data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
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 $m$ and $n$ are positive integers such that $75m = n^{3}$. What is the minimum possible value of $m + n$?... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "56145439-639e-44ed-9398-319d502f7a95"
} |
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 polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0.$ Find the v... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "464f29a4-8faf-40f1-ae19-ebe3c61ddba6"
} |
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 circle of radius $1$ is surrounded by $4$ circles of radius $r$ as shown. The original answer is in the form $k+\\sq... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "46a72764-62f4-4d5e-95eb-2e2b9b98f1eb"
} |
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 $a$, $b$, and $c$ be digits with $a\\ne 0$. The three-digit integer $abc$ lies one third of the way from the squar... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8ef258d5-49f9-4f21-9adc-6980c0f43e68"
} |
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 product of the two $99$-digit numbers \n$303,030,303,...,030,303$ and $505,050,505,...,050,505$ \nhas thousa... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b46d0504-3575-43ab-908a-d9a2c8f9edcf"
} |
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 wheel shown is spun twice, and the randomly determined numbers opposite the pointer are recorded. The first number... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "65ee4a64-a6e0-4304-91b7-66a3110980e7"
} |
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\nRhombus $ABCD$, with side length $6$, is rolled to form a cylinder of volume $6$ by taping $\\overline{AB}$ to $\\over... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "066ed339-dbb9-4ae2-8f62-0547fa340c2d"
} |
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 set of 25 square blocks is arranged into a \\(5 \\times 5\\) square. Find the number of different combinations of 3 ... | MATH | {
"ground_truth": "600",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cdb33833-c8bb-4ab9-ba82-38c8b8debe3c"
} |
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\nCorners are sliced off a unit cube so that the six faces each become regular octagons. What is the total volume of the... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8c3f743a-f064-4338-9b51-6e417952b854"
} |
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 parallelogram bounded by the lines $y=ax+c$, $y=ax+d$, $y=bx+c$, and $y=bx+d$ has area $18$. The parallelogram bou... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ba0f1e0f-c4e5-487a-8bf6-fc0c2d69f1bc"
} |
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 first $2007$ positive integers are each written in base $3$. How many of these base-$3$ representations are palind... | MATH | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "62956e78-8ca6-4945-aea5-fa28b8fa8609"
} |
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\nTwo cards are dealt from a deck of four red cards labeled $A$, $B$, $C$, $D$ and four green cards labeled $A$, $B$, $C... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "85b1a874-9c20-476e-9cac-cdef73d9ca0c"
} |
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 each positive integer $n$, let $S(n)$ denote the sum of the digits of $n.$ Find the number of values of $n$ such t... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "10308e37-9489-475b-8441-d19a21897e2f"
} |
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 lemming sits at a corner of a square with side length $10$ meters. The lemming runs $6.2$ meters along a diagonal to... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bdc110e2-9a32-48e2-81a2-41a4e72e64f2"
} |
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 pyramid with a square base is cut by a plane that is parallel to its base and $2$ units from the base. The surface a... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "15108274-4d71-41bf-9d80-bf756fd49445"
} |
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\nSquare \\(ABCD\\) has area \\(36,\\) and \\(\\overline{AB}\\) is parallel to the \\(x\\)-axis. Vertices \\(A,\\) \\(B\... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0209e8b8-c475-4375-8a38-afd1d52e9818"
} |
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 area of the shaded pinwheel shown in the $5 \\times 5$ grid? Provide your answer as an integer.\n\nRemembe... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3d891953-ddcb-4f8b-a299-8f8b36cd0354"
} |
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 $n$ denote the smallest positive integer that is divisible by both $4$ and $9,$ and whose base-$10$ representation... | MATH | {
"ground_truth": "4944",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "21b7f648-0d7e-4f40-910c-891c5e972532"
} |
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 pairs of positive integers $(a,b)$ are there such that ${gcd}(a,b)=1$ and $\\frac{a}{b} + \\frac{14b}{9a}$ is... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eadb7e8b-79a3-4d05-aa25-11bb7494d134"
} |
