data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|
math_dapo-Qwen-instruct | [
{
"content": "The sum of the two $5$-digit numbers $AMC10$ and $AMC12$ is $123422$. What is $A+M+C$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1b30ef91-405e-4582-b0e7-d19469e5ddab"
} |
math_dapo-Qwen-instruct | [
{
"content": "Cassandra sets her watch to the correct time at noon. At the actual time of $1:00$ PM, she notices that her watch reads $12:57$ and $36$ seconds. Assuming that her watch loses time at a constant rate, calculate the total time discrepancy in seconds between her watch and the actual time when her watch first reads $10:00$ PM. Please provide your answer as an integer representing the number of seconds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1500",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "42a9503c-8437-4469-9695-f156e2e16158"
} |
math_dapo-Qwen-instruct | [
{
"content": "Sally has five red cards numbered $1$ through $5$ and four blue cards numbered $3$ through $6$. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "380b2b8d-178c-46d1-b593-0cfdc80d8af9"
} |
math_dapo-Qwen-instruct | [
{
"content": "What is the largest integer that is a divisor of \\((n+1)(n+3)(n+5)(n+7)(n+9)\\) for all positive even integers \\(n\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5b24f76c-9912-499c-a4fd-13cf7eca485c"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $n$ be the largest integer that is the product of exactly $3$ distinct prime numbers $d$, $e$, and $10d+e$, where $d$ and $e$ are single digits. Find the sum of the digits of $n$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a4781f8a-749f-427b-ba75-b691e4b40e8b"
} |
math_dapo-Qwen-instruct | [
{
"content": "Given that $3^8\\cdot5^2=a^b,$ where both $a$ and $b$ are positive integers, find the smallest possible value for $a+b$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "407",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b4939968-8782-4e54-bd81-d8f987d8fd2b"
} |
math_dapo-Qwen-instruct | [
{
"content": "Points \\(K, L, M,\\) and \\(N\\) lie in the plane of the square \\(ABCD\\) such that \\(AKB\\), \\(BLC\\), \\(CMD\\), and \\(DNA\\) are equilateral triangles. If \\(ABCD\\) has an area of \\(16\\), find the area of \\(KLMN\\). The original answer is in the form \\(k + m\\sqrt{3}\\). Please give the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "940e9238-fb71-4049-a50a-555db4ca577c"
} |
math_dapo-Qwen-instruct | [
{
"content": "In this addition problem, each letter stands for a different digit.\n$$\\begin{array}{cccc}&T&W&O\\\\+&T&W&O\\\\\\hline F&O&U&R\\end{array}$$\nIf $T = 7$ and the letter $O$ represents an even number, what is the only possible value for $W$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "45560eca-ea9c-4bc5-b352-78347d9ca30f"
} |
math_dapo-Qwen-instruct | [
{
"content": "A regular octagon \\(ABCDEFGH\\) has an area of one square unit. What is the area of the rectangle \\(ABEF\\)? Provide your answer in the form \\(\\frac{k}{m}\\) as a simplified fraction, and give the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0c1eb3f5-f179-48a0-b86c-3d02193bde16"
} |
math_dapo-Qwen-instruct | [
{
"content": "A point \\(P\\) is chosen at random in the interior of equilateral triangle \\(ABC\\). What is the probability that \\(\\triangle ABP\\) has a greater area than each of \\(\\triangle ACP\\) and \\(\\triangle BCP\\)? Express your answer in the form \\(\\frac{k}{m}\\), where \\(k\\) and \\(m\\) are coprime positive integers. Find the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d4038288-d240-4acd-8fe2-ead63ec79390"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three semicircles of radius \\(1\\) are constructed on diameter \\(\\overline{AB}\\) of a semicircle of radius \\(2\\). The centers of the small semicircles divide \\(\\overline{AB}\\) into four line segments of equal length, as shown. Find the area of the shaded region that lies within the large semicircle but outside the smaller semicircles. The original answer is in the form \\(\\frac{k}{m}\\pi - \\frac{\\sqrt{n}}{p}\\). Please calculate the value of \\(k + m + n + p\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8acae241-65ad-4cb9-8254-bd1d316d170a"
