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": "Determine the number of ordered quadruples $(a,b,c,d)$ of nonnegative real numbers such that:\n\\begin{align*}\na^2 + b^2 + c^2 + d^2 &= 4, \\\\\n(a + b + c + d)(a^4 + b^4 + c^4 ... | 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": "Suppose $ A_1,\\dots, A_6$ are six sets each with four elements and $ B_1,\\dots,B_n$ are $ n$ sets each with two elements, Let $ S \\equal{} A_1 \\cup A_2 \\cup \\cdots \... | math | {
"ground_truth": "9",
"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": "Find the slope of the line $\\frac{x}{4} + \\frac{y}{3} = 1$.\nA) $-\\frac{3}{4}$ \nB) $-\\frac{4}{3}$ \nC) $\\frac{3}{4}$ \nD) $\\frac{4}{3}$",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{A) } -\\frac{3}{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": "Define a binary operation $x \\, \\star \\, y$ for all $x, y > 0$ such that $x \\, \\star \\, y$ simplifies to $\\log_y x$. Suppose the operation $x \\, \\star \\, y$ satisfies $... | math | {
"ground_truth": "\\frac{\\log 3}{2 \\log 5} + \\frac{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": "Evaluate $\\sqrt{3 - \\sqrt{3 - \\sqrt{3 - \\!\\sqrt{3 - \\cdots}}}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-1 + \\sqrt{13}}{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": "Let $ABCD$ be a square, and let $M$ be the midpoint of side $BC$ . Points $P$ and $Q$ lie on segment $AM$ such that $\\angle BPD=\\angle BQD=135^\\circ$ . Given that ... | math | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a $7 \\times 7$ grid of squares, determine the total number of possible symmetric scanning codes.",
"role": "user"
}
] | math | {
"ground_truth": "1022",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cube with side length 2 is sliced by a plane that passes through two diagonally opposite vertices A and C and the points B and D, which are located one-third and two-thirds alo... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that one root of the equation $x^2 + mx - 5 = 0$ with respect to $x$ is $x = -1$, determine the other root of the equation.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"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 checkerboard of $15$ rows and $19$ columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered $3, 4, \\ldots, 21$, the s... | math | {
"ground_truth": "440",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following equations using appropriate methods. Use the factorization method for (1) and (2):\n(1) $(3x-1)^2 = (x+1)^2$ \n(2) $(x-1)^2+2x(x-1)=0$ \n(3) Solve the equa... | 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": "Given that the line $2x-y-4=0$ intersects with the line $x-2y+1=0$ at point $P$. \n(1) Find the equation of line $l_1$ that passes through point $P$ and is perpendicular to the ... | math | {
"ground_truth": "x+y-5=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": "\\[\n\\frac{\\left(\\frac{(3.2-1.7)}{0.003}\\right)}{\\left(\\frac{29}{35}-\\frac{3}{7}\\right) \\cdot 4 / 0.2} - \\frac{\\left(1 \\frac{13}{20}-1.5\\right) \\cdot 1.5}{\\left(2.... | math | {
"ground_truth": "12",
"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": "Two ships are moving in straight lines at a constant speed towards the same port. Initially, the positions of the ships and the port form an equilateral triangle. After the secon... | math | {
"ground_truth": "240 \\, \\text{km}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the positive value of $x$ which satisfies\n\\[\\log_5 (x - 2) + \\log_{10} (x^2 - 2) + \\log_{\\frac{1}{5}} (x - 2) = 3.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{127}",
"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 curve $C$ is defined by the parametric equations $\\begin{cases} x=\\frac{8k}{1+k^2}, \\\\ y=\\frac{2(1-k^2)}{1+k^2} \\end{cases}$ (where $k$ is a parameter) and line $l$... | math | {
"ground_truth": "x+2y-4=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": "12 people sat around a round table; some of them are knights (who always tell the truth), and others are liars (who always lie). Then each of them said, \"There is a liar among m... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We have a $100\\times100$ garden and we’ve plant $10000$ trees in the $1\\times1$ squares (exactly one in each.). Find the maximum number of trees that we can cut such that... | math | {
"ground_truth": "2500",
"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 smallest integer value of $y$ for which $10 - 5y < 5$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find all positive integers $N$ that are perfect squares and their decimal representation consists of $n$ digits equal to 2 and one digit equal to 5, where $n$ takes positiv... | math | {
