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": "In an isosceles trapezoid \\(ABCD\\), the larger base \\(AD = 12\\) and \\(AB = 6\\). Find the distance from point \\(O\\), the intersection of the diagonals, to point \\(K\\), t... | math | {
"ground_truth": "\\frac{12(3 - \\sqrt{2})}{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": "How many ways can change be made for 50 cents using standard U.S. coins, but without using more than one type of any coin? Coins include pennies, nickels, dimes and quarters. (Ex... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Petya is creating a password for his smartphone. The password consists of 4 decimal digits. Petya wants the password to exclude the digit 7, and it must contain at least two (or ... | math | {
"ground_truth": "3537",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An L-shaped region is formed by attaching two $2$ by $5$ rectangles to adjacent sides of a $2$ by $2$ square as shown below.\n[asy] size(6cm);\ndraw((0,0)--(7,0)--(7,2)--... | math | {
"ground_truth": "208",
"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": "Determine all non-empty subsets $A, B, C$ of $\\mathbf{N}^{*}$ such that:\n1. $A \\cap B = B \\cap C = C \\cap A = \\varnothing$;\n2. $A \\cup B \\cup C = \\mathbf{N}^{*}$;\n3. F... | math | {
"ground_truth": "\\left(\\left\\{3k-1 \\mid k \\in \\mathbf{Z}^{+} \\right\\}, \\left\\{3k-2 \\mid k \\in \\mathbf{Z}^{+} \\right\\}, \\left\\{3k \\mid k \\in \\mathbf{Z}^{+} \\right\\}\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ a$ and $ b$ be positive real numbers with $ a\\ge b$ . Let $ \\rho$ be the maximum possible value of $ \\frac{a}{b}$ for which the system of equations\r\n\\[ a^2\\... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\sin (\\frac{\\pi}{3} - x) = \\frac{3}{5}$, find the value of $\\cos (x + \\frac{\\pi}{6})$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a $5 \\times 3 \\times 2$ rectangular parallelepiped with vertices $D$, $A$, $B$, and $C$ such that $D$ is at $(0,0,0)$, $A$ at $(5,0,0)$, $B$ at $(0,3,0)$, and $C$ at $... | math | {
"ground_truth": "1.9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a square $ABCD$ with side length $4$, $OG \\perp$ plane $ABCD$ and $OG = 2$, $E$ and $F$ are the midpoints of $AB$ and $AD$ respectively. Find the distance from point $B$ t... | math | {
"ground_truth": "\\frac{2 \\sqrt{11}}{11}",
"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 traffic light runs repeatedly through the following modified cycle: green for 50 seconds, then yellow for 2 seconds, and then red for 40 seconds. If Maria picks a random three-... | math | {
"ground_truth": "\\frac{9}{92}",
"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": "Mark the number 1 at the endpoints of a diameter of a circle. Divide each resulting semicircular arc into equal parts and label the division points with the sum of the numbers at... | math | {
"ground_truth": "2 \\times 3^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 polygon, the sum of interior angles is $1620^{\\circ}$. Calculate the number of sides of this polygon.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"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": "Ann and Drew have purchased a mysterious slot machine; each time it is spun, it chooses a random positive integer such that $k$ is chosen with probability $2^{-k}$ for every ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Expand the product $(5x + 3y + 2)(2x + 5y + 3)$ and determine the sum of the coefficients of the terms which contain a nonzero power of $y$.",
"role": "user"
}
] | math | {
"ground_truth": "65",
"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 boy named Vasya wrote down the non-zero coefficients of a 9th degree polynomial \\( P(x) \\) in a notebook. Then, he calculated the derivative of the resulting polynomial and w... | math | {
"ground_truth": "9",
"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 an integer be such that when divided by 20, the remainder is 11. What is the sum of the remainders when the same integer is divided by 4 and by 5? Additionally, find the smal... | math | {