} |
math_dapo-Qwen-instruct | [
{
"content": "An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies $75\\%$ of the volume of the frozen ice cream. What is the ratio of the cone's height to its radius? Provide your answer in the form $x:1$, where $x$ is a positive integer. Please find the value of $x$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "97eafbac-972a-4ae3-a233-65d491ae7555"
} |
math_dapo-Qwen-instruct | [
{
"content": "Square \\(ABCD\\) has sides of length \\(4\\), and \\(M\\) is the midpoint of \\(\\overline{CD}\\). A circle with radius \\(2\\) and center \\(M\\) intersects a circle with radius \\(4\\) and center \\(A\\) at points \\(P\\) and \\(D\\). Find the distance from \\(P\\) to \\(\\overline{AD}\\). The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "69c8b66f-66ce-4ccb-8d6f-df30ba6d322b"
} |
math_dapo-Qwen-instruct | [
{
"content": "If \\(\\log (xy^3) = 1\\) and \\(\\log (x^2y) = 1\\), find the value of \\(\\log (xy)\\). The answer should be in the form \\(\\frac{k}{m}\\), where \\(\\frac{k}{m}\\) is in its simplest form. Please provide the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0fef2ea2-38fe-44d1-ba38-32f6a2f15835"
} |
math_dapo-Qwen-instruct | [
{
"content": "What is the largest integer that is a divisor of $(n+1)(n+3)(n+5)(n+7)(n+9)$ for all positive even integers $n$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7325212e-6dad-4570-b240-573da46cbc98"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $n$ be a $5$-digit number, and let $q$ and $r$ be the quotient and the remainder, respectively, when $n$ is divided by $100$. Find the number of values of $n$ for which $q+r$ is divisible by $11$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8181",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6374b0bd-8674-4beb-9bf9-513dc680f49f"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three semicircles of radius $1$ are constructed on diameter $\\overline{AB}$ of a semicircle of radius $2$. The centers of the small semicircles divide $\\overline{AB}$ into four line segments of equal length, as shown. Find the area of the shaded region that lies within the large semicircle but outside the smaller semicircles. The original answer is in the form \\(\\frac{k}{m}\\pi - \\frac{\\sqrt{n}}{p}\\). Please calculate the value of k + m + n + p. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a1e8378a-8c59-4d44-a3e0-f420698e785b"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let \\(S\\) be the set of permutations of the sequence \\(1,2,3,4,5\\) for which the first term is not \\(1\\). A permutation is chosen randomly from \\(S\\). The probability that the second term is \\(2\\), in lowest terms, is \\(\\frac{a}{b}\\). Please find the value of \\(a + b\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9f929886-dc17-45ec-8617-9273a84d4a56"
} |
math_dapo-Qwen-instruct | [
{
"content": "In rectangle \\(ABCD\\), \\(AB=5\\) and \\(BC=3\\). Points \\(F\\) and \\(G\\) are on \\(\\overline{CD}\\) so that \\(DF=1\\) and \\(GC=2\\). Lines \\(AF\\) and \\(BG\\) intersect at \\(E\\). The area of \\(\\triangle AEB\\) is in the form \\(\\frac{k}{m}\\). Please give the value of \\(k+m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "042cdd87-5c37-48c4-80b8-395718ba7b78"
} |
math_dapo-Qwen-instruct | [
{
"content": "How many $15$-letter arrangements of $5$ A's, $5$ B's, and $5$ C's have no A's in the first $5$ letters, no B's in the next $5$ letters, and no C's in the last $5$ letters? Provide your answer as a sum of binomial coefficients in the form \\(\\sum\\limits_{k=0}^{n}\\binom{m}{k}^{p}\\), and then calculate the value of m + n + p. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6a0b6613-91b1-4d66-9c1b-947e9f60e55c"
} |
math_dapo-Qwen-instruct | [
{
"content": "A bag contains two red beads and two green beads. You reach into the bag and pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are red after three such replacements? Express your answer in the form of \\frac{k}{m}, where k and m are coprime integers. Please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "41",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "31fe02ce-4583-4ef4-8cc1-ac4e3fb2a86e"