"ground_truth": "25 \\text{ and } 225",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the complex numbers \\( z_{1} = -3 - \\sqrt{3} \\, \\mathrm{i} \\), \\( z_{2} = \\sqrt{3} + \\mathrm{i} \\), and \\( z = \\sqrt{3} \\sin \\theta + \\mathrm{i} (\\sqrt{3} \\co... | math | {
"ground_truth": "2 (\\sqrt{3} + 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": "How many four-digit numbers have the following property? \"For each of its digits, when this digit is deleted the resulting three-digit number is a factor of the original number.... | 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": "Solve for $y$: $7 + y = 3$.",
"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": "If $3^{4x} = 16$, evaluate $81^{x+1}$.",
"role": "user"
}
] | math | {
"ground_truth": "1296",
"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 a positive real number $p$ , find all real solutions to the equation\n\\[\\sqrt{x^2 + 2px - p^2} -\\sqrt{x^2 - 2px - p^2} =1.\\]",
"role": "user"
}
] | math | {
"ground_truth": "x = \\pm \\sqrt{\\frac{p^2 + \\frac{1}{4}}{1 - 4p^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": "When Applejack begins to buck trees, she starts off with 100 energy. Every minute, she may either choose to buck $n$ trees and lose 1 energy, where $n$ is her current energy,... | math | {
"ground_truth": "4293",
"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 $\\overrightarrow{a}=(-2,3)$ and $\\overrightarrow{b}=(m,1)$. If the vector $\\left( \\overrightarrow{a}-2 \\overrightarrow{b}\\right)$ is parallel to $\\overrighta... | math | {
"ground_truth": "-\\dfrac{2}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At 4 o'clock, the hour hand and the minute hand form an angle of 120°. What is the angle formed by the hour hand and the minute hand at 4:30?",
"role": "user"
}
] | math | {
"ground_truth": "45°",
"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 snowman is built on a level plane by placing a ball radius $6$ on top of a ball radius $8$ on top of a ball radius $10$ as shown. If the average height above the plane of... | math | {
"ground_truth": "61",
"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": "There are $n{}$ wise men in a hall and everyone sees each other. Each man will wear a black or white hat. The wise men should simultaneously write down on their piece of paper ... | math | {
"ground_truth": "2^{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given proposition p: ∃x∈R, x^2 > 2^x, find the negation of p.",
"role": "user"
}
] | math | {
"ground_truth": "\\forall x\\in \\mathbb{R}, x^{2}\\leqslant 2^{x}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four marbles are randomly selected, without replacement, from a bag containing three red, two blue, and two green marbles. What is the probability that one marble of each color i... | math | {
"ground_truth": "\\frac{12}{35}",
"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 of digits $1$ and $2$ is determined by the following two properties:\n\ni) The sequence is built by writing, in some order, blocks $12$ and blocks $11... | math | {
"ground_truth": "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": "Bag A contains 5 white marbles and 6 black marbles. Bag B has 8 yellow marbles and 6 blue marbles. Bag C has 3 yellow marbles and 7 blue marbles. Bag D has 1 yellow and 4 blue ma... | math | {
"ground_truth": "\\frac{136}{275}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the range of integers that can be expressed as the sum of four distinct members of the set $\\{2, 5, 8, 11, 14, 17, 20\\}$?",
"role": "user"
}
] | math | {
"ground_truth": "29 \\text{ to } 62",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation of line $l$ as $ρ\\sin (θ+ \\frac {π}{4})= \\sqrt {2}$, and the equation of curve $C$ as $ \\begin{cases} x=\\cos θ \\\\ y=\\sin θ \\end{cases}(θ \\text{ is a ... | math | {
"ground_truth": "\\sqrt {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": "Given that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and $S_n = 2a_n - 2 (n \\in \\mathbb{N}^*)$, in the sequence ${b_n}$, $b_1 = 1$, and the point $P(b_n,... | math | {
"ground_truth": "T_n = (2n - 3)2^{n+1} + 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": "The equation of the line on which the light is reflected after being reflected by the line y=x when it is incident along the line y=2x+1 is what equation.",
"role": "user"
... | math | {
"ground_truth": "y=\\frac{1}{2}x-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a parallelogram $EFGH$ where point $E$ is at coordinates (1,3), point $F$ is at coordinates (5,3), point $G$ is at coordinates (6,1) and point $H$ is at coordinates (2,1), ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When three different numbers from the set $\\{ -3, -2, -1, 4, 5 \\}$ are multiplied, find the largest possible product.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"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 $S$ be a set of $n$ distinct real numbers. Let $A_{S}$ be the set of numbers that occur as averages of two distinct\nelements of $S$ . For a given $n \\geq 2$ , what ... | math | {