"ground_truth": "51",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A_1,B_1,C_1,D_1$ be the midpoints of the sides of a convex quadrilateral $ABCD$ and let $A_2, B_2, C_2, D_2$ be the midpoints of the sides of the quadrilateral $A_1B_... | math | {
"ground_truth": "96",
"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 an odd function $f(x)$ defined on $\\mathbb{R}$ that satisfies: for $x \\geqslant 0$, $f(x) = \\log_{2}(x+m)$, calculate $f(m-16)$.",
"role": "user"
}
] | 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 an isosceles triangle \\(ABC\\), the base \\(AC\\) is 32 units, and each of the legs is 20 units. From vertex \\(B\\), a perpendicular is drawn to the base, intersecting the b... | math | {
"ground_truth": "7\\text{ and }25",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N$ be a positive integer. Two persons play the following game. The first player writes a list of positive integers not greater than $25$ , not necessarily different, such... | math | {
"ground_truth": "N = 11",
"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 baking a batch of bread, Maya mixes 75 mL of milk for every 250 mL of flour. How many mL of milk does she need if she uses 1200 mL of flour?",
"role": "user"
}
] | math | {
"ground_truth": "360",
"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 function \\( f: \\mathbf{N}^{\\star} \\rightarrow \\mathbf{R} \\) satisfies \\( f(1)=1003 \\), and for any positive integer \\( n \\), it holds that\n\\[ f(1) + f(2) + \\cdot... | math | {
"ground_truth": "\\frac{1}{2007}",
"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 triangle $ABC$, let side $AB = 16$ and the ratio $BC:AC = 3:4$. What is the largest area this triangle can achieve?",
"role": "user"
}
] | math | {
"ground_truth": "128",
"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 two-dimensional space, the one-dimensional measure of a circle (circumference $l=2\\pi r$) and its two-dimensional measure (area $S=\\pi r^{2}$); in a three-dimensional spac... | math | {
"ground_truth": "2\\pi r^{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 6-hour bike trip, Alberto travels continuously at a speed of 12 miles per hour, while Bjorn, who bikes at a speed of 10 miles per hour, takes a 1-hour rest. Calculate the di... | math | {
"ground_truth": "22",
"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 particle moves such that its position at time \\(t\\) is given by \\((3t + 8, 5t - 15)\\). Determine the speed of the particle, measured in units of distance per unit of time."... | math | {
"ground_truth": "\\sqrt{34}",
"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 ratio of the length to the width of a rectangle is $5$ : $2$. If the rectangle has a diagonal of length $13$ units, find the constant $k$ such that the area of the rectangle ... | math | {
"ground_truth": "\\frac{10}{29}",
"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": "Consider a sequence of $50$ terms; each term is given by $Q + m$, where $Q$ is the product $2 \\times 3 \\times 5 \\times\\ldots \\times 53$ of all prime numbers less than or equ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence ${\\{(a_{n})\\}}$ where each term is greater than zero, the first term $a_{1}$ equals 1, and the sum of the first $n$ terms $S_{n}$ satisfies $S_{n} \\sqrt{{S}_{... | math | {
"ground_truth": "640",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate:<br/>$(1)$ Solve the equation: $\\frac{2x}{x-2}+\\frac{3}{2-x}=1$.<br/>$(2)$ Solve the system of inequalities: $\\left\\{\\begin{array}{l}{2x-1≥3(x-1)}\\\\{\\frac{5-x}{... | math | {
"ground_truth": "-\\frac{1}{3} < x \\leq 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 20-inch by 20-inch square is partitioned into four congruent L-shaped regions and one smaller square at the center. If each L-shaped region occupies 1/5 of the total area of th... | math | {
"ground_truth": "\\text{(B)}\\ 4\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given King Middle School has 1500 students, with each student taking 5 classes a day, and each teacher now teaching 5 classes with 25 students per class, determine the number of ... | math | {
"ground_truth": "60",
"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": "How many distinct $x$-intercepts does the graph of $y = (x-5)(x^2+7x+12)(x-1)$ have?",
