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": "How many seconds are in \\( \\frac{11}{3} \\) minutes?",
"role": "user"
}
] | math | {
"ground_truth": "220",
"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 m ounces of a m% solution of acid, x ounces of water are added to yield a (m-10)% solution, find the value of x in terms of m.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{10m}{m-10}",
"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": "Joyce made $12$ of her first $30$ shots in the first three games of this basketball game, so her seasonal shooting average was $40\\%$. In her next game, she took $10$ shots and ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A supermarket sells two types of mosquito repellent bracelets, type A and type B. One day, they sold 3 type A bracelets and 1 type B bracelet for a total income of $128. Another ... | math | {
"ground_truth": "31",
"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 range of the function $h(x) = \\frac{3}{3 + 9x^2}$ and express it as an interval $(c,d]$. What is $c+d$?",
"role": "user"
}
] | 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": "Given a triangular array of $2211$ coins formed with $1$ coin in the first row, $2$ coins in the second row, and so on until the $N$th row, find the sum of the digits of $N$.",
... | math | {
"ground_truth": "12",
"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 set Φ consists of a finite number of points on the plane. The distance between any two points from Φ is at least $\\sqrt{2}$ . It is known that a regular triangle with side ... | math | {
"ground_truth": "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": "Laura bought a new scooter and paid $20\\%$ of the cost upfront, which was $\\$240$. Additionally, she agreed to pay the remaining amount in 12 equal monthly installments. What w... | math | {
"ground_truth": "\\$80",
"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": "An equilateral triangle is inscribed in a circle of radius \\( R \\). The altitudes of the triangle are extended until they intersect with the circle. These points of intersectio... | math | {
"ground_truth": "R^2 (\\pi - \\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": "Among all two-digit numbers consisting of two different digits, find the smallest quotient obtained when each two-digit number is divided by the sum of its digits.",
"role": ... | math | {
"ground_truth": "1.9",
"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": "Mr. Smith teaches a chemistry class of 20 students with an initial average score of 76. After including a late submission from a student named Alex, the average score for the cla... | math | {
"ground_truth": "116",
"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 positive integer divisors of \\(220^6\\) are perfect squares or perfect cubes (or both)?\nA) 137\nB) 142\nC) 145\nD) 150\nE) 153",
"role": "user"
}
] | math | {
"ground_truth": "C) 145",
"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 $\\sin 2\\alpha=\\frac{1}{3}$, determine $\\cos^{2}\\left(\\alpha-\\frac{\\pi}{4}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{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": "Triangle $ABC$ with $AB=4$ , $BC=5$ , $CA=6$ has circumcircle $\\Omega$ and incircle $\\omega$ . Let $\\Gamma$ be the circle tangent to $\\Omega$ and the sides $AB$... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=e^{x}+x^{3}- \\frac {1}{2}x-1$, there are exactly two points, $P_{1}$ and $P_{2}$, on its graph such that there exist two points, $Q_{1}$ and $Q_{2}$, on... | math | {
"ground_truth": "m=\\frac {1}{2}- \\frac {1}{e}",
"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 the polynomial \\(f(x) = x^{2009} - 19x^{2008} + 1\\) having distinct zeroes \\(r_1, r_2, \\ldots, r_{2009}\\). Define another polynomial \\(P\\) of degree 2009 such tha... | math | {
"ground_truth": "\\frac{36}{49}",
"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 minimum positive value of $ 1*2*3*4*...*2020*2021*2022$ where you can replace $*$ as $+$ or $-$",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for \\(k\\) in the quadratic equation \\(3x^2 - (k+2)x + 6 = 0\\) such that the equation has real roots and one of the roots is equal to 3.\nA) 9\nB) -9\nC) -6√2 and 6√2\nD... | math | {