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 pairs of positive integers $(a,b)$ are there such that $a$ and $b$ have no common factors greater than $1$ an... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c6c541e1-b8a0-41ab-8888-97c8533f8093"
} |
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\nCall a set of integers spacy if it contains no more than one out of any three consecutive integers. How many subsets o... | MATH | {
"ground_truth": "129",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "757d384a-5158-4867-b146-555e0aa92e82"
} |
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 bakery owner turns on his doughnut machine at $8:30$ AM. At $11:10$ AM the machine has completed one third of the da... | MATH | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "512a619e-e760-49a9-8b62-ff64545c15c1"
} |
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 $4\\times 4$ block of calendar dates is shown. First, the order of the numbers in the second and the fourth rows are... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "86335d8e-1589-40e4-9703-58a86cf0c046"
} |
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 $4\\times 4$ block of calendar dates is shown. First, the order of the numbers in the second and the fourth rows are... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5f414a9a-7aab-4417-a43a-bcd8205dec29"
} |
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 ten-letter code $BEST ~OF ~LUCK$ represents the ten digits $0-9$, in order. What $4$-digit number is represented b... | MATH | {
"ground_truth": "8671",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0133b1e2-751e-4267-90b7-2343e1b038d1"
} |
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 circle \\(O\\), points \\(C\\) and \\(D\\) are on the same side of diameter \\(\\overline{AB}\\), \\(\\angle AOC = ... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4a80e7e9-78ee-4d67-aa29-7aad9f3f5086"
} |
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 the figure, the outer equilateral triangle has area $16$, the inner equilateral triangle has area $1$, and the thre... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8d08a373-ee24-49bc-a19a-7a792877b525"
} |
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 a cube whose surface area is twice that of a cube with volume $1$? Provide your answer in the fo... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d9531521-9e20-4690-bfb1-26fb05e0a357"
} |
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\nOlder television screens have an aspect ratio of $4: 3$. That is, the ratio of the width to the height is $4: 3$. The ... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2746dfe2-0ef0-47a9-9462-cc5d81dca997"
} |
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 \\(A\\) and \\(B\\) are on a circle of radius \\(5\\) and \\(AB = 6\\). Point \\(C\\) is the midpoint of the mi... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "968fbdae-0a74-48fb-9b77-175e35757822"
} |
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\nEach of the sides of a square $S_1$ with area $16$ is bisected, and a smaller square $S_2$ is constructed using the bi... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0d431a23-caf1-4a64-be09-1ee2e023f7b1"
} |
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 \\(A\\) and \\(B\\) are on a circle of radius \\(5\\) and \\(AB=6\\). Point \\(C\\) is the midpoint of the mino... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "199636bb-aa84-48f0-b6a1-1a5717f8dd6b"
} |
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 cone-shaped mountain has its base on the ocean floor and has a height of $8000$ feet. The top $\\frac{1}{8}$ of the ... | MATH | {
"ground_truth": "4000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4b7e56d5-9668-4f04-b7a2-ddbb010a2c6d"
} |
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 ball is dropped from a height of $3$ meters. On its first bounce, it rises to a height of $2$ meters. It keeps falli... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9f5d32d3-d865-43a2-bf93-57aadeeeae7d"
} |
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 \\(A\\) and \\(B\\) lie on a circle centered at \\(O\\), and \\(\\angle AOB = 60^\\circ\\). A second circle is ... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "97a1f616-853a-4e32-8495-05effb63bfb0"
} |
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\nVertex \\(E\\) of equilateral \\(\\triangle{ABE}\\) is in the interior of unit square \\(ABCD\\). Let \\(R\\) be the r... | MATH | {
"ground_truth": "56",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "32360713-2b9d-4270-b78d-9d46f2cb34a2"
} |
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 area of the region defined by the inequality $|3x-18|+|2y+7|\\le3$?\n\nRemember to put your answer on its ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a99dcd1d-017c-4bdd-b6a1-e422febe35dd"
} |
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 $OAB$ has $O=(0,0)$, $B=(5,0)$, and $A$ in the first quadrant. In addition, $\\angle ABO=90^\\circ$ and $\\an... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "77772733-0730-497d-a2a0-bfac2e68d423"
} |
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 circle has a radius of \\(\\log_{10}{(a^2)}\\) and a circumference of \\(\\log_{10}{(b^4)}\\). Find the value of \\(... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ef9a2be9-93f9-4f9c-80bd-3faae00bbf15"
