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": "Compute $(3+5+7)^2 + (3^2 + 5^2 + 7^2)$.",
"role": "user"
}
] | math | {
"ground_truth": "308",
"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 points $(3,1)$, $(6,4)$, and $(10, k+9)$ lie on the same straight line, determine the value of $k$.",
"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": "Solve the inequality system $\\left\\{\\begin{array}{l}{\\frac{x+7}{3} \\leq x+3}\\\\{2(x+1) < x+3}\\end{array}\\right.$.",
"role": "user"
}
] | math | {
"ground_truth": "-1 \\leq x < 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": "On an island, there are knights, who always tell the truth, and liars, who always lie. There are 15 islanders in a room. Each of the islanders in the room made two statements: \"... | math | {
"ground_truth": "9 \\text{ knights}",
"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": "It is given positive integer $n$ . Let $a_1, a_2,..., a_n$ be positive integers with sum $2S$ , $S \\in \\mathbb{N}$ . Positive integer $k$ is called separator if you can ... | 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": "For $x$ real, solve the inequality $2 \\leq |x-3| \\leq 5$.\n**A)** $-2 \\leq x \\leq 1$ or $5 \\leq x \\leq 8$ \n**B)** $-3 \\leq x \\leq 0$ or $6 \\leq x \\leq 9$ \n**C)** $0... | math | {
"ground_truth": "5 \\leq x \\leq 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": "In a faraway kingdom, there are 17 islands, each inhabited by 119 people. The inhabitants of the kingdom are divided into two castes: knights, who always tell the truth, and liar... | math | {
"ground_truth": "1013",
"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": "Every team plays every other conference team three times. The number of ways a team can play another team is $\\binom{10}{2} = 45$. However, this counts each pair of teams playin... | math | {
"ground_truth": "185",
"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 average of 10, 25, $x$, and $y$ is 20. Additionally, the product of $x$ and $y$ is known to be 156. What are the values of $x$ and $y$?",
"role": "user"
}
] | math | {
"ground_truth": "(x, y) = (12, 33) \\text{ or } (33, 12)",
"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": "Josh writes the numbers $1,2,3,\\dots,199,200$. He marks out $1$, skips the next two numbers $(2$ and $3)$, marks out $4$, and continues skipping two numbers and marking out the ... | math | {
"ground_truth": "C) 81",
"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 the arithmetic sequence $\\{a\\_n\\}$ has a sum of $S\\_n$ for its first $n$ terms, and $2^{n+1}$, $S\\_n$, $a$ form an arithmetic sequence ($n∈\\mathbb{N}^*$).\n\n1. ... | math | {
"ground_truth": "T\\_n = (2n - 3) \\cdot 2^{n} + 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": "Calculate: $|-3|+2^{2}-(\\sqrt{3}-1)^{0}$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( \\triangle ABC \\), it is known that \\( \\sin A = \\frac{3}{5} \\) and \\( \\cos B = \\frac{5}{13} \\). Find the complex number \\( \\cos C + \\mathrm{i} \\sin C... | math | {
"ground_truth": "\\frac{16}{65} + \\frac{63}{65}i",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of polynomials of the form $a_0x^n + a_1x^{n-1} + \\cdots + a_{n-1}x + a_n$, where all coefficients are integers, the sum of the absolute values of the coefficien... | math | {
"ground_truth": "C) 6",
"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 \\\\(f(x)\\\\) is an odd function defined on \\\\([-1,1]\\\\), and when \\\\(x \\in [-1,0]\\\\), the function's expression is \\\\(f(x) = \\frac{1}{4^x} - \\frac{1}{2^... | math | {
"ground_truth": "f(x)_{\\min} = -2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that triangle $ABC$ is an isosceles right triangle with $AB=AC=3$, let $M$ be the midpoint of hypotenuse $\\overline{BC}$. Points $I$ and $E$ lie on sides $\\overline{AC}$ ... | math | {
"ground_truth": "12",
"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": "Let $k$ and $n$ be positive integers. Consider an array of $2\\left(2^n-1\\right)$ rows by $k$ columns. A $2$ -coloring of the elements of the array is said to be *accep... | math | {
"ground_truth": "k = 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": "Let $a^2=\\frac{9}{25}$ and $b^2=\\frac{(3+\\sqrt{3})^2}{15}$, where $a$ is a negative real number and $b$ is a positive real number. If $(a+b)^3$ can be expressed in the simplif... | math | {
"ground_truth": "\\frac{-5670\\sqrt{3} + 1620\\sqrt{5} + 15\\sqrt{15}}{50625}",
"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 standard 12-sided die is rolled once. The number rolled is the diameter of a circle in units. Calculate the probability that the numerical value of the circumference of the cir... | 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": "Given the equation $x^2 + px + p = 0$, determine the number of real values of $p$ for which the roots of the equation are equal.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given the function $f(x)=a\\sin x- \\frac {3}{2}(a\\in\\mathbb{R})$, if the number of zeros of the function $f(x)$ in $(0,\\pi)$ is $2$, then the maximum value of $f(x)$ when $x\... | math | {
