data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two circles are centered at the origin. The point \\( P(8,6) \\) is on the larger circle and the point \\( S(0, k) \\) is on the smaller circle. If the distance \\( QR = 3 \\), c... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the diagram, $\\mathrm{ABCD}$ and $\\mathrm{EGFO}$ are both squares. The point $\\mathrm{O}$ is the center of square $\\mathrm{ABCD}$ and $\\mathrm{EF} \\parallel \\mathrm{... | math | {
"ground_truth": "11.5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the even function $f(x)=\\sin (\\omega x+\\phi )$, where $\\omega > 0$. If $f(x)$ has at least one zero point in the interval $[0,\\pi]$, then the minimum value of $\\omega$ ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A quadratic equation is given by $2ax^2 + 3bx + 4c = 0$. Find the condition among $a, b$, and $c$ such that the discriminant is equal to $25$.",
"role": "user"
}
] | math | {
"ground_truth": "ac = \\frac{9b^2 - 25}{32}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression $\\frac{6m+12}{3}$ to a form $cm+d$, where $c$ and $d$ are integers, and find the value of $\\frac{c}{d}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = ax^2 + bx$, and $1 \\leq f(-1) \\leq 2$, $2 \\leq f(1) \\leq 4$, then the range of values for $f(-2)$ expressed as an interval is.",
"role": "user"
}
] | math | {
"ground_truth": "[6,10]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $y=f(x)$ is an odd function defined on $\\mathbb{R}$ and satisfies $f(x-1)=f(x+1)$ for all $x \\in \\mathbb{R}$. When $x \\in (0,1]$ and $x_1 \\neq x_2$, ... | math | {
"ground_truth": "(1) (2) (3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number of distinct pairs of integers $(x, y)$ such that $0 < x < y$ and $\\sqrt{2016} = \\sqrt{x} + \\sqrt{y}$ is:\nA) 0\nB) 1\nC) 3\nD) 4\nE) 7",
"role": "user"
}
] | math | {
"ground_truth": "C) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given is a rectangle with perimeter $x$ cm and side lengths in a $1:2$ ratio. Suppose that the area of the rectangle is also $x$ $\\text{cm}^2$ . Determine all possible va... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the arithmetic sequence $\\{a\\_n\\}$, $a\\_2+a\\_7=-32$, $a\\_3+a\\_8=-40$.\n(1) Find the general term formula of the sequence $\\{a\\_n\\}$;\n(2) Suppose the sequence $\\{a\... | math | {
"ground_truth": "2n^{2}+2^{n}-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is $2:1$ and the ratio of the rectangle's length to its width is $2:1$... | math | {
"ground_truth": "12.5\\%",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Liam read an average of $40$ pages per day for the first three days and an average of $50$ pages per day for the next three days. On the seventh day, he attended two reading sess... | math | {
"ground_truth": "315",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of the parallelogram generated by $\\begin{pmatrix} 2 \\\\ 4 \\\\ -1 \\end{pmatrix}$ and $\\begin{pmatrix} -1 \\\\ 1 \\\\ 3 \\end{pmatrix}$.",
"role": "user"
... | math | {
"ground_truth": "\\sqrt{230}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Square $EFGH$ has sides of length 3. Set $T$ is the set of all line segments that have length 3 and whose endpoints are on adjacent sides of the square. The midpoints of the line... | math | {
"ground_truth": "258",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $T$ be the sum of all positive integers $n$ such that $n^2 + 10n - 2010$ is a perfect square. Find the remainder when $T$ is divided by $1000.$",
"role": "user"
}
] | math | {
"ground_truth": "304",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of solutions in positive integers to the equation $3x + 5y = 805$.",
"role": "user"
}
] | math | {
"ground_truth": "53",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all nonnegative solutions $(x,y,z)$ to the system $\\sqrt{x+y}+\\sqrt{z} = 7$ , $\\sqrt{x+z}+\\sqrt{y} = 7$ , $\\sqrt{y+z}+\\sqrt{x} = 5$ .",
"role": "user"
}
] | math | {
"ground_truth": "(1, 4, 4)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A geometric progression of positive integers has $n$ terms; the first term is $10^{2015}$ and the last term is an odd positive integer. How many possible values of $n$ are ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "All positive integer solutions $(a, b)$ of the equation $a^{3}-a^{2} b+a^{2}+2 a+2 b+1=0$ are $\\qquad$ .",
"role": "user"
}
] | math | {
