messages listlengths 1 1 | label stringlengths 1 23 | metadata dict | data_source stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $n$ be the largest integer that is the product of exactly 3 distinct prime numbers: $x$, $y$, and $10x+y$, where $... | 12 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "41143612-091d-4038-b9bf-20f2429834bc"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知函数 $f:\\{1,2, \\cdots, 10\\} \\rightarrow\\{1,2, \\cdots, 5\\}$ ，且对一切 $k=1,2, \\cdots, 9$ ，有 \n$|f(k+1)-f(k)| \\geq... | 288 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ae2232eb-d68e-48a0-be30-e9fc4cf3e101"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n求最大的正整数 n，使得存在 n 个正整数 x_1<x_2<\\cdots<x_n，满足x_1+x_1x_2+\\cdots+x_1x_2\\cdots x_n=2021.\n\nRemember to put your answer ... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "8e4be8fd-053a-474c-96cf-1bd5a1e617b7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the smallest possible value of $x + y$ where $x, y \\ge 1$ and $x$ and $y$ are integers that satisfy $x^2 - 29y^2... | 11621 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0f81be76-1260-473b-a32c-0ce34389bca5"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知 f(x) 和 g(x) 是两个二次项系数均为 1 的二次函数. 若 g(6)=35，\\df{f(-1)}{g(-1)}=\\df{f(1)}{g(1)}=\\df{21}{20}，则 f(6)=__________.\n\nRe... | 35 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "fd12e2cc-4986-41aa-9a83-fe6f2133b36f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知 $\\theta$ 为 $g(x)=x^{4}-7 x^{2}+1$ 的一个零点, $h(x)$ 为一个有理系数的二次函数, 且满足 $h\\left(\\theta^{2}-1\\right)=0$. 请给出 $h(x)=0$ ... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c27fc3bc-2ac8-46c6-ac88-a82cf44a95b8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n过椭圆 $\\frac{x^{2}}{3}+\\frac{y^{2}}{2}=1$ 的右焦点 $F$ 作两条垂直的弦 $A B 、 C D$. 设 $A B 、 C D$ 的中点分别为 $M 、 N$.\\n（1）证明：直线 $M N$... | 9 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5d94e5a5-1f99-453d-89f7-2553944840b9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $C_1$ and $C_2$ be circles defined by:\n\\[\n(x - 10)^2 + y^2 = 36\n\\]\nand\n\\[\n(x + 15)^2 + y^2 = 81\n\\]\nres... | 20 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "509d8230-6701-49da-917d-d38e85ac24a8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTim has a working analog 12-hour clock with two hands that run continuously. He also has a clock that runs at half the... | 33 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f7258c7e-b1dc-44c6-9199-b1c8aa29207d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $N$ be a positive integer whose digits add up to $23$. What is the greatest possible product the digits of $N$ can... | 4374 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0216cb0f-727f-4686-a54d-461375baed0b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe only prime factors of an integer $n$ are 2 and 3. If the sum of the divisors of $n$ (including itself) is $1815$, ... | 648 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "44d3f03a-cfac-4a3f-9bc0-c94c2b418d92"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n12. What is the sum of all possible $\\left(\\begin{array}{l}i \\\\ j\\end{array}\\right)$ subject to the restrictions... | 27633 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5eafc7da-a423-46c9-b000-c203bed5d6c8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf $a,$ $b$ and $c$ are three (not necessarily different) numbers chosen randomly and with replacement from the set $\... | 184 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f309d3b4-d528-4e48-ab8c-086296ad3bef"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n请给出正整数 $a_{1}, a_{2}, \\cdots, a_{18}$, 使得 $a_{1}=1$, $a_{2}=2, a_{18}=2019$, 且对任意的 $k(3 \\leqslant k \\leqslant 18)$,... | 5304 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bd22fd43-a329-4f56-a1d2-d67cba8e0d24"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of solutions to\n\\[\\sin x = \\left( \\frac{1}{2} \\right)^x\\]on the interval $(0,100 \\pi).