"ground_truth": "a- \\frac {3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow{a}=(2,-1,3)$, $\\overrightarrow{b}=(-1,4,-2)$, and $\\overrightarrow{c}=(1,3,\\lambda)$, if the three vectors lie in the same plane, determine the... | 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": "Bob earns $25 per hour, of which $2.5\\% is deducted to pay local taxes. How many cents per hour of Bob's wages are used to pay local taxes?\nA) 25 cents \nB) 50 cents \nC) 62.5 ... | math | {
"ground_truth": "C) 62.5 cents",
"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 distinguishable arrangements of the letters in the word \"BALLOON\" are there if all the vowels must appear first?\nA) 12\nB) 24\nC) 36\nD) 48\nE) 60",
"role": "user... | math | {
"ground_truth": "C) 36",
"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 prime factor of $999999999999$ is greater than $2006$ . Determine the remainder obtained when this prime factor is divided by $2006$ .",
"role": "user"
}
] | math | {
"ground_truth": "1877",
"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": "Three identical cones with radius 10 cm and height 15 cm are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 30 cm.... | math | {
"ground_truth": "1500\\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": "A quadrilateral $ABCD$ is inscribed in a circle. Suppose that $|DA| =|BC|= 2$ and $ |AB| = 4$ . Let $E $ be the intersection point of lines $BC$ and $DA$ . Suppose tha... | 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": "A circle is circumscribed around a regular $2n$-gon. A set of three distinct vertices of the polygon is called one-sided if there exists a semicircle on which these vertices lie ... | math | {
"ground_truth": "\\frac{3n}{2(2n-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": "The equation $z(z+i)(z+3i)=2002i$ has a zero of the form $a+bi$, where $a$ and $b$ are positive real numbers. Find $a.$",
"role": "user"
}
] | math | {
"ground_truth": "10\\sqrt{2}",
"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": "Let $r$ be a fixed positive real number. It is known that for some positive integer $n$ the following statement is true: for any positive real numbers $a_1,...,a_n$ satisfy... | math | {
"ground_truth": "n = 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 and simplify the product $2(x + 3)(x + 8)$.",
"role": "user"
}
] | math | {
"ground_truth": "2x^2 + 22x + 48",
"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": "Liam is investigating the prevalence of three types of dietary deficiencies, denoted by D, E, and F, within a group of students. For each of the three deficiencies, the probabili... | math | {
"ground_truth": "423",
"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": "What is the area of the region defined by the inequality $|4x-20|+|3y+9| \\le 6$?\nA) 7\nB) 8\nC) 9\nD) 10\nE) 11",
"role": "user"
}
] | math | {
"ground_truth": "C) 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": "In an experiment, the Wang Bo study group measured the length $y$ (in cm) of a spring hanging an object with the mass $x$ (in kg) as follows:\n\n| Mass of Hanging Object $x$/kg |... | math | {
"ground_truth": "42 \\text{ cm}",
"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": "How many divisors of 54 are also divisors of 81?",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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": "Emma rotated point $P$ 450 degrees clockwise about point $Q$ and it landed at point $R$. Luke rotated the original point $P$ $y$ degrees counterclockwise about point $Q$ and it a... | math | {
"ground_truth": "270^\\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 underground tunnel with a circular cross-section of radius $r=2,3 \\mathrm{~m}$ requires a leveling concrete layer at the bottom. The surface of the concrete layer is horizont... | math | {
"ground_truth": "50 \\text{ q}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of sets of three or more consecutive positive integers whose sum is 225.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Among all triangles formed by any three vertices of a cube, calculate the total number of irregular triangles.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"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 the securities transaction stamp duty rate is adjusted from 3‰ to 1‰ and a person purchases stocks worth 100,000 yuan, calculate the difference in the amount of securities tra... | math | {
"ground_truth": "200",
