data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ S\\subset\\mathbb N$ is called a square set, iff for each $ x,y\\in S$ , $ xy\\plus{}1$ is square of an integer.\r\na) Is $ S$ finite?\r\nb) Find maximum number of elemen... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $ab>0$, and points $A(a,0)$, $B(0,b)$, $C(-2,-2)$ are collinear, then the minimum value of $ab$ is $\\boxed{16}$.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In regular decagon $ABCDEFGHIJ$, $P$ and $Q$ are midpoints of $\\overline{CD}$ and $\\overline{HI}$ respectively. Compute $[ABEP]/[FGHQP]$. ($[ABCD]$ denotes the area of polygon ... | math | {
"ground_truth": "\\frac{5}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On a plane several straight lines are drawn in such a way that each of them intersects exactly $15$ other lines. How many lines are drawn on the plane? Find all possibilities a... | math | {
"ground_truth": "16, 18, 20, 30",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integer $n$ and nonnegative integer $a_1,a_2,\\dots,a_n$ satisfying: $i$ divides exactly $a_i$ numbers among $a_1,a_2,\\dots,a_n$ , for each $i=1,2,\\d... | math | {
"ground_truth": "n = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the exact value of\n\\[\n\\sqrt{\\left( 2 - \\sin^2 \\frac{\\pi}{8} \\right) \\left( 2 - \\sin^2 \\frac{2 \\pi}{8} \\right) \\left( 2 - \\sin^2 \\frac{3 \\pi}{8} \\righ... | math | {
"ground_truth": "\\frac{\\sqrt{17}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $12$. Find the sum of the $x$-coordinates of the midpoints of the sides of this triangl... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute \\[\\frac{(N+1)!(N-2)}{(N+2)!}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{N!(N-2)}{N+2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We define a permutation $(a_1,a_2,a_3,a_4,a_5)$ of $(1,2,3,4,5)$ as stripe-tailed if $a_1 + a_2 < a_3 + 2a_4 + a_5$. How many stripe-tailed permutations exist among all permutati... | math | {
"ground_truth": "D) 56",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sarah bought a scooter for $\\$3200$ for her courier service. She earns $\\$15$ for each package she delivers, but she has to spend $\\$4$ on fuel for each delivery. What is the ... | math | {
"ground_truth": "291",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence an is defined by $a_0 = 4, a_1 = 1$ and the recurrence formula $a_{n+1} = a_n + 6a_{n-1}$ . The sequence $b_n$ is given by\n\\[b_n=\\sum_{k=0}^n \\binom nk a_k.... | math | {
"ground_truth": "b_n = \\frac{9}{5} \\cdot 4^n + \\frac{11}{5} \\cdot (-1)^n",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Al and Barb start their new jobs on the same day. Al's schedule is 5 work-days followed by 2 rest-days. Barb's schedule is 4 work-days followed by 1 rest-day. Calculate how many ... | math | {
"ground_truth": "C) 14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the pyramid \\(FABC\\), \\(AB = BC\\), \\(FB = FK\\), where \\(K\\) is the midpoint of segment \\(AC\\), and the tangent of the angle between the planes \\(FAB\\) and \\(ABC\\... | math | {
"ground_truth": "5:11 \\text{ or } 1:19",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A dart board is in the shape of a regular decagon (10-sided polygon) with a side length of 1 unit each, and there is a center square connecting the midpoints of every alternate s... | math | {
"ground_truth": "B) 0.085",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a rectangle $ABCD$ with $BC = 2 \\cdot AB$ . Let $\\omega$ be the circle that touches the sides $AB$ , $BC$ , and $AD$ . A tangent drawn from point $C$ to the ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the number \\(8^4 \\cdot 7^3 \\cdot 9^1 \\cdot 5^5\\). How many distinct, natural-number factors does it have?",
"role": "user"
}
] | math | {
"ground_truth": "936",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two ships depart from the same port in opposite directions, with ship A going downstream and ship B going upstream. The speed of the water flow is $a$ km/h. \n$(1)$ If the speed... | math | {
"ground_truth": "m=2a",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the men's Olympic football group stage, each group consists of four teams, and each team plays against each other once. A win earns a team 3 points, a loss earns 0 points, and... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a positive integer \\(n\\), let\n\\[\nT_n = 1 + \\frac{1}{2\\cdot2!} + \\frac{1}{3\\cdot3!} + \\dots + \\frac{1}{n\\cdot n!}.\n\\]\nCompute\n\\[\n\\sum_{n = 1}^\\infty \\frac... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)= \\begin{cases} -x+2,x\\leqslant 0 \\\\ x+2,x > 0\\\\ \\end{cases}$, find the solution set for the inequality $f(x)\\geqslant x^{2}$.",