"ground_truth": "(5, 7)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let side $AD$ of convex quadrilateral $ABCD$ be extended through $D$, and let side $BC$ be extended through $C$, to meet in point $E.$ Let $S$ be the degree-sum of angles $CDE$ a... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all positive integers $n$ such that, given an unlimited supply of stamps of denominations $4, n,$ and $n+2$ cents, $73$ cents is the greatest postage that cannot ... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graduation ceremony program at a certain school consists of 6 events. Considering the overall effect, there are the following requirements for the order of the program: Event... | math | {
"ground_truth": "24 + 24 + 72 = 120",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a modified sequence of numbers, the first number is \\(1\\), and for all \\(n \\geq 2\\), the formula for the \\(n\\)-th number in the sequence changes so that \\(a_{n+1} = \\... | math | {
"ground_truth": "\\textbf{(B) } \\frac{134}{27}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Kuzya the flea can make a jump in any direction on a plane for a distance of exactly 19 mm. Her task is to get from point $A$ to point $B$ on the plane, with the distance between... | math | {
"ground_truth": "n_{\\min} = 954 \\, \\text{jumps}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation\n\\[\n\\left(x_{1}^{2}+1\\right)\\left(x_{2}^{2}+2^{2}\\right) \\cdots\\left(x_{n}^{2}+n^{2}\\right)=2^{n} \\cdot n! x_{1} \\cdot x_{2} \\cdots x_{n},\n\\]\nwh... | math | {
"ground_truth": "x_{1}=1, x_{2}=2, \\cdots, x_{n}=n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a particular European city, there are only $7$ day tickets and $30$ day tickets to the public transport. The former costs $7.03$ euro and the latter costs $30$ euro. A... | math | {
"ground_truth": "1401.34",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression: $\\frac{3 \\times 10^9}{6 \\times 10^5}$.",
"role": "user"
}
] | math | {
"ground_truth": "5000",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assume that $x_1,x_2,\\ldots,x_7$ are real numbers such that\n\\[\\begin{aligned} \nx_1+3x_2+5x_3+7x_4+9x_5+11x_6+13x_7 &= 0, \\\\ \n3x_1+5x_2+7x_3+9x_4+11x_5+13x_6+15x_7 &= 10, ... | math | {
"ground_truth": "282",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The largest fraction in the set \\(\\{\\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}, \\frac{1}{5}, \\frac{1}{10}\\}\\) is what fraction?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of \\( a^3 + b^3 \\) given that \\( a+b=12 \\) and \\( a-b=4 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "1344",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The plane is divided using a repeating pattern of congruent hexagons and equilateral triangles. Each hexagon is surrounded symmetrically by 6 triangles. If the side of each hexag... | math | {
"ground_truth": "C) 50%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are seven teams that play each other once in a tournament, with a win earning $3$ points, $0$ points for any draw where both teams earn $0$ points, and $1$ point... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A marble rolls on a horizontal table with a speed $v_0$ . The marble bounces elastically in a vertical cut at a horizontal distance $D$ from the edge of the table. After hitti... | math | {
"ground_truth": "v_0 = 2D \\sqrt{\\frac{g}{2h}}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\[2011^{2011^{2012}} = x^x\\] for some positive integer $x$ , how many positive integer factors does $x$ have?\n\n*Author: Alex Zhu*",
"role": "user"
}
] | math | {
"ground_truth": "2012",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the vectors $\\overrightarrow{a}=(1,1)$, $\\overrightarrow{b}=(1,-1)$, and $\\overrightarrow{c}=(-1,2)$, express $\\overrightarrow{c}$ in terms of $\\overrightarrow{a}$ and... | math | {
"ground_truth": "\\left(\\frac{1}{2}\\overrightarrow{a}-\\frac{3}{2}\\overrightarrow{b}\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a polygon, except for two of its interior angles, the sum of its interior angles is 2002°. Calculate the number of sides of this polygon.",
"role": "user"
}
] | math | {
"ground_truth": "14 \\text{ or } 15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the complex number \\( z \\) satisfying the equation \\( 3z - 4i\\bar{z} = -5 + 4i \\).",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{7} + \\frac{8}{7}i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A shopkeeper displays a number of dresses each having a specific marked price. A sign in front of them reads “$\\frac{1}{4}$ off on these dresses.” It is known that the cost of t... | math | {
"ground_truth": "\\frac{15}{32}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the magnitude of the complex number $3-4i$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the equation of the tangent line to the curve $f(x)=\\frac{1}{2}x^{2}$ at the point $(1, \\frac{1}{2})$.",
"role": "user"
}
] | math | {