"ground_truth": "A) 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": "Find all pairs of prime numbers $p\\,,q$ for which:\n\\[p^2 \\mid q^3 + 1 \\,\\,\\, \\text{and} \\,\\,\\, q^2 \\mid p^6-1\\]\n\n*Proposed by P. Boyvalenkov*",
"role": "user... | math | {
"ground_truth": "\\{(3, 2), (2, 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": "Determine the smallest positive integer $n$ such that $6^n \\equiv n^5 \\pmod{4}$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that $\\alpha$ is an obtuse angle, and $3\\sin 2\\alpha = \\cos\\alpha$, calculate the value of $\\sin\\alpha$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {1}{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": "Given the expression $\\frac{x^2-4x+3}{x^2-6x+9} \\div \\frac{x^2-3x+2}{x^2-4x+4},$ simplify the expression.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x-2}{x-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 that a blue ball and an orange ball are randomly and independently tossed into bins numbered with the positive integers, where for each ball the probability that it is toss... | math | {
"ground_truth": "\\frac{7}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An ant lies on each corner of a $20 \\times 23$ rectangle. Each second, each ant independently and randomly chooses to move one unit vertically or horizontally away from its co... | math | {
"ground_truth": "130",
"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 order to save money on gas and use up less fuel, Hannah has a special battery installed in the family van. Before the installation, the van averaged $18$ miles per gallon o... | math | {
"ground_truth": "108",
"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 minimum value of the quotient of a 4-digit number with each digit different and non-zero and condition \\( a = c + 1 \\), \\( b = d + 1 \\), where \\( a, b, c, d \\) are... | math | {
"ground_truth": "C) 192.67",
"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": "Given six distinct positive integers are randomly chosen between $1$ and $2006$, inclusive, determine the probability that some pair of these integers has a difference that is 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": "The mean of four numbers is 92. If the largest of these numbers is 120 and one of the other numbers is half of the largest number, find the mean of the remaining three numbers.",... | math | {
"ground_truth": "Let the four numbers be $a, b, c,$ and $120$. Given that $b = \\frac{120}{2} = 60$, the equation for their arithmetic mean is:\n \\[\n \\frac{a + 60 + c + 120}{4} = 92\n \\]\n\n2. Multiply both sides of the equation by $4$ to solve for the sum:\n \\[\n a + 60 + c + 120 = 368\n \\]\n\n3.... | {
"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 fraction $\\frac{x-2}{x+1}$, determine the value of $x$ for which the fraction is undefined.",
"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": "90 students arrived at the camp. It is known that among any 10 students, there are necessarily two friends. A group of students is said to form a chain of friendships if the chil... | 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": "Consider the function $f(x)=e^x+2x-a$ (where $a \\in \\mathbb{R}$, and $e$ is the base of natural logarithms). If there exists a point $(x_0, y_0)$ on the curve $y=\\sin x$ such ... | math | {
"ground_truth": "[-1+e^{-1}, e+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": "If $x=3$ is the solution to the equation $\\frac{x-a}{2}-2=x-1$, then the solution set of the inequality $(2-\\frac{a}{5})<\\frac{1}{3}x$ is _____.",
"role": "user"
}
] | math | {
"ground_truth": "x>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": "A 4x4x4 cube is made of $64$ normal dice. Each die's opposite sides sum to $7$. Calculate the smallest possible sum of all the values visible on the $6$ faces of the large cube."... | math | {
"ground_truth": "144",