$\n\nRem... | 100 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d7f7d173-5369-4b5e-b6cb-237339818838"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn equilateral triangle is inscribed in the ellipse whose equation is $x^2+4y^2=4$. One vertex of the triangle is $(0,... | 937 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "489e00dc-2830-4513-93c3-9f0fff9701b9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAmong the coordinates $(x,y)$ where $1 \\leq x,y \\leq 101$, choose some points such that there do not exist $4$ point... | 201 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "501e9dff-444b-4e17-9795-fbf5656775c4"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe equation $ax^3 + bx^2 + cx + d = 0$ has three distinct solutions. How many distinct solutions does the following e... | 2 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "14a383a2-3ea1-4509-984d-0e45e847599b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor how many integer values of $n$ between 1 and 474 inclusive does the decimal representation of $\\frac{n}{475}$ ter... | 24 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ac424338-7797-4942-80fe-626956e72264"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nElfs and trolls are seated at a round table, with a total of 60 creatures. Trolls always lie, and all elfs always spea... | 20 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bee76889-d61e-479d-ae24-415335e21e1b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$A_1A_2A_3A_4$ is a cyclic quadrilateral inscribed in circle $\\Omega$, with side lengths $A_1A_2 = 28$, $A_2A_3 =12\\... | 784 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "68a1bced-c716-40bc-a5c8-225c2ef08e96"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTwenty five of King Arthur's knights are seated at their customary round table. Three of them are chosen - all choices... | 57 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "66c94f39-ab2e-4ec5-aa4a-5d3a43fed0f8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe same eight people sit in a certain church pew every week, but not always in the same order. Every week, each perso... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "6a8affd6-2186-419b-b019-8b04f493cbbb"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the 3-digit positive integer that has the most divisors.\n\nRemember to put your answer on its own line after \"A... | 840 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "69753844-8563-4c85-987b-298c5ec806f8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA particle moving on a straight line starts from rest and attains a velocity $2$ after traversing a distance $2$. If t... | 2 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "669f9c57-667b-4a46-9336-b6a40b0e4b81"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJohann has $64$ fair coins. He flips all the coins. Any coin that lands on tails is tossed again. Coins that land on t... | 56 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bfde3cfe-d9f1-48f2-9531-0ce4402703a9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n数列 $\\left\\{a_{n}\\right\\}$ 满足: $a_{1}=\\frac{5}{2}, a_{n+1}=a_{n}^{2}-2$，求 $\\left[a_{2023}\\right]$ 除以 7 的余数。\n\nR... | 2 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "12bc4ede-ce4a-4b52-8c24-01da62067e9a"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAt a certain university, the division of mathematical sciences consists of the departments of mathematics, statistics,... | 88 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b26fede9-3db5-4316-8d61-ab31eb445a4c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the sum (in base $10$) of all the natural numbers less than $64$ which have exactly three ones in their base $... | 630 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e81974b9-1456-4621-b149-e2ed44001561"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFunctions $f$ and $g$ are defined so that $f(1) = 4$, $g(1) = 9$, and for each integer $n \\ge 1$, $f(n+1) = 2f(n) + 3... | 1999 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "65109fc5-4d4c-4476-a937-f4e99b20333e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvery card in a deck has a picture of one shape - circle, square, or triangle, which is painted in one of the three co... | 117 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "aa0db087-d606-4f82-84dd-8dd4dfe21bd4"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the largest prime number that divides the quantity $0! + (1!) \\times 1 + (2!) \\times 2 + (3!) \\times 3 + \\cdo... | 47 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "73a1d8c4-7a69-4dfa-a957-7095c013350a"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n若 \\(\\triangle A B C\\) 的三边 \\(a, b, c\\) 满足 \\(a^{2}+b^{2}+3c^{2}=7\\)，则 \\(\\triangle A B C\\) 的面积的最大值是 \\(\\frac{\... | 11 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "11be317d-26b5-4bc5-88d7-3c7f1f4873f6"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor how many positive integers $x$ less than $4032$ is $x^2 - 20$ divisible by $16$ and $x^2 - 16$ divisible by $20$?