"ground_truth": "2n-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": "Using the completing the square method to solve the equation $x^{2}+8x+7=0$, find the correct transformed result.",
"role": "user"
}
] | math | {
"ground_truth": "(x+4)^{2} = 9",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An urn contains 3 white balls and 5 black balls. Three balls are drawn one by one, with each ball being returned to the urn after the draw. Find the probability that among the dr... | math | {
"ground_truth": "\\frac{81}{256}",
"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": "Last year, a skateboard cost $120 and a protective padding set $30. This year the cost of the skateboard increased by 8%, and the cost of the padding increased by 15%. Calculate ... | math | {
"ground_truth": "C) 9.4%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$A$ and $B$ ran around a circular path with constant speeds. They started from the same place and at the same time in opposite directions. After their first meeting, $B$ took 1 m... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest integer $n$ , such that there are $n+4$ points $A$ , $B$ , $C$ , $D$ , $X_1,\\dots,~X_n$ in the plane with $AB\\ne CD$ that satisfy the following con... | math | {
"ground_truth": "n = 4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P$ be a square pyramid whose base consists of the four vertices $(0, 0, 0), (3, 0, 0), (3, 3, 0)$ , and $(0, 3, 0)$ , and whose apex is the point $(1, 1, 3)$ . Let $Q$... | math | {
"ground_truth": "\\frac{27}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the operation \"minus the reciprocal of,\" defined by \\(a \\diamond b = a - \\frac{1}{b}\\). Evaluate the expression \\(((2 \\diamond 3) \\diamond 4) - (2 \\diamond (3 ... | math | {
"ground_truth": "Provide the final answer given the choices: A) \\(-\\frac{29}{132}\\)",
"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": "Triangle $\\triangle ABC$ has circumcenter $O$ and incircle $\\gamma$ . Suppose that $\\angle BAC =60^\\circ$ and $O$ lies on $\\gamma$ . If \\[ \\tan B \\tan C = a + \... | math | {
"ground_truth": "408",
"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 result of the expression \\( 210 \\times 6 - 52 \\times 5 \\) is \\(\\qquad\\)",
"role": "user"
}
] | math | {
"ground_truth": "1000",
"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 ratio of the distance saved by taking a shortcut along the diagonal of a rectangular field to the longer side of the field is $\\frac{1}{2}$, determine the ratio of the... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that 70% of students enjoy painting and 30% do not, and of those who enjoy painting 25% negate it while of those who do not enjoy painting 15% incorrectly claim they like i... | math | {
"ground_truth": "40.698\\%",
"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 value of $\\log_{10}{25}$ is between which two consecutive integers $c$ and $d$? Find $c+d$.",
"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": "The line joining the midpoints of the diagonals of a trapezoid has length $5$. If the longer base is $105,$ then the shorter base is:\nA) 92\nB) 94\nC) 95\nD) 97\nE) 99",
"ro... | math | {
"ground_truth": "C) 95",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Multiply $(x^4 + 8x^2 + 16)(x^2 - 4)$.",
"role": "user"
}
] | math | {
"ground_truth": "x^4 + 8x^2 + 12",
"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": "One third of the people in a room left. One fourth of those remaining started to dance. There were then $15$ people who were not dancing. Find the original number of people in th... | math | {
"ground_truth": "C) 30",
"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": "Square $PQRS$ is constructed along diameter $PQ$ of a semicircle. The semicircle and square $PQRS$ are coplanar. Line segment $PQ$ has a length of 10 centimeters. If point $N$ is... | math | {
"ground_truth": "5\\sqrt{10}",
"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 $ABC$ be the triangle with vertices located at the center of masses of Vincent Huang's house, Tristan Shin's house, and Edward Wan's house; here, assume the three are not c... | math | {
"ground_truth": "6049",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a pyramid $P-ABCD$ with a rectangular base $ABCD$ where $AB = CD = 2$ and $BC = DA = 1$, the vertex $P$ is directly above the center of rectangle $ABCD$ and equidistant fro... | math | {
"ground_truth": "\\frac{\\sqrt{1 + \\cot^2(\\theta)}}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( AC \\) be a diameter of a circle \\( \\omega \\) of radius 1, and let \\( D \\) be the point on \\( AC \\) such that \\( CD = \\frac{1}{5} \\). Let \\( B \\) be the point... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Aunt Anne is 36 years old, Derek is twice as old as Caitlin, and Caitlin is 3 years younger than Brianna, and Brianna is $\\frac{2}{3}$ the age of Aunt Anne, determine... | math | {