"ground_truth": "2x - 2y - 1 = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Add $263_9 + 504_9 + 72_9$. Express your answer in base $9$.",
"role": "user"
}
] | math | {
"ground_truth": "850_9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum $1 + 3 + 5 + \\cdots + 21 + 23$.",
"role": "user"
}
] | math | {
"ground_truth": "144",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( f(x) = x^5 + 3x^3 + 4x \\), evaluate \\( f(3) - f(-3) \\).",
"role": "user"
}
] | math | {
"ground_truth": "672",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the daughter and the two sons together got three-quarters of the estate, sharing it in a ratio of 5:3:2, the gardener received $\\textdollar{400}$, and Ms. M's daughte... | math | {
"ground_truth": "\\textdollar{4266.67}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a simple graph, there exist two vertices $A,B$ such that there are exactly $100$ shortest paths from $A$ to $B$ . Find the minimum number of edges in the graph.\n\n*CSJ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $y\\%$ of three-digit numbers have a repeated digit (the repeated digits do not need to be adjacent), then what is $y$? Express your answer as a decimal to the nearest tenth."... | math | {
"ground_truth": "28.0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Karl's rectangular garden is $30$ feet by $50$ feet, and he decides to allocate $300$ square feet for planting trees. Makenna's garden is of size $35$ feet by $45$ feet. If both ... | math | {
"ground_truth": "**B) Makenna's vegetable garden is larger by 375 square feet.**",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The famous mathematician Hu Luogeng once said: \"The combination of shape and number is good in a hundred ways, and the division and separation is stopped in ten thousand things.... | math | {
"ground_truth": "5\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two points, A and B, are 30 cm apart. Two strings, A and B, start simultaneously from A and B respectively and move towards each other. String A is 151 cm long and moves at 2 cm ... | math | {
"ground_truth": "40 \\ \\text{s}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with radius 5 units has an equilateral triangle ABC inscribed in it, such that point B is at the top of the circle (0,5). Sides AC and AB are symmetric with respect to t... | math | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of two numbers is $40$. If we triple the larger number and subtract twice the smaller number, the result is 10. What is the positive difference between the two numbers?",... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $|-3| \\times 2$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following inequalities for $x$: \n(1) $x^{2}-2a|x|-3a^{2}<0$ \n(2) $ax^{2}-(2a+1)x+2>0$ \n(where $a \\in \\mathbf{R}$).",
"role": "user"
}
] | math | {
"ground_truth": "(\\frac{1}{a}, 2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all 4-digit numbers $\\overline{abcd}$ that are multiples of $11$ , such that the 2-digit number $\\overline{ac}$ is a multiple of $7$ and $a + b + c + d = d^2$ .",
... | math | {
"ground_truth": "3454",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the graph of the function $y=f(x)$ be symmetric to the graph of $y=2^{x-a}$ about the line $y=-x$, and $f(-2)+f(-4)=1$, then $a=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A basketball team has 16 players which includes 3 sets of twins: Beth and Ben, Carla and Chris, Dee and Don. In how many ways can we pick 7 players for a game if at most one play... | math | {
"ground_truth": "1380",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the value of \\[M = 101^2 + 100^2 - 99^2 - 98^2 + 97^2 + \\cdots + 5^2 + 4^2 - 3^2 - 2^2,\\] where the additions and subtractions alternate in pairs.",
"role": "user"... | math | {
"ground_truth": "5304",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a $5\\times 5$ block of calendar dates as shown below. First, the order of the numbers in the second, third, and fifth rows are reversed. Then, the numbers on each diago... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If five boys and three girls are randomly divided into two four-person teams, calculate the probability that all three girls will end up on the same team.",
"role": "user"
... | math | {
"ground_truth": "\\frac{1}{7}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The cost price of a certain product is $400$ yuan. When sold, the marked price is $600$ yuan. Later, due to the accumulation of this product, the store is preparing to offer a di... | math | {