\... | 403 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e7f922f2-b9c9-4503-842a-5d07c84a9ac1"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor any positive integer $x_{}$, let $S(x)$ be the sum of the digits of $x_{}$, and let $T(x)$ be $|S(x+2)-S(x)|.$ Fo... | 223 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "60b35757-54cf-4ba5-bcd8-ab1e02f9b22b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTo transmit a positive integer less than 1000, the Networked Number Node offers two options.\n\nOption 1. Pay $\\$$d t... | 503 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "18000c51-953d-4d19-826c-3658fe51f6b4"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJerry buys a bottle of 150 pills. Using a standard 12 hour clock, he sees that the clock reads exactly 12 when he take... | 1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a56c68fa-4894-4225-bd43-f267ef582ea0"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n若正整数 $a, b, c$ 满足 $2017 \\geqslant 10 a \\geqslant 100 b \\geqslant 1000 c$ ，则数组 $(a, b, c)$ 的个数为\n\n\nRemember to put... | 574 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "23ca632c-99bf-4724-a819-be40b4710aa9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPoints $E$ and $F$ lie inside rectangle $ABCD$ with $AE=DE=BF=CF=EF$. If $AB=11$ and $BC=8$, find the area of the quad... | 32 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "6c763e41-0bc0-4b1d-b47a-787f94e4b3b0"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTriangle $ABC$ has $AB=25$, $AC=29$, and $BC=36$. Additionally, $\\Omega$ and $\\omega$ are the circumcircle and incir... | 252 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "98c102da-3245-4fcb-994b-b0ca721dee75"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the greatest number of balls with a radius of $\\frac{1}{2}$ that can be placed within a rectangular box of si... | 106 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ea8fda8c-5835-40c4-b372-d0739d6dce7f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $H$ be a convex, equilateral heptagon whose angles measure (in degrees) $168^\\circ$, $108^\\circ$, $108^\\circ$, ... | 132 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "17baf355-1bb3-4bce-a40f-f9107ffde6e6"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\mathcal{R}$ be the region consisting of the set of points in the coordinate plane that satisfy both $|8 - x| + ... | 365 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "8dd930d1-7077-47d1-9b69-013ad927bb64"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n记 $I=\\lim\\limits_{x \\rightarrow+\\infty}\\left(\\sin \\frac{1}{x^{2}}+\\cos \\frac{1}{x}\\right)^{2 x^{2}}$, 则 $[10... | 27 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "77a7971f-e9ce-46b7-ab95-9ed90bfbd12d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSeven people of seven different ages are attending a meeting. The seven people leave the meeting one at a time in rand... | 25 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "fe49ee44-dd12-466d-b336-60c244a56a96"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet there be a tiger, William, at the origin. William leaps $ 1$ unit in a random direction, then leaps $2$ units in a... | 1240 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3ba35d9f-e54f-489c-88cd-ae5d8c83dd62"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n在正六棱锥中，侧面与底面的夹角均为 \\df{\\pi}{3}，则其外接球与内切球的半径的比值为__________.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\nRemember to... | 19 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "df123b2c-373f-4ed2-8955-e016bb9804ba"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a_n$ denote the remainder when $(n+1)^3$ is divided by $n^3$; in particular, $a_1=0$. Compute the remainder when ... | 693 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c37a0c3f-9467-4cfe-9896-28ae88ae991e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe graph of $y^2 + 2xy + 40|x|= 400$ partitions the plane into several regions. What is the area of the bounded regi... | 800 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ad47333b-ac0e-4717-8099-d8addcb34ec7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nOn the number line, point $A$ is located at 0, point $B$ is located at 4, and point $C$ is located at 6. [asy]\ndefaul... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c9539398-39c5-4f43-83c9-c2b03371dc41"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the volume of the region in three-dimensional space defined by the inequalities \\( |x|+|y|+|z|\\le1 \\) and \... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1563e5c0-11f5-4a9e-ad42-a695611fe1e9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $a$ and $b$ are nonzero integers such that two of the roots of\n\\[x^3 + ax^2 + bx + 9a\\]coincide, and a... | 1344 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "23024e6a-b5cd-4017-98ad-3c7d1c062aed"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设 \\(f(x)=\\mathrm{e}^{a x}(a>0)\\)，过点 \\(P(a, 0)\\) 且平行于 \\(y\\) 轴的直线与曲线 \\(C: y=f(x)\\) 的交点为 \\(Q\\)，曲线 \\(C\\) 过点 \... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5475bfe8-afde-4c16-8bd6-686b722b4130"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe sum of the proper divisors of 18 is 21. What is the sum of the proper divisors of 198?\n\nRemember to put your ans... | 270 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "41047e19-55ca-41a1-b4d2-234471f4037f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn $\\triangle ABC$, $AC=BC$, and $m\\angle BAC=40^\\circ$. What is the number of degrees in angle $x$? [asy]\nsize(80... | 140 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1aa9bd52-f8f0-427b-ab73-d0093f5d974f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPoints $P$ and $Q$ are midpoints of two sides of the square. What fraction of the interior of the square is shaded? Ex... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "43bbdd00-2eae-428a-b123-b87a781578de"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设 $a_{1}, a_{2}, a_{3}, a_{4}$ 是 4 个有理数, 使得\n$$\n\\left\\{a_{i} a_{j} \\mid 1 \\leqslant i<j \\leqslant 4\\right\\}=\\... | 0 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9ea217aa-d6f7-4cb0-b758-386691e8f66b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn a magic square , the sum of the three entries in any row, column, or diagonal is the same value. The figure shows f... | 200 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2f91d555-a6c8-40d7-a89d-bc8fd4c16afd"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSix distinct positive integers are randomly chosen between $1$ and $2006$, inclusive. What is the probability that som... | 1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3ca1293b-9398-4039-8670-477cd8c02ded"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知正方体 $A B C D-A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime}$ 的棱长为 1, 点 $M, N$ 分别为线段 $A B^{\\prime}, A C$ 上的动点, 点 $T... | 8 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "76c03a72-598b-4e70-bee7-5b17c75b3759"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nChord $[AD]$ is perpendicular to the diameter $[BC]$ of a circle. Let $E$ and $F$ be the midpoints of the arcs $AC$ an... | 91 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "92298c16-5151-46d5-87b3-ffa5ac4024a8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a,$ $b,$ $c,$ $d,$ and $e$ be the distinct roots of the equation $x^5 + 7x^4 - 2 = 0.$ Find\n\\begin{align*}\n&\... | 0 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "264df53b-3d5a-4815-9f8d-d6125b9fe231"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRectangle $ABCD$ measures $70$ by $40$. Eighteen points (including $A$ and $C$) are marked on the diagonal $AC$, divid... | 600 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e938a84f-eaa7-4a63-9f25-ee6788fe2c04"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $x^{10} + x + 1 = 0$ and $x^{100} = a_0 + a_1x + \\ldots + a_9x^9$. Find $a_5$.\n\nRemember to put your a... | 252 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e0120ddd-71cd-4d1f-9045-cd921543e571"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of integer values of $k$ in the closed interval $[-500,500]$ for which the equation $\\log(kx)=2\\log(... | 501 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a208ad4e-651b-4b75-a619-31bf1314bbed"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ABC$ be a triangle with angle $A< \\angle C<90^\\circ < \\angle B$. Consider the bisectors of the external angles... | 24 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "58d522d4-1c7d-459d-87b4-118772034926"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n有理数加群 $(\\mathbb{Q},+)$ ，记所有分母不超过的 $10$ 的有理数构成的子集为 $G$ ，其对应的陪集 $G \\mathbb{Z}$ 记为 $\\bar{G}$ ，则 $\\mathbb{Q} / \\mathb... | 2520 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2dac427e-7b7a-45ae-94f3-f9538df45c7f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $n = 10$. There are $n$ points in the plane, no three of them collinear. Each day, Tom erases one of the points, u... | 12 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "4f08e628-1371-4d6f-98d0-e2f8f6243cdd"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn regular hexagon \\(ABCDEF\\), points \\(W\\), \\(X\\), \\(Y\\), and \\(Z\\) are chosen on sides \\(\\overline{BC}\\... | 38 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a074fda4-f898-4859-a6fe-670c383bbbb9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知数列 \\{a_n\\} 中，a_1=1, a_2=2, a_{n+2}-3a_{n+1}+2a_n=1. 设 T_n 为数列 \\left\\{\\df{8}{a_n}\\right\\} 的前 n 项和，则 [T_{2023}]... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "26e8e45b-6aa4-401e-b00a-7c95be69bb92"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTriangle \\(ABC\\) is equilateral with \\(AB=1\\). Points \\(E\\) and \\(G\\) are on \\(\\overline{AC}\\) and points \... | 34 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e42acb3f-9aff-42fc-953e-c392e13d1c89"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\vartriangle ABC$ be a triangle. Let $Q$ be a point in the interior of $\\vartriangle ABC$, and let $X, Y,Z$ den... | 11 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ad867f5b-ac0a-4615-9e9f-2bba5d2785f1"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many ordered triples of integers \\((x, y, z)\\) satisfy \n\\[36x^2 + 100y^2 + 225z^2 = 12600?\\]\n\nRemember to p... | 48 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "eea9575b-a5ee-4ec4-a882-f25d5a360379"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn trapezoid $ABCD$ with $\\overline{BC}\\parallel\\overline{AD}$, let $BC = 1000$ and $AD = 2008$. Let $\\angle A = 3... | 504 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "6715d037-4e21-4974-84ae-d531b29093f6"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is a heads up coin on every integer of the number line. Lucky is initially standing on the zero point of the num... | 6098 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f7dc6592-1c73-432c-b86c-1a1f928e9449"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe streets of a city are represented on a map as straight lines that divide a square into 25 smaller squares of side ... | 60 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7283fee2-aab1-4525-9f81-12a2efad8d65"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n在 \\triangle ABC 中，AB=6,BC=4，边 AC 上的中线长为 \\sqrt{10}，则 \\sin^6\\df{A}{2}+\\cos^6\\df{A}{2} 的值为__________.原始的答案是\\frac{m... | 467 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "085fec33-eed7-4a21-b91b-4afa52ae1e8f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设 $F_{1}, F_{2}$ 为椭圆 $\\Omega$ 的焦点, 在 $\\Omega$ 上取一点 $P$ (异于长轴端点), 记 $O$ 为 $\\Delta P F_{1} F_{2}$ 的外心, 若 $\\overright... | 10 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d17e3f19-0123-4d74-bf4a-b66e286c2725"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设集合 $\\left\\{\\left.\\frac{3}{a}+b \\right\\rvert\\, 1 \\leqslant a \\leqslant b \\leqslant 2\\right\\}$ 中的最大元素与最小元素分... | 10 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b8583c38-62e8-44da-a83e-5d5252b517e2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlice and Bob play a game involving a circle whose circumference is divided by $12$ equally-spaced points. The points ... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e6fd3ad6-c38f-49f4-81df-eb1edb26f847"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of real solutions of the equation\n\\[\\frac{4x}{x^2 + x + 3} + \\frac{5x}{x^2 - 5x + 3} = -\\frac{3}{... | 2 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9482db15-dbe2-4a0b-97a6-d64d48650d10"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSelect two distinct diagonals at random from a regular octagon. What is the probability that the two diagonals interse... | 26 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "01ef8cfd-8882-4ccd-bf29-25b367649b5a"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDetermine the remainder when\n$$\\sum_{i=0}^{2015} \\left\\lfloor \\frac{2^i}{25} \\right\\rfloor$$\nis divided by 100... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "08ead0d6-e56d-48e9-ace5-4db5f3df165e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the greatest common divisor of $654321$ and $543210$?