"ground_truth": "42",
"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 $sin(x- \\frac {π}{4})= \\frac {2}{3}$, find the value of $sin2x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{9}",
"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": "Suppose $f(x) = ax + b$ and $g(x) = -2x + 7$. If $h(x) = f(g(x))$ and $h^{-1}(x) = x + 9$, find the value of $a - b$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $\\sqrt[3]{466560000}$.",
"role": "user"
}
] | math | {
"ground_truth": "360",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle ABC, where $AB = x + 5$, $AC = 3x$, and $BC = x + 16$, identify all the restrictions on x, necessary to make $\\angle A$ the largest angle in the triangle. Subsequent... | math | {
"ground_truth": "2.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each two adjacent sides of a planar (self-intersecting!) 14-gon are mutually perpendicular; no two of its sides lie on the same line. What is the maximum possible number of point... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the language of wolves has two letters $F$ and $P$ , any finite sequence which forms a word. А word $Y$ is called 'subpart' of word $X$ if Y is obtained from X by del... | math | {
"ground_truth": "2^n - 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A man has $\\textdollar{15,000}$ to invest. He invests $\\textdollar{6,000}$ at 3% and $\\textdollar{4,500}$ at 4.5%. \nIn order to have a yearly income of $\\textdollar{700}$, h... | math | {
"ground_truth": "**C)** 7.05%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $x$ is an integer that satisfies the following congruences: \n\\begin{align*}\n4+x &\\equiv 3^2 \\pmod{2^3} \\\\\n6+x &\\equiv 2^2 \\pmod{3^3} \\\\\n8+x &\\equiv 7^2... | math | {
"ground_truth": "x \\equiv 1 \\pmod{30}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A round-robin tournament has six competititors. Each round between two players is equally likely to result in a win for a given player, a loss for that player, or a tie. The resu... | math | {
"ground_truth": "m = 3690",
"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": "Alice and Bob play a game with a basketball. On each turn, if Alice has the ball, there is a 1/3 chance that she will toss it to Bob and a 2/3 chance that she will keep the ball.... | math | {
"ground_truth": "\\frac{37}{108}",
"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 number is considered a visible factor number if it is divisible by each of its non-zero digits. Determine how many visible factor numbers exist from 100 through 200, inclusive.... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the greatest possible sum of the digits in the base-nine representation of a positive integer less than $3000$?",
"role": "user"
}
] | math | {
"ground_truth": "24",
"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 number of sedans sold exceeds the number of sports cars sold by at least 20 vehicles, where for every 3 sports cars sold, 5 sedans are sold, and the number of sports cars sol... | math | {
"ground_truth": "75",
"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 set $A=\\{x|3\\leq x<10\\}$, and $B=\\{x|2x-8\\geq0\\}$, then $\\complement_{\\mathbb{R}}(A\\cap B)=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|x<4 \\text{ or } x\\geq10\\}",
"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 arithmetic mean (average) of the squares of the first $n$ positive integers. What is this mean?\nA) $\\frac{n(n+1)}{6}$ \nB) $\\frac{n(n+1)(2n+1)}{6}$ \nC) $\\fra... | math | {
"ground_truth": "\\textbf{(C)}\\ \\frac{(n+1)(2n+1)}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $\\frac{(0.3)^4}{(0.03)^3}$.",
"role": "user"
}
] | math | {
"ground_truth": "300",
"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": "Two siblings sold their flock of sheep. Each sheep was sold for as many florins as the number of sheep originally in the flock. They divided the revenue by giving out 10 florins ... | 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 a quadratic equation $x^{2}-2023x+1=0$ with two roots $x_{1}$ and $x_{2}$, the value of $\\frac{1}{{{x_1}}}+\\frac{1}{{{x_2}}}$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "2023",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the area of the quadrilateral with vertices given as $(2,1)$, $(5,3)$, $(7,1)$, and $(4,6)$?\nA) 5.5 B) 7.5 C) 8.5 D) 10 E) 12.5",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(B)} \\: 7.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The smaller base radius of a truncated cone is 5 cm, the larger base radius is 10 cm, and the slant height AB is 20 cm (where B is on the circumference of the larger base). Find ... | math | {