"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": "In the diagram, $\\triangle AOB$ is a triangle with coordinates $O=(0,0)$, $A=(0,30)$, and $B=(40,0)$. Let $C$ be the point on $AB$ for which $OC$ is perpendicular to $AB$.\n(a) ... | 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": "Let $a$ and $b$ be nonzero real numbers. Find the minimum value of:\n\\[a^2 + b^4 + \\frac{1}{a^2} + \\frac{b^2}{a^2}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{\\sqrt[3]{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 the equations $y=(x-1)^2$ and $xy - y = -3$, determine the pairs of values of $x$ and $y$ that are the common solutions.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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": "Vasya is inventing a 4-digit password for a combination lock. He does not like the digit 2, so he does not use it. Moreover, he doesn't like when two identical digits stand next ... | math | {
"ground_truth": "504",
"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 number of rotations needed for AJHSME1989 to reappear must be determined.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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 following equation:\n\\[\n\\frac{1}{x + 11} + \\frac{1}{x + 8} = \\frac{1}{x + 12} + \\frac{1}{x + 7}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "x = -\\frac{19}{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": "A point $P$ is located inside rectangle $ABCD$ such that $PA=5$, $PB=3$, and $PC=4$. Find the length of $PD$.",
"role": "user"
}
] | math | {
"ground_truth": "4\\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": "The Ivanov family decided to purchase an apartment using a mortgage. The total cost of the apartment was 7,000,000 rubles, and since their own funds were insufficient, they decid... | math | {
"ground_truth": "24045.84",
"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": "Non-negative integers $a, b, c, d$ satisfy the equation $a + b + c + d = 100$ and there\n exists a non-negative integer n such that $$ a+ n =b- n= c \\times n = \\frac{d}{n}... | math | {
"ground_truth": "(24, 26, 25, 25, 1), (12, 20, 4, 64, 4), (0, 18, 1, 81, 9)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest positive integer $n$, different from 2004, such that there exists a polynomial $f(x)$ with integer coefficients for which the equation $f(x) = 2004$ has at... | math | {
"ground_truth": "(1002!)^2 + 2004",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$(a)$ Let $x, y$ be integers, not both zero. Find the minimum possible value of $|5x^2 + 11xy - 5y^2|$ . $(b)$ Find all positive real numbers $t$ such that $\\frac{9t}{10... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate \\[\\frac{3}{\\log_3{1000^4}} + \\frac{4}{\\log_7{1000^4}}\\], giving your answer as a fraction in lowest terms.",
"role": "user"
}
] | math | {
"ground_truth": "\\log_{10} (3^{1/4} \\cdot 7^{1/3})",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two vector fields $\\mathbf{F},\\mathbf{G}$ are defined on a three dimensional region $W=\\{(x,y,z)\\in\\mathbb{R}^3 : x^2+y^2\\leq 1, |z|\\leq 1\\}$ . $$ \\mathbf{F}(x,y,z) ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $$f(x)= \\begin{cases} ax+1-4a, & x < 1 \\\\ x^{2}-3ax, & x \\geq 1\\end{cases}$$, if there exist $x_1$, $x_2 \\in \\mathbb{R}$, $x_1 \\neq x_2$, such that $f(... | math | {
"ground_truth": "(\\frac{2}{3}, +\\infty) \\cup (-\\infty, 0]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that line $l$ passes through the intersection point of the two lines $2x+y-8=0$ and $x-2y+1=0$.\n(1) If line $l$ is parallel to the line $3x-2y+4=0$, find the equation of l... | math | {
"ground_truth": "3x+4y-17=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": "**p10.** Three rectangles of dimension $X \\times 2$ and four rectangles of dimension $Y \\times 1$ are the pieces that form a rectangle of area $3XY$ where $X$ and $Y$... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real numbers $k$ such that\n\\[\\left\\| k \\begin{pmatrix} 3 \\\\ -2 \\end{pmatrix} - \\begin{pmatrix} 5 \\\\ 8 \\end{pmatrix} \\right\\| = 3 \\sqrt{13}.\\]",
"role... | math | {
"ground_truth": "\\frac{-1 + \\sqrt{365}}{13}, \\frac{-1 - \\sqrt{365}}{13}",