"role": "user... | math | {
"ground_truth": "-2\\leqslant x\\leqslant 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let proposition p: The function $f(x) = (a+2)^x$ is an increasing function on $\\mathbb{R}$, and proposition q: The equation $x^2+2x+a=0$ has solutions. If \"p and q\" is a false... | math | {
"ground_truth": "(-\\infty, -1] \\cup (1, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a box, there are $a$ white balls and $3$ red balls. After thoroughly mixing the balls each time, one ball is randomly picked, its color is noted, and then it is placed back in... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given triangle $\\triangle XYZ$ has a right angle at $Y$, point $W$ is the foot of the altitude from $Y$, $XW=5$, and $WZ=3$, calculate the area of $\\triangle XYZ$.",
"role"... | math | {
"ground_truth": "4\\sqrt{15}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Pedro decided to take all of his children, boys and girls, to an ice cream parlor called Sorvete Matemático. In the ice cream parlor, there are 12 different flavors of ice cream,... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $5\\sin 2α=6\\cos α,α∈(0, \\dfrac {π}{2})$, find the value of $\\tan \\dfrac {α}{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $15^{-1}\\pmod{1003}$. Express your answer as a residue from $0$ to $1002$, inclusive.",
"role": "user"
}
] | math | {
"ground_truth": "937",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider an isosceles right triangle where the ratio of one leg to the hypotenuse is equal to some ratio \\( k \\). Find \\( k^2 \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider two right circular cones with vertices pointing downwards, each filled with the same amount of water. The radius of the water surface in the first cone is 4 cm, while in... | math | {
"ground_truth": "4:1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer o... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Delete all perfect squares from the sequence of positive integers $1, 2, 3, \\cdots$. Find the 2003rd term of the new sequence.",
"role": "user"
}
] | math | {
"ground_truth": "2048",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S_n$ be the sum of the first $n$ terms of the sequence $\\{a_n\\}$, where $a_n=2n-49$. Find the value of $n$ when $S_n$ is minimized.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $s$ be any real number. Compute $\\sqrt{s^6 + s^3}$.",
"role": "user"
}
] | math | {
"ground_truth": "|s|\\sqrt{s(s^3 + 1)}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the coefficients of the following cubic polynomial\n\n\\[ \nf(x) \\equiv Ax^{3}+Bx^{2}+Cx+D\n\\]\n\ngiven that when \\( x = 1 \\), \\( f(1) = 0 \\), and\n\n\\[ \n\\begi... | math | {
"ground_truth": "15 x^3 - 37 x^2 + 30 x - 8.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sophie has a total of $126 in her wallet. She has one dollar bills, two dollar bills, and five dollar bills. If there are a total of 55 bills in Sophie's wallet, how many one dol... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The range of the slope angle of a tangent line to the graph of the function $f(x)= \\frac{1}{3}x^{3}-x^{2}$ is $\\boxed{[\\frac{3\\pi}{4},\\pi]}$",
"role": "user"
}
] | math | {
"ground_truth": "[0, \\frac{\\pi}{2})\\cup[\\frac{3\\pi}{4},\\pi)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the length of an interval $[x\\_1, x\\_2]$ is defined as $|x\\_2 - x\\_1|$, the domain and range of the function $f(x) = \\frac{(m^2 + m)x - 1}{m^2x} (m \\in \\mathbb{... | math | {
"ground_truth": "\\frac{2\\sqrt{3}}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many bases between two and nine inclusive does the representation of $725_{10}$ have a final digit of 1?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The area of the largest triangle that can be inscribed in a semi-circle whose radius is $r$, calculate this area.",
"role": "user"
}
] | math | {
"ground_truth": "r^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all values of \\( a \\) for which the system of equations\n\n\\[\n\\left\\{\\begin{array}{c}\\log _{\\mid x+3}(a x+4 a)=2 \\log _{\\mid x+3}(x+y), \\\\ x+1+\\sqrt{x^{2}+2 x+... | math | {
"ground_truth": "(4; 4.5) \\cup (4.5; 16/3]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Circle $I$ is inside Circle $II$ and passes through the center of Circle $II$. The radius of Circle $I$ is 3 inches. If the radius of Circle $II$ is twice the radius of Circle $I... | math | {
"ground_truth": "36\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. Given a point P on the terminal side of angle $\\alpha$ with coordinates $(-\\sqrt{3}, 2)$, find $\\sin\\alpha$, $\\cos\\alpha$, and $\\tan\\alpha$.\n2. What are the angles wi... | math | {