"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 $E(n)$ denote the sum of the even digits of $n$. Define a new function $F(n)$ to be the sum $E(n)$ only for those numbers $n$ where $n$ ends in digit 4. For example, $E(134) ... | math | {
"ground_truth": "The final answer is D) 68.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define an operation \"$F$\" on an integer $n$ as follows:\n1. When $n$ is odd, the result is $3n+5$.\n2. When $n$ is even, the result is $\\dfrac{n}{2^{k}}$ (where $k$ is the sma... | math | {
"ground_truth": "8",
"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 positive integer $n$ for which there exist real number $a_1,a_2,\\ldots,a_n$ such that $$ \\{a_j-a_i|1\\le i<j\\le n\\}=\\left\\{1,2,\\ldots,\\frac{n(n-1)}2\\right\... | math | {
"ground_truth": "n \\in \\{2, 3, 4\\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the integer value of $y$ in the arithmetic sequence $3^2, y, 3^3$?",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the graphs $y=Ax^2$ and $x^2 + 5 = y^2 + 6y$, where $A$ is a positive constant, and $x$ and $y$ are real variables. Determine how many points do the two graphs intersect... | math | {
"ground_truth": "A) exactly 4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all ordered pairs of real numbers $(a,b)$ such that the line $y=ax+b$ intersects the curve $y=\\ln(1+x^2)$ in exactly one point.",
"role": "user"
}
] | math | {
"ground_truth": "(0, 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": "Ms. Johnson gives an exam to two classes. The mean of the scores in the morning class is 75, and in the afternoon class, it is 65. The ratio of the number of students in the morn... | math | {
"ground_truth": "69",
"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 \\( \\left|x_{i}\\right| < 1 \\) for \\( i = 1, 2, \\cdots, n \\). If \\( \\left|x_{1}\\right|+\\left|x_{2}\\right|+\\cdots+\\left|x_{n}\\right| = 2016+\\left|x_{1}+x_{2}+\\c... | math | {
"ground_truth": "2018",
"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$$\n7 \\cos ^{3} z - 6 \\cos z = 3 \\cos (3z)\n$$",
"role": "user"
}
] | math | {
"ground_truth": "z = 90^\\circ + k \\cdot 180^\\circ, \\quad z = 39^\\circ 14' + k \\cdot 180^\\circ, \\quad z = 140^\\circ 46' + k \\cdot 180^\\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": "Determine integers $a$ and $b$ for which the roots of the polynomial $x^2 - 2x - 2$ are also roots of the polynomial $x^5 - ax^3 - bx^2 - 2$.",
"role": "user"
}
] | math | {
"ground_truth": "1408",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\log_2(2^b \\times p) = \\log_2 q + z$, solve for $p$ in terms of $q$ and $z$.\n**A)** $\\frac{2^b \\cdot q}{z}$\n**B)** $\\frac{q}{2^{b+z}}$\n**C)** $\\frac{q \\cdot 2^z}{2... | math | {
"ground_truth": "\\frac{q \\cdot 2^z}{2^b}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of positive integers less than or equal to $2019$ that are no more than $10$ away from a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "905",
"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": "For what value of $x$ does $5^{3x^2 - 4x + 3} = 5^{3x^2 + 6x - 5}$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{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": "Larry, Julius, and Maria are playing a sequential game where they take turns throwing a ball at a bottle on a ledge. Larry goes first, then Julius, followed by Maria, and the seq... | math | {
"ground_truth": "\\frac{729}{5985}",
"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 $n$ is a positive integer and the equation $2x+2y+z=n$ has 28 solutions in positive integers $x$, $y$, and $z$, determine the possible values of $n$.",
"role": "us... | math | {
"ground_truth": "17 \\text{ or } 18",
"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": "Convert the binary number \\\\(1011_{(2)}\\\\) to a decimal number.",
"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": "In Pascal's Triangle, each number is the sum of the number directly above it and to the left and the number directly above it and to the right. Calculate the sum of the numbers i... | math | {
"ground_truth": "1024",
"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": "We have $2021$ colors and $2021$ chips of each color. We place the $2021^2$ chips in a row. We say that a chip $F$ is *bad* if there is an odd number of chips that have a... | math | {
"ground_truth": "1010",
"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 random variable $\\eta\\sim B(n,p)$, and $E(2\\eta)=8$, $D(4\\eta)=32$, find the respective values of $n$ and $p$.",
"role": "user"
}
] | math | {
"ground_truth": "0.5",
"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": "Determine that all $ k \\in \\mathbb{Z}$ such that $ \\forall n$ the numbers $ 4n\\plus{}1$ and $ kn\\plus{}1$ have no common divisor.",
"role": "user"
}
] | math | {
"ground_truth": "k = 4 + 2^m",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four circles, no two of which are congruent, have centers at $A$, $B$, $C$, and $D$. Points $P$ and $Q$ lie on all four circles. The radius of circle $A$ is $\\tfrac{4}{7}$ times... | math | {