"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 largest even whole number such that nine times the number is less than 150.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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": "From the numbers 1 through 15 inclusive, form pairs of numbers such that the difference between the first and second numbers is evenly divisible by 7.",
"role": "user"
}
] | math | {
"ground_truth": "8 \\& 1, 9 \\& 2, 10 \\& 3, 11 \\& 4, 12 \\& 5, 13 \\& 6, 14 \\& 7, 15 \\& 8, 15 \\& 1",
"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 functions $f(x) = \\ln x - ax^2 + (2-a)x$ and $g(x) = \\frac{x}{e^x} - 2$.\n(1) Find the extreme values of the function $f(x)$.\n(2) If for any given $x_0 \\in (0, e]$,... | math | {
"ground_truth": "\\frac{3 + 2e}{e^2 + e} \\leq a < e",
"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 the remainder when $7 \\times 17 \\times 27 \\times \\ldots \\times 197$ is divided by $7$.",
"role": "user"
}
] | 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": "Solve the following system of equations:\n\n$$\n\\begin{aligned}\n& x^{2}+x y+y=1 \\\\\n& y^{2}+x y+x=5\n\\end{aligned}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "(x, y) = (-1, 3) \\text{ or } (x, y) = (-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": "Let the complex number $z$ satisfy $i(z + 1) = -3 + 2i$, then the real part of $z$ 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": "A highway strip that is 40 feet wide and stretches for one mile is temporarily closed. Initially, Robert decides to ride his bike in large semicircles across the strip. After 528... | math | {
"ground_truth": "\\frac{\\pi}{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 the function $f(x) = \\ln x - ax + b$, where $a, b \\in \\mathbb{R}$.\n\n(Ⅰ) Determine the monotonic intervals of the function $f(x)$.\n\n(Ⅱ) If $a=1$, $b \\in [0, 2]$, and... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right triangle has sides with lengths 6, 8, and 10. There are both an inscribed circle and a circumscribed circle around the triangle. What is the distance between the centers ... | math | {
"ground_truth": "\\sqrt{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": "The complex number $\\frac{3-i}{1-i}$ equals $1+2i$.",
"role": "user"
}
] | math | {
"ground_truth": "2+i",
"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": "Draw the graph of the function $y = \\frac{| x^3 - x^2 - 2x | }{3} - | x + 1 |$ .",
"role": "user"
}
] | math | {
"ground_truth": "y = \\frac{| x^3 - x^2 - 2x | }{3} - | x + 1 |",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the quadratic equation $y = 3x^2 - 5x + 2$, draw the graph of the equation obtained by replacing $x$ with $-x$ in the given equation, draw the line $y = x + 1$, and determi... | math | {
"ground_truth": "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 the sets \\( P = \\{ y \\mid y = x^2 + 3x + 1, x \\in \\mathbb{R} \\} \\) and \\( Q = \\{ y \\mid y = -x^2 - 3x + 1, x \\in \\mathbb{R} \\} \\), find \\( P \\cap Q \\).",
... | math | {
"ground_truth": "\\left[-\\frac{5}{4}, \\frac{13}{4}\\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": "What is the sum of the numbers 12345, 23451, 34512, 45123, and 51234?",
"role": "user"
}
] | math | {
"ground_truth": "166665",
"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": "For how many positive integers $n$ less than or equal to $15$ is $n!$ evenly divisible by $1^2 + 2^2 + \\cdots + n^2?$",
"role": "user"
}
] | math | {
"ground_truth": "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": "Consider $x = {2 + \\frac{\\sqrt{3}}{2 + \\frac{\\sqrt{3}}{2 + ...}}}$. Find $\\frac{1}{(x+2)(x-3)}$. When your answer is in the form $\\frac{A + \\sqrt{B}}{C}$, where $A$, $B$, ... | math | {
"ground_truth": "120",
"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, b, c\\) be positive integers. All the roots of each of the quadratics\n\\[ a x^{2}+b x+c, \\quad a x^{2}+b x-c, \\quad a x^{2}-b x+c, \\quad a x^{2}-b x-c \\]\nare inte... | math | {
"ground_truth": "(1, 10, 24)",