"ground_truth": "698^\\circ44'",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many positive integers $n$ is $\\frac{n+2}{50-n}$ also a positive integer?\nA) 2\nB) 3\nC) 4\nD) 5\nE) 6",
"role": "user"
}
] | math | {
"ground_truth": "A) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sets $M=\\{-1, 1, 2\\}$ and $N=\\{y|y=x^2, x\\in M\\}$, find the intersection of $M$ and $N$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{1\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Randry drove the first half of his trip on a gravel road, the next $30$ miles on pavement, and the remaining one-fourth on a dirt road. Let $x$ be the total length of Randy's tri... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the value of the positive integer \\( b \\) is the correct choice, the expression \\( (2021)_{b}-(221)_{b} \\) in base \\( b \\) is not divisible by 3.",
"role": "user"
... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The ratio of $u$ to $v$ is $5:2$, the ratio of $x$ to $y$ is $4:1$, and the ratio of $v$ to $y$ is $3:4$. What is the ratio of $u$ to $x$?\nA) $\\frac{15}{32}$\nB) $\\frac{10}{21... | math | {
"ground_truth": "\\frac{15}{32}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $64$ booths around a circular table and on each one there is a chip. The chips and the corresponding booths are numbered $1$ to $64$ in this order. At the center ... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What are the times between $7$ and $8$ o'clock, correct to the nearest minute, when the hands of a clock will form an angle of $120^{\\circ}$?",
"role": "user"
}
] | math | {
"ground_truth": "7:16 \\text{ and 7:56}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Points E and F lie on line segment $\\overline{GH}$. The length of $\\overline{GE}$ is $3$ times the length of $\\overline{EH}$, and the length of $\\overline{GF}$ is $7$ times t... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Anna and Berta play a game in which they take turns in removing marbles from a table. Anna takes the first turn. When at the beginning of the turn there are $n\\geq 1$ marbles ... | math | {
"ground_truth": "131070",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The solution set of the system of equations\n\\[\n\\begin{cases}\n& x+y=5 \\\\\n& x-y=1\n\\end{cases}\n\\]\nexpressed by the listing method is __________.",
"role": "user"
... | math | {
"ground_truth": "\\{(3,2)\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many unique pairs of parallel edges does a regular octahedron have?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What are the last two digits when $7^{10}$ is multiplied out?",
"role": "user"
}
] | math | {
"ground_truth": "49",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the partial derivatives of the following functions:\n\n1. \\( z = x^3 + x^2 y + y^3 \\)\n\n2. \\( f(x, y) = \\sqrt{x^2 - y^2} \\) at the point \\((5, -3)\\)\n\n3. \\( \\varp... | math | {
"ground_truth": "\\begin{aligned}\n1.\\ & \\frac{\\partial z}{\\partial x} = 3x^2 + 2xy, \\ \\frac{\\partial z}{\\partial y} = x^2 + 3y^2, \\\\\n2.\\ & f_x^{\\prime}(5, -3) = \\frac{5}{4}, \\ f_y^{\\prime}(5, -3) = \\frac{3}{4}, \\\\\n3.\\ & \\varphi_x^{\\prime}(0, 3) = 3 \\ln 2, \\ \\varphi_y^{\\prime}(0, 3) = 0.\... | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A function \\( f \\) satisfies the following conditions for all nonnegative integers \\( x \\) and \\( y \\):\n\n- \\( f(0, x) = f(x, 0) = x \\)\n- If \\( x \\geq y \\geq 0 \\), ... | math | {
"ground_truth": "101",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular hexagon with side length 6 and congruent arcs with radius 3 drawn with the center at each of the vertices, find the area of the region inside the hexagon but outs... | math | {
"ground_truth": "54\\sqrt{3} - 9\\pi",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The distance between line $l_1: x+y+1=0$ and line $l_2: 2x+2y+3=0$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{2}}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a circle of radius $4$ with center $O_1$ , a circle of radius $2$ with center $O_2$ that lies on the circumference of circle $O_1$ , and a circle of radius $1$ ... | math | {
"ground_truth": "\\sqrt{6}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The points $(2, 9), (12, 14)$, and $(4, m)$, where $m$ is an integer, are vertices of a triangle. What is the sum of the values of $m$ for which the area of the triangle is a min... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $\\sqrt{3600} + \\sqrt{1600}$.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\varphi(n)$ denote the count of natural numbers less than $n$ that are coprime to $n$, and let $\\sigma(n)$ denote the sum of the divisors of $n$. Determine all exponents $... | math | {