"ground_truth": "B) 168",
"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": "Michael has 18 coins, each of which is a 5-cent coin, a 10-cent coin, or a 20-cent coin. The total number of different values that can be obtained by combining one or more of his... | math | {
"ground_truth": "\\textbf{(B) } 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": "Given the expression $\\left(\\left((3+2)^{-1}-1\\right)^{-1}-1\\right)^{-1} -1$, evaluate its value.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{13}{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 that a regular hexagon of side length $1$ is surrounded by six regular hexagons as shown, find the area of $\\triangle{ABC}$.",
"role": "user"
}
] | math | {
"ground_truth": "3\\sqrt{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": "In a mining site, there are three different types of mineral deposits denoted as $X$, $Y$, and $Z$. The average purity percentage of minerals in deposit $X$ is $30\\%$, in deposi... | math | {
"ground_truth": "B) 65",
"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": "Equilateral triangle ∆DEF is inscribed in equilateral triangle ∆ABC such that DE ∥ BC. Find the ratio of the areas S_∆DEF: S_∆ABC.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{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": "Simplify $(2)(3b)(4b^2)(5b^3)(6b^4)(7c^2)$.",
"role": "user"
}
] | math | {
"ground_truth": "5040b^{10}c^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": "If the domain of the function $f(x)= \\frac {kx+7}{kx^{2}+4kx+3}$ is $\\mathbb{R}$, then the range of values for the real number $k$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[0, \\frac {3}{4}\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many of the integers from \\(2^{10}\\) to \\(2^{18}\\) inclusive are divisible by \\(2^{9}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "511",
"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 sum of the geometric series $2 + \\left(\\frac{1}{3}\\right) + \\left(\\frac{1}{3}\\right)^2 + \\left(\\frac{1}{3}\\right)^3 + \\dots$. Express your answer as a com... | 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": "A trapezoid has side lengths 4, 6, 8, and 10. The trapezoid can be rearranged to form different configurations with sides 4 and 8 as the parallel bases. Calculate the total possi... | math | {
"ground_truth": "48\\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": "Given the function $f(x)= \\begin{cases} x+2,x\\leqslant 2015 \\\\ f(x-5),x > 2015 \\end{cases}$, find $f(2019)=$ _____ .",
"role": "user"
}
] | math | {
"ground_truth": "2016",
"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 function $f(x) = |2x+1| + |2x-3|$. \n(1) Find the solution set $A$ for the inequality $f(x) > 6$; \n(2) If the solution set $B$ for the expression $f(x) > |a-1|$ is a... | math | {
"ground_truth": "a \\leq -5 \\text{ or } a \\geq 7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice and Bob each flip $20$ fair coins. Given that Alice flipped at least as many heads as Bob, what is the expected number of heads that Alice flipped?\n\n*Proposed by Adam B... | math | {
"ground_truth": "20 \\cdot \\frac{2^{38} + \\binom{39}{19}}{2^{39} + \\binom{39}{19}}",
"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": "For a given number of stones $k$ on the table, if Alper is the first player, determine for how many values of $k$ Alper can guarantee that he does not lose the game.",
"role"... | 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": "In each cell of a $5 \\times 5$ table, a natural number is written with invisible ink. It is known that the sum of all the numbers is 200, and the sum of the three numbers inside... | math | {
"ground_truth": "16",
"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 rectangle $ABCD$, $AB = 4$ and $BC = 8$. The rectangle is folded so that points $A$ and $C$ coincide, forming the pentagon $ABEFD$. What is the length of segment $EF$? Express... | math | {
"ground_truth": "2\\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": "Let $(a_n)_n\\geq 0$ and $a_{m+n}+a_{m-n}=\\frac{1}{2}(a_{2m}+a_{2n})$ for every $m\\geq n\\geq0.$ If $a_1=1,$ then find the value of $a_{2007}.$",
"role": "user"
... | math | {
"ground_truth": "2007^2",
"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": "Solve for $y$: $2y + 3y = 500 - (4y + 6y)$.",
"role": "user"
}
] | math | {
"ground_truth": "y = \\frac{100}{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": "Suppose that there exist nonzero complex numbers $a$ , $b$ , $c$ , and $d$ such that $k$ is a root of both the equations $ax^3+bx^2+cx+d=0$ and $bx^3+cx^2+dx+a=0$ . Fi... | math | {
"ground_truth": "1, -1, i, -i",
