maximum possible value of $s = AA' + BB' + CC'$ where $s = AA' + BB' + C... | math | {
"ground_truth": "2r(a + b + c)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mark has $\\frac{5}{8}$ of a dollar and Carolyn has $\\frac{2}{5}$ of a dollar. How many dollars do they have altogether? (Give your answer in fraction and as a decimal.)",
"... | math | {
"ground_truth": "\\frac{41}{40}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a > b$, fill in the blanks with \">\" or \"<\": (1) $a-3 \\quad b-3$; (2) $-4a \\quad -4b$.",
"role": "user"
}
] | math | {
"ground_truth": "-4a < -4b",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the inequality $x^2 - 3x + t < 0$ has the solution set $\\{x | 1 < x < m, x \\in \\mathbb{R}\\}$ \n(1) Find the values of $t$ and $m$; \n(2) If the function $f(x) = -x^2 ... | math | {
"ground_truth": "\\{x | 0 < x < \\frac{1}{2} \\text{ or } 1 < x < \\frac{3}{2}\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following equation for positive integers \\( x \\), \\( y \\), \\( z \\), and \\( v \\).\n\n\\[ x+\\frac{1}{y+\\frac{1}{z+\\frac{1}{v}}}=\\frac{101}{91} \\]",
"role... | math | {
"ground_truth": "1, 9, 9, 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\{a_n\\}$ that satisfies: $a_1=2$, $a_{n+1}=1-\\frac{1}{a_n}$, find the value of $a_{2016}$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two identical cylindrical containers are connected at the bottom by a small tube with a tap. While the tap was closed, water was poured into the first container, and oil was pour... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a total of 1,480,000 votes were cast and Karen received 83% of them, determine the number of people who voted for her.",
"role": "user"
}
] | math | {
"ground_truth": "1228400",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For positive integer $n$ let $a_n$ be the integer consisting of $n$ digits of $9$ followed by the digits $488$ . For example, $a_3 = 999,488$ and $a_7 = 9,999,999,488... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The American Mathematics College is holding its orientation for incoming freshmen. The incoming freshman class contains fewer than $600$ people. When the freshmen are told to lin... | math | {
"ground_truth": "322",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the real numbers $1$, $x$, $y$, $4$ form an arithmetic sequence, and $-2$, $a$, $b$, $c$, $-8$ form a geometric sequence, calculate the value of $\\dfrac{y-x}{b}$.",
"role... | math | {
"ground_truth": "-\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A baker has a batch of 120 cookies that he wants to distribute evenly among 7 employees. After distributing the cookies, he plans to donate the remaining cookies to a local chari... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function \\( f(x)=\\frac{x^{3}}{1+x^{3}} \\), find the value of the sum\n\n\\[ \nf\\left(\\frac{1}{1}\\right)+f\\left(\\frac{2}{1}\\right)+\\ldots+f\\left(\\frac{2007}{... | math | {
"ground_truth": "\\frac{2007^2}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If z(1-i)=2, calculate the value of z.",
"role": "user"
}
] | math | {
"ground_truth": "1+i",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John and Janet each bought 8 ounces of coffee in a 12-ounce cup. John drank 3 ounces of his coffee and then added 3 ounces of cream. Janet added 3 ounces of cream, stirred the co... | math | {
"ground_truth": "\\frac{33}{15}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many integers, $x$, satisfy $|7x - 4| \\le 10$?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers n such that $ (n ^{ 2} + 11n - 4) n! + 33.13 ^ n + 4 $ is the perfect square",
"role": "user"
}
] | math | {
"ground_truth": "(n, m) = \\{(1, 21^2), (2, 75^2)\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive integers $k$ and $n$ satisfying the equation $$ k^2 - 2016 = 3^n $$ (Stephan Wagner)",
"role": "user"
}
] | math | {
"ground_truth": "k = 45",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If it costs 3 cents to copy a page, how many pages can you copy for $15?",
"role": "user"
}
] | math | {
"ground_truth": "500",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose\n$$a(3+i)^5 + b(3+i)^4 + c(3+i)^3 + d(3+i)^2 + b(3+i) + a = 0,$$\nwhere $a, b, c, d$ are integers whose greatest common divisor is $1$. Determine $|d|$.",
"role": "us... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bridge needs to be constructed over a river with a required elevation of 800 feet from one side to the other. Determine the additional bridge length required if the gradient is... | math | {
"ground_truth": "13333.33",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The negation of the proposition \"There exists $x \\in \\mathbb{R}$, such that $x^2 + 2x + 2 \\leq 0$\" is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{For all } x \\in \\mathbb{R}, x^2 + 2x + 2 > 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Any graph $G$ that contains at least one cycle satisfies $g(G) \\leqslant 2 \\operatorname{diam} G+1$.",
"role": "user"
}
] | math | {
"ground_truth": "g(G) \\leq 2 \\operatorname{diam} G + 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Real numbers $x$ and $y$ satisfy $x + y = 3$ and $x \\cdot y = 1$. Calculate the value of $x + \\frac{x^4}{y^3} + \\frac{y^4}{x^3} + y$.",
"role": "user"
}
] | math | {
"ground_truth": "849",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all polynomials $ P(x,y)$ such that for all reals $ x$ and $y$ ,\n\\[P(x^{2},y^{2}) =P\\left(\\frac {(x + y)^{2}}{2},\\frac {(x - y)^{2}}{2}\\right).\\]",
"role": "... | math | {
"ground_truth": "P(x, y) \\equiv Q(x + y, xy(x - y)^2)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define: If \\( a: b = b: c \\), then \\( b \\) is called the mean proportional of \\( a \\) and \\( c \\). For example, in \\( 1: 2 = 2: 4 \\), \\( 2 \\) is the mean proportional... | math | {
"ground_truth": "0.48",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $\\left\\lfloor \\left\\lceil \\left(\\frac{15}{8}\\right)^2\\right\\rceil + \\frac{19}{5} \\right\\rfloor$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the result of $(x^{2}+ax+2)(2x-4)$ does not contain the term $x^{2}$, find the value of $a$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In their base $10$ representations, the integer $a$ consists of a sequence of $2023$ nines and the integer $b$ consists of a sequence of $2023$ sixes. What is the sum of the digi... | math | {
"ground_truth": "C) 20235",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An ice cream vendor offers three different flavors. A person buys an ice cream with 5 scoops. How many possible combinations are there (the order of scoops does not matter)?",
... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ n$ and $ k$ be given natural numbers, and let $ A$ be a set such that \\[ |A| \\leq \\frac{n(n+1)}{k+1}.\\] For $ i=1,2,...,n+1$ , let $ A_i$ be sets of size $ n$... | math | {
"ground_truth": "\\frac{n(n+1)}{k+1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a modified game of Deal or No Deal, participants choose a box at random from a set of 30 boxes, each containing one of the following values:\n\\[\n\\begin{tabular}{|c|c|}\n\\h... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=|\\sin^2x-4\\sin x-a|$ has a maximum value of $4$, find the constant $a=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Construct a quadratic equation whose roots ($x_{1}$ and $x_{2}$) satisfy the following relations:\n\n\\[ x_{1} x_{2} + x_{1} + x_{2} - a = 0, \\]\n\\[ x_{1} x_{2} - a(x_{1} + x_{... | math | {
"ground_truth": "x^2 - x + (a - 1) = 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
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