"ground_truth": "1, 3, 7, 15, 31",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = x^3 - ax - 1$, if $f(x)$ is monotonically decreasing on the interval $(-1, 1)$, determine the range of values for $a$.",
"role": "user"
}
] | math | {
"ground_truth": "a \\geqslant 3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest $n$ such that every subset of $\\{1, 2, 3, . . . , 2004 \\}$ with $n$ elements contains at least two elements that are relatively prime.",
"role": "us... | math | {
"ground_truth": "1003",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The area of an isosceles trapezoid, circumscribed around a circle, is $32 \\text{ cm}^2$; the acute angle of the trapezoid is $30^\\circ$. Determine the sides of the trapezoid.",... | math | {
"ground_truth": "8 \\, \\text{cm}; \\, 8-4\\sqrt{3} \\, \\text{cm}; \\, 8+4\\sqrt{3} \\, \\text{cm}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\frac{n}{m}=\\frac{3}{7}$, then the value of $\\frac{m+n}{m}$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{10}{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the final two numbers after 5 is added to each number and then each of the resulting numbers is tripled, given that the sum of two original numbers is $S$.",
"role... | math | {
"ground_truth": "3S + 30",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the sign and units digit of the product of all negative integers divisible by 3, strictly less than $198$ and greater than $0$.\nA) It is a negative number ending with a... | math | {
"ground_truth": "C) It is a negative number ending with a 6.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the plane rectangular coordinate system $(xoy)$, suppose $P$ is a moving point on the graph of the function $f(x)=e^{x} (x > 0)$. The tangent line $l$ at point $P$ intersects ... | math | {
"ground_truth": "\\frac{1}{2}(e + e^{-1})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Laurie loves multiplying numbers in her head. One day she decides to multiply two $2$ -digit numbers $x$ and $y$ such that $x\\leq y$ and the two numbers collectively have... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_1,a_2,\\dots,a_{2017}$ be reals satisfied $a_1=a_{2017}$ , $|a_i+a_{i+2}-2a_{i+1}|\\le 1$ for all $i=1,2,\\dots,2015$ . Find the maximum value of $\\max_{1\\le i<j\... | math | {
"ground_truth": "508032",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the average age of 8 people in Room X is 30 years, and the average age of 5 people in Room Y is 45 years, what is the average age of all 13 people combined?",
"role": "use... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find a two-digit number such that if it is divided by the product of its digits, the quotient is $16 / 3$, and if you subtract 9 from it, the difference is also a two-digit numbe... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many integers are between $(11.5)^3$ and $(11.7)^3$?",
"role": "user"
}
] | math | {
"ground_truth": "81",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many positive integers $n$ less than or equal to $30$ is $n!$ evenly divisible by $1 + 2 + \\cdots + n$?",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "You are given an unlimited supply of red, blue, and yellow cards to form a hand. Each card has a point value and your score is the sum of the point values of those cards. The poi... | math | {
"ground_truth": "168",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integer triples $(a, b, c)$ satisfying the equation $$ 5 a^2 + 9 b^2 = 13 c^2. $$",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0, 0)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the redesigned version of Mathland's licensing system, all automobile license plates still contain four symbols. The first is a vowel (A, E, I, O, U), the second a non-vowel (... | math | {
"ground_truth": "\\frac{1}{10,500}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "3n students are sitting in 3 rows of n. The students leave one at a time. All leaving orders are equally likely. Find the probability that there are never two rows where the numb... | math | {
"ground_truth": "\\frac{6n \\cdot (n!)^3}{(3n)!}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given sets $A=\\{x|2^{x} \\gt 4\\}$ and $B=\\{x\\in Z|\\log _{2}x \\lt 3\\}$, find the interval of the real numbers where $(\\complement _{R}A)\\cap B$ is defined.",
"role": ... | math | {