"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 \\(\\bold{v} = \\begin{pmatrix} 7 \\\\ -4 \\\\ 3 \\end{pmatrix}\\), \\(\\bold{w} = \\begin{pmatrix} 13 \\\\ -1 \\\\ 2 \\end{pmatrix}\\), and \\(\\bold{u} = \\begin{pmatrix} 1... | math | {
"ground_truth": "265",
"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": "Péter took one stamp each of values 1, 2, 3, ..., 37 forints from his stamp collection. He wants to group them so that each group has the same total value of stamps. In how many ... | math | {
"ground_truth": "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": "Given lines $l_1: ax + (a+1)y + 1 = 0$ and $l_2: x + ay + 2 = 0$, if $l_1$ is perpendicular to $l_2$, find the value(s) of $a$.",
"role": "user"
}
] | math | {
"ground_truth": "-2 \\text{ or } 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": "Let $k$ be a positive integer such that $1 +\\frac12+\\frac13+ ... +\\frac{1}{13}=\\frac{k}{13!}$ . Find the remainder when $k$ is divided by $7$ .",
"role": "user"
}... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a modified calculator that has a key for squaring the displayed number, and another key for taking the reciprocal. Now, let $z$ be the result after starting with a numbe... | math | {
"ground_truth": "x^{(-1)^n 2^{\\lfloor n/2 \\rfloor}}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the curves $C_1: y = -x^2 + 4x - 2$, $C_2: y^2 = x$, if $C_1$ and $C_2$ are symmetric about the line $l$, then find the equation of $l$.",
"role": "user"
}
] | math | {
"ground_truth": "x + y + 2 = 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": "If $n$ is an integer, what is the remainder when the sum of $7 - 2n$ and $n + 5$ is divided by $8$?",
"role": "user"
}
] | math | {
"ground_truth": "4 - n",
"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": "Suppose we have a $n$ -gon. Some $n-3$ diagonals are coloured black and some other $n-3$ diagonals are coloured red (a side is not a diagonal), so that no two diagonals of t... | math | {
"ground_truth": "\\lceil \\frac{3}{4}(n-3)^2 \\rceil",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A family took a mortgage loan of 2 million rubles from a commercial bank at an annual interest rate of 10% for 5 years. The loan is repaid according to the following scheme: in t... | math | {
"ground_truth": "573583",
"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": "Sandwiches at Joe's Fast Food cost $$3$ each and sodas cost $$2$ each. Calculate the total cost of purchasing $5$ sandwiches and $8$ sodas.",
"role": "user"
}
] | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The parabola $y=ax^{2}+bx+c(a$,$b$,$c$ are constants, $c \\lt 0)$ passes through the three points $\\left(1,1\\right)$, $\\left(m,0\\right)$, $\\left(n,0\\right)$, where $n\\geqs... | math | {
"ground_truth": "②③④",
"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 vectors $\\overset{⇀}{a}=(1,-2)$ and $\\overset{⇀}{b}=(4,m)$ in the plane, where $\\overset{⇀}{a}$ is perpendicular to $\\overset{⇀}{b}$, determine the vector $5\\overs... | math | {
"ground_truth": "(-7,-16)",
"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 $A=\\{-2,-1,0,1,2\\}$ and $B=\\{x|0\\leqslant x \\lt \\frac{5}{2}\\}$, find the intersection of the sets $A$ and $B$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{0, 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": "Determine the transformation of the graph of the function $y=\\sin (x+\\frac{\\pi }{4}),x\\in R$ from the graph of the function $y=\\sin x,x\\in R$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi }{4} \\text{ units to the left}",
"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 $n \\ge 2$ be a fixed integer. [list=a] [*]Determine the largest positive integer $m$ (in terms of $n$ ) such that there exist complex numbers $r_1$ , $\\dots$ , $r_n... | math | {
"ground_truth": "\\{2^n\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the line $l: \\begin{cases} & x=5+\\frac{\\sqrt{3}}{2}t \\\\ & y=\\sqrt{3}+\\frac{1}{2}t \\\\ \\end{cases} (t$ is a parameter), with the origin as the pole and the positive... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An isosceles triangle $DEF$ has $DE = DF = 5\\sqrt{3}$, and a circle with radius $3\\sqrt{3}$ is tangent to line $DE$ at $E$ and to line $DF$ at $F$. What is the area of the circ... | math | {