} |
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 right triangles have integer leg lengths $a$ and $b$ and a hypotenuse of length $b+1$, where $b<100$? Provide... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "82089f83-3b1a-4d1c-ba00-0f7571aef1fb"
} |
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 $k={2008}^{2}+{2}^{2008}$. What is the units digit of $k^2+2^k$?\n\nRemember to put your answer on its own line af... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8e006ff2-9c39-4c17-a3c4-e24a9a6b8196"
} |
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 Theresa's first $8$ basketball games, she scored $7, 4, 3, 6, 8, 3, 1$ and $5$ points. In her ninth game, she score... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "75977b17-ed07-4e1d-99fc-d2865fdf6281"
} |
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 rectangular floor measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. An artist paints a... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2931e3ec-3751-4e99-b449-cd892c188a07"
} |
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\nTwo fair coins are to be tossed once. For each head that results, one fair die is to be rolled. What is the probabilit... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6ab514f8-5bc0-4066-83b9-6aa335ea7541"
} |
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 numbers $\\log(a^3b^7)$, $\\log(a^5b^{12})$, and $\\log(a^8b^{15})$ are the first three terms of an arithmetic seq... | MATH | {
"ground_truth": "112",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8cff39d2-27f9-42c2-9667-330e2f325b53"
} |
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 shape is created by joining seven unit cubes, as shown. Find the ratio of the volume in cubic units to the surface a... | MATH | {
"ground_truth": "37",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a526a0ab-ecc4-407b-b239-4d0552ead1f7"
} |
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 has side length \\(6\\). Find the area of the region containing all points that are outside th... | MATH | {
"ground_truth": "63",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2281be2b-fa39-48a1-b892-3b54cbc3e158"
} |
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 $a_1,a_2,\\ldots$ be a sequence determined by the rule $a_n=\\frac{a_{n-1}}{2}$ if $a_{n-1}$ is even and $a_n=3a_{... | MATH | {
"ground_truth": "502",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b8d9d232-41d8-47c0-ad67-b0056fe08a51"
} |
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 $A$, $B$ and $C$ be three distinct points on the graph of $y=x^2$ such that line $AB$ is parallel to the $x$-axis ... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d5f71f81-ed73-41bd-a530-c8054cf24bf3"
} |
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\\), with sides of length \\(5\\), \\(6\\), and \\(7\\), has one vertex on the positive \\(x\\)-axis, o... | MATH | {
"ground_truth": "95",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "43ce626c-0d3c-4a34-83af-714de09381e5"
} |
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\nTwo circles that share the same center have radii $10$ meters and $20$ meters. An aardvark runs along the path shown, ... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eafaa17f-7fe6-4b95-bea3-e88f948f6464"
} |
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 \\(PQRS\\) lies in a plane with \\(PQ=RS=2\\) and \\(QR=SP=6\\). The rectangle is rotated \\(90^\\circ\\) cl... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5d94448d-d281-4e5b-b721-ca4a3a472bba"
} |
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 cylindrical tank with a radius of $4$ feet and a height of $9$ feet is lying on its side. The tank is filled with wa... | MATH | {
"ground_truth": "87",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "65da7224-5f07-48e3-9b01-3c9ea1dfb036"
} |
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 the expansion of\n\\[\\left(1 + x + x^2 + \\cdots + x^{27}\\right)\\left(1 + x + x^2 + \\cdots + x^{14}\\right)^2,\... | MATH | {
"ground_truth": "224",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1d1bd543-f693-4f20-af35-2edc2172e370"
} |
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 function \\(f\\) is defined by \\(f(z) = (4 + i) z^2 + \\alpha z + \\gamma\\) for all complex numbers \\(z\\), where... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "739be673-f088-4feb-8db4-bd2286ac8203"
} |
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\nEight points are spaced at intervals of one unit around a \\(2 \\times 2\\) square, as shown. Two of the \\(8\\) point... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c953274a-5853-42f5-9faa-abfd37e370bd"
} |
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\nTrapezoid $ABCD$ has bases $\\overline{AB}$ and $\\overline{CD}$ and diagonals intersecting at $K.$ Suppose that $AB =... | MATH | {
"ground_truth": "98",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "69e845d1-a319-4a27-a30a-386c8e94db74"
} |
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 faces of a cubical die are marked with the numbers $1$, $2$, $2$, $3$, $3$, and $4$. The faces of another die are ... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a44f7411-7a12-4e96-850f-1059302e499c"