"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": "Two candidates participated in an election with \\(p+q\\) voters. Candidate \\(A\\) received \\(p\\) votes and candidate \\(B\\) received \\(q\\) votes, with \\(p > q\\). During ... | math | {
"ground_truth": "\\frac{1}{2019}",
"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:<br/>$(1)$ Simplify $\\frac{{x-1}}{x}÷\\frac{{2x-2}}{{{x^2}}}$;<br/>$(2)$ Simplify first, then evaluate $(2-\\frac{{a-1}}{{a+1}})÷\\frac{{{a^2}+6a+9}}{{a+1}}$, where $a... | math | {
"ground_truth": "\\frac{1}{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": "As $x$ ranges over all real numbers, find the range of\n\\[ g(x) = \\cos^4 x + \\sin^2 x. \\]",
"role": "user"
}
] | math | {
"ground_truth": "\\left[ \\frac{3}{4}, 1 \\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": "How many ways are there to permute the first $n$ positive integers such that in the permutation, for each value of $k \\le n$ , the first $k$ elements of the permutation hav... | math | {
"ground_truth": "2^{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "You have two blackboards $A$ and $B$ . You have to write on them some of the integers greater than or equal to $2$ and less than or equal to $20$ in such a way that each n... | math | {
"ground_truth": "49",
"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 a company with 200 employees, of which 120 are no more than 45 years old and 80 are older than 45 years, calculate the number of employees who are no more than 45 years old... | math | {
"ground_truth": "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": "What value should \\( x \\) be given, so that\n\n\\[ \n\\frac{4 x^{4} - 20 x^{2} + 18}{x^{4} - 5 x^{2} + 4} < 3 ? \n\\]",
"role": "user"
}
] | math | {
"ground_truth": "(-2, -\\sqrt{3}) \\cup (\\sqrt{3}, 2) \\cup (-\\sqrt{2}, -1) \\cup (1, \\sqrt{2})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that construction teams A and B each have a certain number of workers. If team A lends 90 workers to team B, then team B's total number of workers will be twice that of tea... | math | {
"ground_truth": "153",
"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 area of a circle whose center is at point $A$ located at coordinates $(1, -2)$ and which also passes through point $B$ at coordinates $(-5, 6)$?",
"role": "user"
... | math | {
"ground_truth": "100\\pi",
"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": "**p1.** Evaluate $S$ . $$ S =\\frac{10000^2 - 1}{\\sqrt{10000^2 - 19999}} $$ **p2.** Starting on a triangular face of a right triangular prism and allowing moves to only adjac... | math | {
"ground_truth": "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": "A circle $C_1$ has its center $O$ on a line $\\ell$. Two points $P$ and $Q$ on $\\ell$ are tangents to $C_1$, with $O$ between $P$ and $Q$. The distances are $OP = 9$, and $OQ = ... | math | {
"ground_truth": "\\sqrt{153}",
"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": "Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. Calcula... | math | {
"ground_truth": "15",
"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": "For what real value of $t$ is $\\frac{-15-\\sqrt{145}}{6}$ a root of $3x^2 + 15x + t$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{20}{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": "Determine the coefficient of the $x^{3}$ term in the expansion of $x(1+2x)^{6}$.",
"role": "user"
}
] | math | {
"ground_truth": "60",
"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": "Joy has 40 thin rods, one of each integer length from 1 cm to 40 cm. She places rods of lengths 4 cm, 8 cm, and 17 cm on a table. She wants to select one more rod to form a quadr... | math | {
"ground_truth": "D) 21",
"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": "**p1.** James has $8$ Instagram accounts, $3$ Facebook accounts, $4$ QQ accounts, and $3$ YouTube accounts. If each Instagram account has $19$ pictures, each Facebook a... | math | {
"ground_truth": "120360",
"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": "Rewrite \\(\\sqrt[3]{4^6 \\cdot 5^3 \\cdot 7^3}\\) as an integer.",
"role": "user"
}
] | math | {
"ground_truth": "560",