} |
math_dapo-Qwen-instruct | [
{
"content": "The area of trapezoid $ABCD$ is $164\\ \\text{cm}^2$. The altitude is $8\\ \\text{cm}$, $AB$ is $10\\ \\text{cm}$, and $CD$ is $17\\ \\text{cm}$. What is the length of $BC$, in centimeters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9550de71-d9db-4c1c-88dd-94d6dbd6e5f2"
} |
math_dapo-Qwen-instruct | [
{
"content": "In rectangle $ABCD$, we have $AB=8$, $BC=9$, $H$ is on $BC$ with $BH=6$, $E$ is on $AD$ with $DE=4$, line $EC$ intersects line $AH$ at $G$, and $F$ is on line $AD$ with $GF \\perp AF$. Find the length of $GF$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "41af28ad-da17-4322-8518-66c861b12957"
} |
math_dapo-Qwen-instruct | [
{
"content": "A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure, we have $3$ rows of small congruent equilateral triangles, with $5$ small triangles in the base row. How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of $2003$ small equilateral triangles? Provide your answer as an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1507509",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d63f9c3c-aacc-45e8-98d9-5d03d8415a90"
} |
math_dapo-Qwen-instruct | [
{
"content": "A regular octagon \\(ABCDEFGH\\) has an area of one square unit. What is the area of the rectangle \\(ABEF\\)? The answer is in the form \\(\\frac{k}{m}\\), where the fraction is in its simplest form. Please find the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "29a5554f-6e1e-40af-91c4-37e5a0ebe18f"
} |
math_dapo-Qwen-instruct | [
{
"content": "How many perfect squares are divisors of the product $1! \\cdot 2! \\cdot 3! \\cdot \\cdots \\cdot 9!$? Provide your answer as an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "672",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9fc56d63-8083-43c8-b3b8-330911f88f1c"
} |
math_dapo-Qwen-instruct | [
{
"content": "The first four terms in an arithmetic sequence are \\(x+y\\), \\(x-y\\), \\(xy\\), and \\(\\frac{x}{y}\\), in that order. What is the fifth term? The original answer is in the form \\(\\frac{k}{m}\\). Please find the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "163",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "83ed6a2f-2377-4ba3-90b6-939116b996f5"
} |
math_dapo-Qwen-instruct | [
{
"content": "Positive integers $a,b,$ and $c$ are chosen so that $a<b<c$, and the system of equations\n\n$2x + y = 2003 \\quad$ and $\\quad y = |x-a| + |x-b| + |x-c|$\n\nhas exactly one solution. What is the minimum value of $c$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1002",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "10a70248-4ecc-4e21-a723-a29dbda348d1"
} |
math_dapo-Qwen-instruct | [
{
"content": "How many distinct four-digit numbers are divisible by $3$ and have $23$ as their last two digits? Provide your answer as an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "14c2b2d7-dd75-435e-b270-b89b851f0f85"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $f(x)= \\sqrt{ax^2+bx}$. Find the number of real values of $a$ for which there is at least one positive value of $b$ such that the domain of $f$ and the range of $f$ are the same set. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "09ee86de-88c5-465f-98cb-4fee23c0b577"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three points are chosen randomly and independently on a circle. Find the probability that all three pairwise distances between the points are less than the radius of the circle. The probability is expressed in the form \\(\\frac{k}{m}\\). Please calculate the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a6545fbc-30c4-4dff-9536-b7abc15ef302"
} |
math_dapo-Qwen-instruct | [
{
"content": "How many two-digit positive integers have at least one $7$ as a digit? Fill in the blank with the correct number of such integers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "59af433a-da48-4247-8258-a63a85756777"
} |
math_dapo-Qwen-instruct | [
{