"ground_truth": "48\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a tetrahedron, calculate the sum of the number of edges, the number of vertices, and the number of faces, assuming Joe counted one vertex twice.",
"role": "user"
}
] | 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 bag contains 70 balls that differ only in color: 20 red, 20 blue, 20 yellow, and the rest are black and white.\n\nWhat is the minimum number of balls that must be drawn from th... | math | {
"ground_truth": "38",
"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": "Anna and Berta play a game in which they take turns in removing marbles from a table. Anna takes the first turn. At the beginning of a turn there are n ≥ 1 marbles on the table, ... | math | {
"ground_truth": "131070",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find, with proof, all irrational numbers $x$ such that both $x^3-6x$ and $x^4-8x^2$ are rational.",
"role": "user"
}
] | math | {
"ground_truth": "\\pm \\sqrt{6}, \\pm (1 + \\sqrt{3}), \\pm (1 - \\sqrt{3})",
"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 diagonals \\(AC\\) and \\(BD\\) of a convex quadrilateral \\(ABCD\\), equal to 3 and 4 respectively, intersect at an angle of \\(75^\\circ\\). What is the sum of the squares ... | math | {
"ground_truth": "12.5",
"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": "A black bishop and a white king are placed randomly on a $2000 \\times 2000$ chessboard (in distinct squares). Let $p$ be the probability that the bishop attacks the king (th... | math | {
"ground_truth": "1333",
"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": "Jackson begins at $1$ on the number line. At each step, he remains in place with probability $85\\%$ and increases his position on the number line by $1$ with probability ... | math | {
"ground_truth": "13446",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(x, y,\\) and \\(z\\) be positive real numbers such that \\(x + y + z = 3\\). Additionally, let \\(y = 2x\\). Find the minimum value of\n\\[\n\\frac{1}{x} + \\frac{1}{y} + ... | math | {
"ground_truth": "\\frac{10}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a>0$, $b>0$, $ab=8$, find the maximum value of $\\log_{2}a \\cdot \\log_{2}(2b)$.",
"role": "user"
}
] | 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": "(Elgin Johnston) Legs $L_1, L_2, L_3, L_4$ of a square table each have length $n$, where $n$ is a positive integer. For how many ordered 4-tuples $(k_1, k_2, k_3, k_4)$ of non... | math | {
"ground_truth": "\\frac{2n^3 + 6n^2 + 7n + 3}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways can change be made for 50 cents using standard U.S. coins? (Exclude using two quarters as making change for 50 cents.)",
"role": "user"
}
] | math | {
"ground_truth": "39",
"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": "Each of the equations \\( a x^{2} - b x + c = 0 \\) and \\( c x^{2} - a x + b = 0 \\) has two distinct real roots. The sum of the roots of the first equation is non-negative, and... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S_n$ and $T_n$ be the sums of the first $n$ terms of the arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$, respectively. If $\\frac{S_n}{T_n} = \\frac{7n+2}{n+3}$, express $... | math | {
"ground_truth": "\\frac{65}{12}",
"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": "Define an operation as follows: $[\\begin{array}{l}{a}&{b}\\\\{c}&{d}\\end{array}]=ad-bc$. Then the conjugate complex number of the complex number $[\\begin{array}{l}{1+i}&{-1}\\... | math | {
"ground_truth": "-1 - 3i",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(For liberal arts) For any real number $x$, the inequality $ax^2-ax-1<0$ always holds. Then, the range of the real number $a$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "(-4,0]",
"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": "Let $(m,n)$ be pair of positive integers. Julia has carefully planted $m$ rows of $n$ dandelions in an $m \\times n$ array in her back garden. Now, Jana un Viviane decide... | math | {