"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 function $f(x) = \\frac{1}{3}x^3 - x^2 + m$, its maximum value on the interval $[-1, 1]$ is $\\frac{2}{3}$.\n1. Find the value of the real number $m$.\n2. Determine the... | math | {
"ground_truth": "[-6, \\frac{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": "Convert 89 to base-4.",
"role": "user"
}
] | math | {
"ground_truth": "1121",
"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 line \\( l \\) with a slope of \\(\\frac{\\sqrt{2}}{2}\\) intersects the ellipse \\(\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1 (a>b>0)\\) at two distinct points \\( P ... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{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 \\\\(a > 0\\\\), \\\\(b > 0\\\\), and \\\\(a+4b={{(ab)}^{\\\\frac{3}{2}}}\\\\).\n\n\\\\((\\\\)I\\\\()\\\\) Find the minimum value of \\\\(a^{2}+16b^{2}\\\\);\n\n\\\\((\\\\)... | math | {
"ground_truth": "32",
"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 all functions \\( f: \\mathbb{N} \\rightarrow \\mathbb{N} \\) which satisfy \\( f(a^{2} + b^{2}) = f(a) f(b) \\) and \\( f(a^{2}) = f(a)^{2} \\) for all positive integers \\... | math | {
"ground_truth": "f \\equiv 1",
"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 $\\triangle DEF$ with integer side lengths, $\\cos D = \\frac{8}{17}$, $\\cos E = \\frac{15}{17}$, and $\\cos F = -\\frac{5}{13}$. Determine the least possible perimeter for $... | math | {
"ground_truth": "503",
"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 roots of the cubic equation $x^3+x^2-2x-1=0$ cannot be in the interval $(0,1)$.",
"role": "user"
}
] | math | {
"ground_truth": "(0, 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": "\\(\\left(a_{n}\\right)\\) is an arithmetic progression with a common difference of 1. It is known that \\( \\mathrm{S}_{2022} \\) is the smallest among all \\( S_{n} \\) (smalle... | math | {
"ground_truth": "(-2022, -2021)",
"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 $x_0$ , $x_1$ , $\\ldots$ , $x_{1368}$ be complex numbers. For an integer $m$ , let $d(m)$ , $r(m)$ be the unique integers satisfying $0\\leq r(m) < 37$ and $m =... | math | {
"ground_truth": "9745",
"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 two-thirds of the boys and $\\frac{3}{4}$ of the girls passed the test, and an equal number of boys and girls passed the test, determine the minimum possible number of... | math | {
"ground_truth": "17",
"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": "Given the function f(x) = $\\frac{1}{\\sqrt{4 + 3x - x^2}}$ with domain set A, and function g(x) = -x² - 2x + 2, x ∈ [-1, 1] with range set B.\n(1) Find A and B;\n(2) Let set C =... | math | {
"ground_truth": "[-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": "I have a drawer with 8 forks, 8 spoons, 8 knives, and 8 plates. If I reach in and randomly remove four items, what is the probability that I get one fork, one spoon, one knife, a... | math | {
"ground_truth": "\\frac{128}{1125}",
"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": "Annie takes a $6$ question test, with each question having two parts each worth $1$ point. On each **part**, she receives one of nine letter grades $\\{\\text{A,B,C,D,E,F,G,... | 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 a point $P(x,y)$ inside the circle $x^{2}+(y-1)^{2}=1$, find the probability that $y\\geqslant x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{4}+\\frac{1}{2\\pi}",
"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 addition shown below where \\(A\\), \\(B\\), \\(C\\), \\(D\\) and \\(E\\) are distinct digits, calculate the number of possible values for \\(D\\).\n\\[\n\\begin{array}{cc... | math | {
"ground_truth": "8",
"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 $cosθ+cos(θ+\\frac{π}{3})=\\frac{\\sqrt{3}}{3},θ∈(0,\\frac{π}{2})$, find $\\sin \\theta$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{-1 + 2\\sqrt{6}}{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": "Given that the endpoint $B$ of line segment $AB$ has coordinates $(4,3)$, and the other endpoint $A$ moves on the circle $(x+1)^{2}+y^{2}=4$, find the trajectory equation of the ... | math | {