"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 convex hexagon, two random diagonals are chosen independently of each other. Find the probability that these diagonals intersect inside the hexagon (i.e., not at a vertex)."... | math | {
"ground_truth": "\\frac{5}{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": "Pegs are placed in a square grid, each 1 unit apart. A rubber band is stretched over four pegs forming a new quadrilateral shape. The pegs used are at coordinates (0,0), (2,0), (... | math | {
"ground_truth": "A) 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": "Given the fraction\n\\[\\frac{1}{98^2}=0.\\overline{b_{n-1}b_{n-2}\\ldots b_2b_1b_0},\\]\nwhere $n$ is the length of the period of the repeating decimal expansion. Determine the ... | math | {
"ground_truth": "**C)** 924",
"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": "Proposition $p$: The line $y=kx+3$ intersects the circle $x^{2}+y^{2}=1$ at points $A$ and $B$; Proposition $q$: The curve $\\frac{x^{2}}{k-6} - \\frac{y^{2}}{k}=1$ represents a ... | math | {
"ground_truth": "k < -2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least value of the expression \\((x+y)(y+z)\\), given that \\(x, y, z\\) are positive real numbers satisfying the equation \\(xyz(x + y + z) = 1\\).",
"role": "user"... | 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": "Solve in $ \\mathbb{R} $ the equation $ [x]^5+\\{ x\\}^5 =x^5, $ where $ [],\\{\\} $ are the integer part, respectively, the fractional part.",
"role": "user"
}
] | math | {
"ground_truth": "[0, 1) \\cup \\mathbb{Z}",
"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 $ABCDEF$ be a regular hexagon, and let $G$ , $H$ , $I$ , $J$ , $K$ , and $L$ be the midpoints of sides $AB$ , $BC$ , $CD$ , $DE$ , $EF$ , and $FA$ , respective... | math | {
"ground_truth": "\\frac{4}{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": "Let $a$, $b$, $c$ be three distinct lines, and $\\alpha$, $\\beta$, $\\gamma$ be three distinct planes. Consider the following propositions:\n1. If $\\alpha \\perp \\gamma$ and $... | math | {
"ground_truth": "2, 3, 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": "Given $2x-3y-z=0$ and $x+3y-14z=0$, $z \\neq 0$, calculate the numerical value of $\\frac{x^2+3xy}{y^2+z^2}$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all $7$ -digit numbers which are multiples of $21$ and which have each digit $3$ or $7$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\{3373377, 7373373, 7733733, 3733737, 7337337, 3777333\\}",
"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": "On a ruler, three marks are indicated: 0, 2, and 5. How can you use this ruler to measure a segment equal to 6?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"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": "Simplify the expression $\\frac{x^2-4x+3}{x^2-6x+9}\\div \\frac{x^2-6x+8}{x^2-8x+15}$.\n**A)** $\\frac{(x-1)(x-5)}{(x-3)(x-4)(x-2)}$\n**B)** $\\frac{x+1}{x-5}$\n**C)** $\\frac{x+... | math | {
"ground_truth": "\\frac{(x-1)(x-5)}{(x-3)(x-4)(x-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": "How many factors of 360 are divisible by 3 but not by 5?",
"role": "user"
}
] | 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": "In a non-isosceles triangle \\( \\triangle ABC \\), the sides opposite to angles \\( A, B, C \\) are \\( a, b, c \\) respectively, and they satisfy the equation \\( (2c - b) \\co... | math | {
"ground_truth": "(0, 4 \\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": "For a set of five distinct lines in a plane, there are exactly \\(N\\) distinct points that lie on two or more of these lines. What is the sum of all possible values of \\(N\\)?\... | math | {
"ground_truth": "C) 55",
"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 \\(a, b, c, x, y\\), and \\(z\\) be complex numbers such that\n\\[ a=\\frac{b+c}{x-2}, \\quad b=\\frac{c+a}{y-2}, \\quad c=\\frac{a+b}{z-2} \\]\n\nIf \\(xy + yz + zx = 67\\) ... | math | {
"ground_truth": "-5892",
"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 the diameter EB is parallel to chord DC and AB is parallel to a new chord FD which is perpendicular to EB, where angles AEB and ABE are in the ratio 3:7, find the degr... | math | {
"ground_truth": "135",
"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 Mersenne primes that are less than 1000.",
"role": "user"
}
] | math | {
"ground_truth": "3, 7, 31, 127",
"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": "Simplify: $\\left(\\frac{{x+2}}{{x^2-2x}}-\\frac{{x-1}}{{x^2-4x+4}}\\right) \\div \\frac{{x-4}}{{x^2-2x}} = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{x-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": "The ratio of the segments r and s in the right triangle formed by the sides a and b, where a:b = 1:3, is what?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{9}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
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