"ground_truth": "7\\%",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\tan 10^{\\circ}\\tan 20^{\\circ}+ \\sqrt {3}(\\tan 10^{\\circ}+\\tan 20^{\\circ})=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $ax+3=4x+1$ with respect to $x$, solve for the integer value of $a$ that yields a positive integer solution for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "2 \\text{ or } 3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the polynomial of minimal degree, with rational coefficients, leading coefficient 1, and roots $3 + \\sqrt{5}$ and $3 + \\sqrt{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "x^4 - 12x^3 + 47x^2 - 66x + 28",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a grid of $6\\times 6$ , write down integer which is more than or equal to 1 and less than or equal to 6 in each grid. For integers $1\\leq i,\\ j\\leq 6$ , denote\ndenot... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the plane Cartesian coordinate system $xOy$, find the area of the shape formed by the points whose coordinates satisfy the condition $\\left(x^{2}+y^{2}+2x+2y\\right)\\left(4-... | math | {
"ground_truth": "2\\pi + 4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$ and $y$ be non-zero numbers such that $x = 2 + \\frac{1}{y}$ and $y = 2 + \\frac{1}{x}$. Determine the value of $y$.\nA) $1 + \\sqrt{2}$\nB) $1 - \\sqrt{2}$\nC) $2$\nD) $... | math | {
"ground_truth": "1 - \\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all values of the parameter \\( a \\) for which the system\n\n\\[\n\\left\\{\\begin{array}{l}\nx = -|y-\\sqrt{a}| + 6 - \\sqrt{a} \\\\\n(|x|-8)^2 + (|y|-15)^2 = 289\n\\end{a... | math | {
"ground_truth": "a \\in \\{ 9, 121, \\left(\\frac{17\\sqrt{2}-1}{2}\\right)^2 \\}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Call an integer \\( n > 1 \\) radical if \\( 2^n - 1 \\) is prime. What is the 20th smallest radical number?",
"role": "user"
}
] | math | {
"ground_truth": "4423",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $B$ be a right rectangular prism (box) with edge lengths $2,$ $3,$ and $5$, together with its interior. For real $r\\geq0$, let $S(r)$ be the set of points in $3$-dimensional... | math | {
"ground_truth": "15.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Usually, two mechanisms work together to complete a certain task. Their efficiencies are not the same, and when working together, they complete the task in 30 hours. Once, the tw... | math | {
"ground_truth": "x = 75 \\text{ hours, } y = 50 \\text{ hours}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all values of the parameter \\(a\\), for which the equation \\(\\left(x^{2}+(2a-1)x-4a-2\\right) \\cdot\\left(x^{2}+x+a\\right)=0\\) has three distinct roots.",
"role": ... | math | {
"ground_truth": "-1.5, -0.75, 0, \\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The eccentricity of the conic section $\\frac{x^{2}}{m} + y^{2} = 1$ is $\\sqrt{7}$, calculate $m$.",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We divided the sides of an equilateral triangle in the ratio $p: q$. The area of the triangle formed by connecting these division points is $\\frac{19}{64}$ of the area of the or... | math | {
"ground_truth": "\\frac{5}{3} \\text{ or } \\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = \\dfrac {\\sqrt {x(4-x)}}{x-1}$, determine its domain.",
"role": "user"
}
] | math | {
"ground_truth": "[0,1)∪(1,4]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,$ $b,$ $c,$ $d$ be the roots of the polynomial $3x^4 - 8x^3 + x^2 + 4x - 12 = 0.$ Find the product $abcd$.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $N(4,3)$ is the midpoint of $\\overline{CD}$ and $C(6,-1)$ is one endpoint, what is the product of the coordinates of point $D$?",
"role": "user"
}
] | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The matrix\n\\[\n\\begin{pmatrix} a & \\frac{18}{45} \\\\ c & \\frac{27}{45} \\end{pmatrix}\n\\]\ncorresponds to a projection. Enter the ordered pair \\((a,c)\\).",
"role": "... | math | {
"ground_truth": "\\left( \\frac{2}{5}, \\frac{3}{5} \\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The real numbers $x, y, z$ , distinct in pairs satisfy $$ \\begin{cases} x^2=2 + y y^2=2 + z z^2=2 + x.\\end{cases} $$ \nFind the possible values of $x^2 + y^2 + z^2$ .",... | math | {
"ground_truth": "5, 6, 9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the vertex of the function $y=x^{2}+2x+k$ with respect to $x$ is on the $x$-axis, then the real number $k$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the first quarter, Masha and Lena received a total of 23 A's, Sveta and Masha received a total of 18 A's, and Sveta and Lena received a total of 15 A's. How many A's did each ... | math | {
"ground_truth": "L = 10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A student walks from intersection A to intersection B on a city grid, only moving east or south, where the probability of choosing each direction is 1/2 at each intersection.",