} |
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\nMichael walks at the rate of $5$ feet per second on a long straight path. Trash pails are located every $200$ feet alo... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "dc112327-1d1d-4012-80c4-d92f5a16b2c2"
} |
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 permutation $(a_1,a_2,a_3,a_4,a_5)$ of $(1,2,3,4,5)$ is heavy-tailed if $a_1 + a_2 < a_4 + a_5$. Find the number of ... | MATH | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7e886369-158e-4e7a-b4e9-09292fbde208"
} |
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\nTwo circles of radius \\(1\\) are to be constructed as follows. The center of circle \\(A\\) is chosen uniformly and a... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2a7b6f4f-5daf-4ee4-b3ac-0730a4f468a4"
} |
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\nJacob uses the following procedure to write down a sequence of numbers. First, he chooses the first term to be \\(6\\)... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fb53e76b-ad17-484f-b13e-d9231aae6803"
} |
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\nThree red beads, two white beads, and one blue bead are placed in line in random order. What is the probability that n... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "642d29dd-f812-4d37-bc55-9832b16d7975"
} |
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 round table has radius \\(4\\). Six rectangular place mats are placed on the table. Each place mat has width \\(1\\)... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c47fb232-2671-4d72-96ad-fc4375628c8c"
} |
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 parking lot has $16$ spaces in a row. Twelve cars arrive, each of which requires one parking space, and their driver... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2b092e16-1e08-4401-91d6-e1a79262ff23"
} |
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 integer values of $n$ are both $\\frac{n}{3}$ and $3n$ three-digit whole numbers?\n\nRemember to... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0c0d0cb9-d069-4b7b-9a4a-4ad69a7c97cf"
} |
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\nTwo subsets of the set $S=\\lbrace a,b,c,d,e\\rbrace$ are to be chosen so that their union is $S$ and their intersecti... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e32220f0-43dc-4133-bfc4-ba7e69a3e790"
} |
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 solutions of the equation $z^4+4z^3i-6z^2-4zi-i=0$ are the vertices of a convex polygon in the complex plane. What... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b7c9c59d-cce0-46ca-bae2-2f7327313224"
} |
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 square \\(ABCE\\), \\(AF=2FE\\) and \\(CD=2DE\\). What is the ratio of the area of \\(\\triangle BFD\\) to the area... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6487d117-7012-40d5-bbb2-320bcd726ad7"
} |
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\nQuadrilateral $ABCD$ has $AB = BC = CD$, $m\\angle ABC = 70^\\circ$ and $m\\angle BCD = 170^\\circ$. If the answer is ... | MATH | {
"ground_truth": "85",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8e71bdb1-5665-4342-865d-1837855abe54"
} |
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 $A_0=(0,0)$. Distinct points $A_1,A_2,\\cdots$ lie on the $x$-axis, and distinct points $B_1,B_2,\\cdots$ lie on t... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c0c4d488-f5bb-454d-a0de-a3ab7a887c21"
} |
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\nTen tiles numbered $1$ through $10$ are turned face down. One tile is turned up at random, and a die is rolled. What i... | MATH | {
"ground_truth": "71",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eb289a43-ae09-4504-bb54-c57fab13b136"
} |
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 sequence \\((a_1,b_1), (a_2,b_2), (a_3,b_3), \\ldots\\) of points in the coordinate plane satisfies\n\\((a_{n + 1}, ... | MATH | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f156d7d6-6fd3-476e-b1d1-bbcad7c50299"
} |
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 $ABCD$ be a trapezoid with $AB||CD, AB=11, BC=5, CD=19,$ and $DA=7$. Bisectors of $\\angle A$ and $\\angle D$ meet... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8ab95cec-65ea-497c-ba51-0558c40788b0"
} |
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 shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same ... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "714fe217-f9a1-4e7a-85e6-c40aa3cda517"
} |
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 rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the ... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0b7ecc37-28ce-4b23-bd46-c3247a8480fb"
} |
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 rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the ... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "293f89ba-f8c8-4134-8152-c11d26b463d9"
} |
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 of the digits of the square of $111111111$? Provide your answer as a single integer.\n\nRemember to pu... | MATH | {