"ground_truth": "(m-1)(n-1) = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sets\n$$\nA=\\{1,3,5,7,9\\}, B=\\{2,4,6,8,10\\}\n$$\n\nIf the set $C=\\{x \\mid x=a+b, a \\in A, b \\in B\\}$, the number of elements in the set $C$ is ______.",
"r... | math | {
"ground_truth": "9",
"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": "Larry can swim from Harvard to MIT (with the current of the Charles River) in $40$ minutes, or back (against the current) in $45$ minutes. How long does it take him to row fr... | math | {
"ground_truth": "14:24",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a right-angled triangle \\( ABC \\) with the right angle at \\( A \\), the altitude \\( AH \\) is drawn. A circle passing through points \\( A \\) and \\( H \\) intersects the... | math | {
"ground_truth": "13.5",
"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": "We call a four-digit number $\\overline{abcd}$ curious if the sum of the two-digit numbers $\\overline{ab}$ and $\\overline{cd}$ equals the two-digit number $\\overline{bc}$. For... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest two-digit integer for which the product of its digits is $17$ more than their sum?",
"role": "user"
}
] | math | {
"ground_truth": "74",
"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": "To buy an apartment, it is necessary to either take exactly 9 small, 6 medium, and 1 large loans, or exactly 3 small, 2 medium, and 3 large loans. What is the required number of ... | math | {
"ground_truth": "4 \\text{ large loans}",
"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": "Jonas selected an angle $x$ strictly between 30 and 120 degrees and wrote the values of $\\sin x$, $\\cos x$, $\\tan x$, and $\\sec x$ on four different cards. He then gave those... | math | {
"ground_truth": "1",
"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 $ABCD$ be an isosceles trapezoid with $AD\\parallel BC$ . Points $P$ and $Q$ are placed on segments $\\overline{CD}$ and $\\overline{DA}$ respectively such that ... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the constant term in the expansion of the binomial $$(x- \\frac {1}{2 \\sqrt {x}})^{9}$$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {21}{16}",
"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 parabola $y=x^2-3mx+m+n$, for all real numbers $m$, find the conditions that $n$ must satisfy to ensure that the parabola intersects the x-axis.",
"role": "user"
... | math | {
"ground_truth": "n \\leq -\\frac{1}{9}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $g(x) = (x-3)^2 - 7$. If the domain of $g$ is all real numbers, then $g$ does not have an inverse function, but if we restrict the domain of $g$ to an interval $[d,\\infty)$,... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The positive real numbers $a,b,c$ are such that $21ab+2bc+8ca\\leq 12$ . Find the smallest value of $\\frac{1}{a}+\\frac{2}{b}+\\frac{3}{c}$ .",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Ahn chooses a two-digit integer, subtracts twice the integer from 300, and triples the result, find the largest number Ahn can get.",
"role": "user"
}
] | math | {
"ground_truth": "840",
"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 sphere of radius \\( R \\) touches the edges of a regular tetrahedral angle, where all plane angles are \\( 60^\\circ \\). The surface of the sphere inside the angle consists o... | math | {
"ground_truth": "\\pi R^2 \\left(\\frac{16}{3} \\sqrt{\\frac{2}{3}} - 2\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Climbing the first flight of stairs takes Jimmy 30 seconds, and each following flight takes 10 seconds more than the preceding one. How many total seconds does it take to climb t... | math | {
"ground_truth": "330 \\text{ seconds}",
"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 the roots of $px^2 + qx + r = 0$ be $u$ and $v$. Determine the quadratic equation with roots $p^2u - q$ and $p^2v - q$.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 + (pq + 2q)x + (p^3r + pq^2 + q^2) = 0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the function defined for every real number \\( x \\) by \\[ g(x) = \\lfloor x \\rfloor \\left(2013^{x-\\lfloor x\\rfloor} - 1\\right). \\] Determine the sum of the lengt... | math | {
"ground_truth": "A) \\( \\log_{2013}(2015) \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.