"ground_truth": "(x-\\frac{3}{2})^2+(y-\\frac{3}{2})^2=1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equations $\\frac{xy}{x+y}= a, \\frac{xz}{x+z}= b, \\frac{yz}{y+z}= c, \\frac{yz}{y-z}= d$, find the value of $x$ in terms of $a, b, c, d$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2ac}{a-c-d}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An isosceles trapezoid \\(ABCD\\) with bases \\(BC\\) and \\(AD\\) is given such that \\(\\angle ADC = 2 \\angle CAD = 82^\\circ\\). Inside the trapezoid, a point \\(T\\) is chos... | math | {
"ground_truth": "38^\\circ",
"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 \\( \\left(\\frac{8}{9}\\right)^3 \\cdot \\left(\\frac{3}{5}\\right)^3 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{512}{3375}",
"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 \\( x > 0 \\), find the range of the function\n\\[ \nf(x) = \\frac{x + \\frac{1}{x}}{[x] \\cdot \\left[\\frac{1}{x}\\right] + [x] + \\left[\\frac{1}{x}\\right] + 1} \n\\]\n... | math | {
"ground_truth": "\\left\\{ \\frac{1}{2} \\right\\} \\cup \\left[ \\frac{5}{6}, \\frac{5}{4} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $(a-4)^2+|2-b|=0$, find $a^b$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "A group of students went on a hike in the Moscow region during their vacation. They walked the first 30 km on foot, then traveled $20\\%$ of the remaining route on a raft along t... | math | {
"ground_truth": "150 \\text{ km}",
"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 the limiting sum of the infinite series $\\frac{1}{8} + \\frac{2}{8^2} + \\frac{3}{8^3} + \\dots$ where the $n$-th term is $\\frac{n}{8^n}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{49}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathbf{A}$ be a $2 \\times 2$ matrix, with real entries, such that $\\mathbf{A}^4 = \\mathbf{0}$ and $\\text{tr}(\\mathbf{A}) = 0$. Determine the number of different possi... | 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": "North High School and South Academy want to assess student interests in sports. North High has 1800 students, with 30% preferring basketball. South Academy has 3000 students, wit... | math | {
"ground_truth": "C) 33%",
"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 sequence $\\left\\{a_{n}\\right\\}$ with terms that are all greater than or equal to 1, satisfying:\n$$\na_{1}=1, \\quad a_{2}=1+\\frac{\\sqrt{2}}{2}, \\quad\\left(\\frac... | math | {
"ground_truth": "\\frac{2}{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": "Between what two consecutive years at Euclid High School was there the largest percentage increase in the number of students taking the AMC 10?",
"role": "user"
}
] | math | {
"ground_truth": "2002\\ \\text{and}\\ 2003",
"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": "Given the set $A=\\{x|x\\in N, \\frac{12}{6-x}\\in N\\}$, find the number of proper subsets of set $A$.",
"role": "user"
}
] | math | {
"ground_truth": "31",
"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 right triangle, if the ratio of the measures of the acute angles is $7:2$, what is the measure of the largest angle of the triangle?",
"role": "user"
}
] | math | {
"ground_truth": "90^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An icosidodecahedron is a convex polyhedron with 20 triangular faces and 12 pentagonal faces. How many vertices does it have?",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider three lines $AB \\parallel CD \\parallel EF \\parallel GH$, where $AB = 300$ cm and $CD = 200$ cm. The line segment $EF$ is halfway between $AB$ and $CD$, and $GH$ anoth... | math | {
"ground_truth": "93.75 \\text{ cm}",
"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": "Amanda drove 450 miles in 7 hours and 30 minutes, then stopped to rest for 1 hour and 45 minutes. Afterwards, she drove an additional 420 miles in 7 hours. What was Amanda's aver... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
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