"ground_truth": "4 \\text{ cm}",
"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 what smallest natural number \\( k \\) does the quadratic trinomial\n\n\\[ y = kx^2 - px + q \\]\n\nwith natural coefficients \\( p \\) and \\( q \\) have two distinct positi... | math | {
"ground_truth": "5",
"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 sets $A=\\{x|1 \\lt x \\lt 2\\}$ and $B=\\{x|x \\lt a\\}$, if $A\\subseteq B$, then the range of $a$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "a \\geqslant 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a circle with a radius of $4$ and a circle with a radius of $5$ are tangent to each line, determine the number of possible values of $k$ as the distance between their ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose \\( x \\) is the fifth power of a positive integer, and \\( d \\) is the number of positive integers that are divisors of \\( x \\). Calculate \\( d \\) for an \\( x \\) ... | math | {
"ground_truth": "216",
"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": "Mr. Lee has 8 children. Assuming that the gender of each child is determined independently and with equal likelihood of being male or female, what is the probability that Mr. Lee... | math | {
"ground_truth": "\\dfrac{37}{256}",
"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 $f(x) = \\sin^2x + \\sqrt{3}\\cos x \\cos\\left(\\frac{\\pi}{2} - x\\right)$.\n\n(I) Find the center of symmetry and the equation of the axis of symmetry of t... | math | {
"ground_truth": "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": "How many two-digit positive integers have at least one 5 as a digit?",
"role": "user"
}
] | math | {
"ground_truth": "19",
"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 conical container with a base radius of 8 cm and height of 24 cm is filled with water. This water is then transferred into a cylindrical container with a base radius of 16 cm. ... | math | {
"ground_truth": "**\\(\\textbf{(B)} ~2 \\text{ cm}\\)**",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a board, the positive integer $N$ is written. In each round, Olive can realize any one of the following operations:\nI - Switch the current number by a positive multiple of ... | math | {
"ground_truth": "\\text{all non-multiples of 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 the town's population increased by $1,200$ people, and then this new population decreased by $11\\%$, then the town now had $32$ less people than it did before the $1,200$ ... | math | {
"ground_truth": "10,000",
"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": "The range of the function $y=x+ \\sqrt{x-2}$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "[2,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\\sin C\\cos B+\\sin B\\cos C=3\\sin A\\cos B$.\n(1) Find the value of $\\cos... | math | {
"ground_truth": "c = \\sqrt{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": "Given sets $P=\\{x|a+1\\leqslant x\\leqslant 2a+1\\}$ and $Q=\\{x|-2\\leqslant x\\leqslant 5\\}$.<br/>$(1)$ If $a=3$, find $(\\complement _{U}P)\\cap Q$;<br/>$(2)$ If \"$x\\in P$... | math | {
"ground_truth": "(-\\infty, 2]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $\\lfloor -6.5 \\rfloor \\cdot \\lceil 6.5 \\rceil \\cdot \\lfloor -5.5 \\rfloor \\cdot \\lceil 5.5 \\rceil \\cdot \\lfloor -4.5 \\rfloor \\cdot \\lceil 4.5 \\rceil \\cd... | math | {
"ground_truth": "-2116800",
"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 $k$ be a given positive integer. Find the smallest positive integer $n$ such that among any $n$ integers, there always exist two positive integers whose sum or difference is ... | math | {
"ground_truth": "k + 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": "Using rectangular blocks marked with +1 and -1 placed in a $10 \\times n$ grid, where the product of the numbers in each row and each column is positive, what is the minimum valu... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A deck of three-colored cards consists of 32 cards: 10 red, 10 yellow, and 10 blue cards, each numbered from 1 to 10, and two special cards called the Joker, each numbered 0. Dra... | math | {
"ground_truth": "1006009",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the following functions:\n\\[ f(x) = 5x^2 - \\frac{1}{x} + 3 \\]\n\\[ g(x) = x^3 - k \\]\nIf \\( f(2) - g(2) = 2 \\), what is the value of \\( k \\)?",
"role": "user... | math | {
"ground_truth": "k = \\frac{-25}{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": "Bucket $A$ contains 3 litres of syrup. Bucket $B$ contains $n$ litres of water. Bucket $C$ is empty.\nWe can perform any combination of the following operations:\n- Pour ... | math | {
"ground_truth": "n \\in \\bigcup_{k=2}^{+\\infty} \\left\\{3k+1, 3k+2\\right\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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