"ground_truth": "81",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "63f02dd4-cc67-4de6-8766-178cd3cf7a63"
} |
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\nKiana has two older twin brothers. The product of their three ages is $128$. What is the sum of their three ages?\n\nR... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "17d2db4c-1d1c-43fb-b59c-abfe6bbc1744"
} |
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\nBy inserting parentheses, it is possible to give the expression\n\\[2\\times3 + 4\\times5\\]\nseveral values. How many... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bd2f0a7c-bc7b-4060-ac98-09fbb7335e2f"
} |
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 carton contains milk that is \\(2\\%\\) fat, an amount that is \\(40\\%\\) less fat than the amount contained in a c... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2de50de6-d1a3-4f44-9854-5fd521c1d82a"
} |
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\nFour congruent rectangles are placed as shown. The area of the outer square is $4$ times that of the inner square. Wha... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5f49f482-8631-4779-93a9-b0c5b75e9b04"
} |
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\nSegment $BD$ and $AE$ intersect at $C$, as shown, $AB=BC=CD=CE$, and $\\angle A = \\frac{5}{2} \\angle B$. What is the... | MATH | {
"ground_truth": "525",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7c8d4e31-d666-4f18-8b34-f2e552f76394"
} |
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\nConstruct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "20418df8-4327-4655-9889-2a75ce80982d"
} |
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 flagpole is originally $5$ meters tall. A hurricane snaps the flagpole at a point $x$ meters above the ground so tha... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "93aa1622-17ee-4a06-a137-f32def860688"
} |
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 particular $12$-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a3c80582-a2c0-40c0-a056-c28f3c1d7b8a"
} |
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 a checkerboard composed of \\(64\\) unit squares, find the probability that a randomly chosen unit square does not ... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "29ecdcb8-b992-47fe-a87f-3e7e996fd1bc"
} |
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 $7$-digit palindromes (numbers that read the same backward as forward) can be formed using the digits $2$, $2... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e6f9178c-5e64-4465-9209-513859bd7847"
} |
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 figures $F_1$, $F_2$, $F_3$, and $F_4$ shown are the first in a sequence of figures. For $n\\ge3$, $F_n$ is constr... | MATH | {
"ground_truth": "761",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5b44d5a8-8c6b-4659-824e-a0d7dcda4bd2"
} |
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 Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pe... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b8e5c93b-7ab5-4359-911f-ada4923b8694"
} |
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\nDistinct points $A$, $B$, $C$, and $D$ lie on a line, with $AB=BC=CD=1$. Points $E$ and $F$ lie on a second line, para... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2d09a3c4-d24e-4df9-ada3-7698de687ef9"
} |
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 Monday, Millie puts a quart of seeds, $25\\%$ of which are millet, into a bird feeder. On each successive day she a... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "05d11cf3-c971-4918-8ae6-9b94304a55d9"
} |
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\nFive unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "78092e15-8b60-41b1-a6ae-9f5d6d7b95cc"
} |
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 what value of $n$ is $i + 2i^2 + 3i^3 + \\cdots + ni^n = 48 + 49i$? Find the value of $n$.\n\nRemember to put your... | MATH | {
"ground_truth": "97",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e6c453c8-d43f-4765-b397-9a792fcc3539"
} |
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 recipe that makes $5$ servings of hot chocolate requires $2$ squares of chocolate, $\\frac{1}{4}$ cup sugar, $1$ cup... | MATH | {
"ground_truth": "39",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "58fd88a6-84bc-42c7-8853-9ec6989e9d1d"
} |
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 $a$, $b$, $c$, and $d$ be real numbers with $|a-b|=2$, $|b-c|=3$, and $|c-d|=4$. Find the sum of all possible valu... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0941b6a5-3b1e-4b37-8c97-ac525d0d27d7"
} |
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 \\(A\\) and \\(C\\) lie on a circle centered at \\(O\\), each of \\(\\overline{BA}\\) and \\(\\overline{BC}\\) ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "43c7be7e-1897-43aa-a374-cf1d30782120"
} |
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\nTrapezoid \\(ABCD\\) has \\(AD \\parallel BC\\), \\(BD = 1\\), \\(\\angle DBA = 23^\\circ\\), and \\(\\angle BDC = 46^... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8d1580d2-3fdf-4773-98b5-a9a8d43d4206"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.