... | math | {
"ground_truth": "\\frac{8}{35}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x = 2z \\), \\( y = 3z - 1 \\), and \\( x = 40 \\), what is the value of \\( y \\)?",
"role": "user"
}
] | math | {
"ground_truth": "59",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, $ABC$ is a straight line. Calculate the value of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "140",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $n$ in the equation $n + (n + 1) + (n + 2) + (n + 3) = 20$?",
"role": "user"
}
] | math | {
"ground_truth": "3.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a five term arithmetic sequence, the first term is $2020$ and the last term is $4040.$ Find the second term of the sequence. \n\n*Proposed by Ada Tsui*",
"role": "user... | math | {
"ground_truth": "2525",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x$ men working $x$ hours a day for $x$ days produce $x^2$ articles and each man's efficiency decreases by $\\frac{1}{2}$ for every additional 10 men beyond 10 men in the work... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The marked price of a book was 30% less than the suggested retail price. Alice purchased the book for half the marked price at a Fiftieth Anniversary sale. Calculate the percenta... | math | {
"ground_truth": "35\\%",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Laura is putting together the following list: $a_0, a_1, a_2, a_3, a_4, ..., a_n$ , where $a_0 = 3$ and $a_1 = 4$ .\nShe knows that the following equality holds for any value... | math | {
"ground_truth": "\\frac{179}{128}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four black $1 \\times 1 \\times 1$ cubes and four white $1 \\times 1 \\times 1$ cubes can be assembled into $\\qquad$ different $2 \\times 2 \\times 2$ cubes (cubes that are iden... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Equilateral $\\triangle ABC$ has side length $2$, and squares $ABDE$, $BCHI$, $CAFG$ lie outside the triangle with sides coinciding with the triangle's sides for $ABDE$ and $BCHI... | math | {
"ground_truth": "14\\sqrt{3} - 12.41",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( \\triangle ABC \\), the sides opposite to \\( A, B, C \\) are \\( a, b, c \\) respectively. Given that \\( \\tan C = \\frac{\\sin A + \\sin B}{\\cos A + \\cos B} ... | math | {
"ground_truth": "a = 2\\sqrt{2}, \\quad c = 2\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\frac{3 \\times 5 + 5 \\times 7 + 7 \\times 9}{2 \\times 4 + 4 \\times 6 + 6 \\times 8} - \\frac{2 \\times 4 + 4 \\times 6 + 6 \\times 8}{3 \\times 5 + 5 \\times 7 + ... | math | {
"ground_truth": "\\frac{74}{119}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow{a}=(1,1,0)$, $\\overrightarrow{b}=(-1,0,2)$, find the value of $k$ such that $k\\overrightarrow{a}+\\overrightarrow{b}$ is perpendicular to $\\ove... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a circle with radius \\( R \\), a chord \\( AB \\) is given. Let \\( M \\) be an arbitrary point on the circle. On the ray \\( MA \\), we place a segment \\( MN \\) such that ... | math | {
"ground_truth": "R \\sqrt{1 + 8 \\cos^2 \\alpha}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The perimeter of an equilateral triangle exceeds the perimeter of a square by $1989 \\ \\text{cm}$. The length of each side of the triangle exceeds the length of each side of the... | math | {
"ground_truth": "663",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy: $|\\overrightarrow{a}|=1$, $(\\overrightarrow{a}+\\overrightarrow{b})\\bot \\overrightarrow{a}$, $(2\\overrigh... | math | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the positive integer n, let 〈n〉 denote the sum of all the positive divisors of n with the exception of n itself. For example, 〈4〉=1+2=3 and 〈12〉=1+2+3+4+6=16. Calculate 〈〈〈... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In convex quadrilateral $KLMN$ side $\\overline{MN}$ is perpendicular to diagonal $\\overline{KM}$ , side $\\overline{KL}$ is perpendicular to diagonal $\\overline{LN}$ ,... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=\\sin x$, the problem asks to shrink the abscissa of all points on the graph to $\\frac{1}{2}$ of the original (with the ordinate unchanged), then shift the... | math | {
"ground_truth": "y=\\sin\\left(2x-\\frac{2\\pi}{3}\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a function \\( f: \\mathbf{N}^{*} \\rightarrow \\mathbf{N}^{*} \\) satisfying \\( f(f(m) + f(n)) = m + n \\) for all \\( m, n \\in \\mathbf{N}^{*} \\), find \\( f(2005) \\)... | math | {
"ground_truth": "2005",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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