"ground_truth": "\\{1,2\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the number of positive integers less than \\(10!\\) which can be expressed as the sum of at most 4 (not necessarily distinct) factorials.",
"role": "user"
}
] | math | {
"ground_truth": "648",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the fraction $\\frac{7x - 13}{3x^2 + 2x - 8}$, express it as the sum of the fractions $\\frac{A}{x + 2}$ and $\\frac{B}{3x - 4}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{27}{10},-\\frac{11}{10}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that when $(a+b+c+d+e+1)^N$ is expanded and like terms are combined, the resulting expression contains exactly 2002 terms that include all five variables $a, b, c, d, e$, e... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle. Let $E$ be a point on the segment $BC$ such that $BE = 2EC$ . Let $F$ be the mid-point of $AC$ . Let $BF$ intersect $AE$ in $Q$ . Determin... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Andrew starts walking from his house toward his friend Ben's house. Concurrently, Ben begins to skate toward Andrew's house. They each travel at a constant speed, and Ben skates ... | math | {
"ground_truth": "C) 1760",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $3000 \\times (3000^{3000})$.",
"role": "user"
}
] | math | {
"ground_truth": "3000^{3001}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(10 points) A swimming pool sells student swim cards for 240 yuan each. The usage rules are as follows: no name registration, each card allows only one person per use, and each c... | math | {
"ground_truth": "80 \\text{ yuan}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $T = \\{3^0, 3^1, 3^2, \\ldots, 3^6\\}$. Consider all possible positive differences of pairs of elements in $T$. Let $M$ denote the sum of all these differences. Find $M$.",
... | math | {
"ground_truth": "5472",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the game of Avalon, there are $10$ players, $4$ of which are bad. A *quest* is a subset of those players. A quest fails if it contains at least one bad player. A randomly ... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find $89^{-1} \\pmod{90}$, as a residue modulo 90. (Give an answer between 0 and 89, inclusive.)",
"role": "user"
}
] | math | {
"ground_truth": "89",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Complex numbers $p,$ $q,$ $r$ form an equilateral triangle with side length 24 in the complex plane. If $|p + q + r| = 48,$ find $|pq + pr + qr|.$ These complex numbers have been... | math | {
"ground_truth": "768",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a fair 8-sided die is rolled until an odd number appears, determine the probability that the even numbers 2, 4, and 6 appear in strictly ascending order at least once befor... | math | {
"ground_truth": "\\frac{1}{512}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For $p=1, 2, \\cdots, 8$ let $S_p$ be the sum of the first $50$ terms of the arithmetic progression whose first term is $p$ and whose common difference is $2p-1$. Calculate $S_1+... | math | {
"ground_truth": "80200",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\\begin{cases} x=1+\\dfrac{\\sqrt{2}}{2}t \\\\ y=2+\\dfrac{\\sqrt{2}}{2}t \\end{cases}$ ($t$ is ... | math | {
"ground_truth": "2\\sqrt{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimum value of the expression\n\\[x^2 + 2xy + 3y^2 + 2xz + 3z^2\\]\nover all real numbers \\(x\\), \\(y\\), and \\(z\\).",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for $y$: $5^{3y} = \\sqrt{625}$. Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function f(x) = 3sin(x) + 4cos(x), if the line x = θ is an axis of symmetry for the curve y = f(x), then cos(2θ) + sin(θ)cos(θ) = $\\boxed{\\text{answer}}$.",
"role... | math | {
"ground_truth": "\\frac{19}{25}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ n>1$ and for $ 1 \\leq k \\leq n$ let $ p_k \\equal{} p_k(a_1, a_2, . . . , a_n)$ be the sum of the products of all possible combinations of k of the numbers $ a_1,a... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that ${(1-i)}^{2}={\\mid 1+i\\mid }^{2}z$ (where $i$ is the imaginary unit), find the sum of the real and imaginary parts of the complex number $z$.",
"role": "user"
... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ABC$ is an equilateral triangle and $l$ is a line such that the distances from $A, B,$ and $C$ to $l$ are $39, 35,$ and $13$ , respectively. Find the largest possibl... | math | {
"ground_truth": "58\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ and $b$ denote the solutions of $3x^{2}+4x-7=0$. What is the value of $(a-2)(b-2)$?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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