\n\nRemember to put your answer on its own line after \"A... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bfc9a52b-5d7a-4c8a-9bb7-8f88d7f9608e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDetermine the largest prime which divides both $2^{24} - 1$ and $2^{16} - 1$.\n\nRemember to put your answer on its ow... | 17 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "887adca6-5d52-46a8-a939-b5c2da641892"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere are $100$ countries participating in an olympiad. Suppose $n$ is a positive integer such that each of the $100$ ... | 20 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e620659c-2465-49c2-85df-14e3c82f8c64"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBefore starting to paint, Bill had $130$ ounces of blue paint, $164$ ounces of red paint, and $188$ ounces of white pa... | 114 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "6e11d37b-4f37-4852-a455-f40214457f04"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA subset $B$ of \\( \\{1, 2, \\dots, 2017\\} \\) is said to have property \\( T \\) if any three elements of \\( B \\)... | 1009 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5658a635-4352-40de-9885-a08362c1dc77"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA 2 by 2003 rectangle consists of unit squares as shown below. The middle unit square of each row is shaded. If a re... | 3004 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "17c571f7-1966-4be1-aa59-029eebf93a69"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $x$ and $y$ are real numbers satisfying \\begin{align*}\n4y - 4x^2 &= 1 \\\\\n4x - 4y^2 &= 1.\n\\end{ali... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f854f853-b113-4c70-ac97-3c2048e839f2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute $\\gcd(6^210^2,15^4)$.\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
... | 225 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a0fc8c1a-c9ce-449c-8662-579d23f9cefe"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n正三棱柱 $A B C-A_{1} B_{1} C_{1}$ 的 9 条棱长都相等, $P$ 是 $C C_{1}$ 的中点, 二面角 $B-A_{1} P-B_{1} = \\alpha$, 则 $\\sin \\alpha = \\... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b492604a-4192-4527-b2ef-60afac444e01"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven that in a convex quadrilateral $ABCD$, $\\angle BAC=30^\\circ, \\angle ACD=40^\\circ,\\angle ADB=50^\\circ,\\ang... | 290 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c722f090-192a-4999-b44e-1cc52f74fc74"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere are exactly $N$ distinct rational numbers $k$ such that $|k|<200$ and \\[5x^2+kx+12=0\\] has at least one intege... | 78 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9e5b41b8-4de3-40ff-99f5-3270ba55f541"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe roots of $x^3 + Px^2 + Qx - 19 = 0$ are each one more than the roots of $x^3 - Ax^2 + Bx - C = 0.$ If $A,$ $B,$ $... | 18 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a69cc58c-636a-4758-b484-84393e747fd7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe five solutions to the equation\\[(z-1)(z^2+2z+4)(z^2+4z+6)=0\\] may be written in the form $x_k+y_ki$ for $1\\le k... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a4022163-9370-41c3-9d4a-df46c1293efe"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet \\(ABC\\) be a triangle such that \\(|AB| = 8\\) and \\(|AC| = 2|BC|\\). What is the largest value of the altitude... | 19 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "55cb3e32-f6c0-479e-93bf-c91b83a83e16"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSequences $a_n$ and $b_n$ are defined for all positive integers $n$ such that $a_1 = 5$, $b_1 = 7$, \n\n$$a_{n+1} = \... | 24 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e791025c-0c68-449d-9414-838f15783b5d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf \\(10^{2y} = 25\\), then find the value of \\(10^{-y}\\). The original answer is in \\(\\frac{k}{m}\\) format, plea... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "18400481-838a-495e-88fe-58c7ad273527"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe area of the region bound by the equations $y = 2\\cos(4x)$, $y = \\sin(2x) + 10$, $x=0$, and $x = 5\\pi$ can be ex... | 50 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "26c96eea-e1c3-4dc6-ab7c-1f7c05e167aa"
}
} | math_dapo |
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