"content": "What is the value of \\(x\\) if \\(|x-1|=|x-2|\\)? Provide your answer in the form of \\(\\frac{k}{m}\\), where \\(k\\) and \\(m\\) are integers. Calculate the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "675b66ee-7762-4ef7-a480-954033781bdf"
} |
math_dapo-Qwen-instruct | [
{
"content": "Bertha has $6$ daughters and no sons. Some of her daughters have $6$ daughters, and the rest have none. Bertha has a total of $30$ daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no daughters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "26",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c3c19e5d-5e2d-4eab-a519-98380292b3e3"
} |
math_dapo-Qwen-instruct | [
{
"content": "An integer \\(x\\), with \\(10 \\leq x \\leq 99\\), is to be chosen. If all choices are equally likely, what is the probability that at least one digit of \\(x\\) is a \\(7\\)? Express your answer as a fraction in simplest form \\(\\frac{a}{b}\\), and provide the value of \\(a + b\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e0fb8963-d8b5-4d53-849d-838123e491c2"
} |
math_dapo-Qwen-instruct | [
{
"content": "A set of three points is randomly chosen from the grid shown. Each three-point set has the same probability of being chosen. What is the probability that the points lie on the same straight line? Express your answer in the form \\(\\frac{k}{m}\\), where \\(k\\) and \\(m\\) are integers, and find the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "903075ef-d81e-48da-9690-1ec062cd18fb"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $U=2\\cdot 2004^{2005}$, $V=2004^{2005}$, $W=2003\\cdot 2004^{2004}$, $X=2\\cdot 2004^{2004}$, $Y=2004^{2004}$ and $Z=2004^{2003}$. Find the largest value among the expressions $U-V$, $V-W$, $W-X$, $X-Y$, and $Y-Z$. The expression $U-V$ can be written in the form $k\\cdot 2004^{m}$. Please find the value of $k + m$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2006",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c198bd00-41fe-4c14-b1eb-622ed7303082"
} |
math_dapo-Qwen-instruct | [
{
"content": "A grocer stacks oranges in a pyramid-like stack whose rectangular base is $5$ oranges by $8$ oranges. Each orange above the first level rests in a pocket formed by four oranges below. The stack is completed by a single row of oranges. How many oranges are in the stack? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9394417a-8c06-4a15-b503-4729ddeecc9b"
} |
math_dapo-Qwen-instruct | [
{
"content": "A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players $A$, $B$, and $C$ start with $15$, $14$, and $13$ tokens, respectively. How many rounds will there be in the game? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "37",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3c35575d-cc11-4996-88a3-6670ce443391"
} |
math_dapo-Qwen-instruct | [
{
"content": "Minneapolis-St. Paul International Airport is $8$ miles southwest of downtown St. Paul and $10$ miles southeast of downtown Minneapolis. Find the number of miles between downtown St. Paul and downtown Minneapolis that is closest to the actual distance. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5e7ef867-26bd-4a07-a67b-1186c33c60f3"
} |
math_dapo-Qwen-instruct | [
{
"content": "Find the number of two-digit positive integers whose digits total $7$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8fc763b9-40c4-466c-8ee9-6ba61073865c"
} |
math_dapo-Qwen-instruct | [
{
"content": "A square has sides of length $10$, and a circle centered at one of its vertices has radius $10$. Find the area of the union of the regions enclosed by the square and the circle. The original answer is in the form of k + m\\pi, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "175",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9481546e-cdf3-4e0c-946e-2131112f208a"
} |
math_dapo-Qwen-instruct | [
{
"content": "Coin $A$ is flipped three times and coin $B$ is flipped four times. What is the probability that the number of heads obtained from flipping the two fair coins is the same? Express your answer as a fraction in simplest form, in the format \\(\\frac{k}{m}\\). Please give the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "163",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "df693bec-b124-42f4-9b6b-9f5ec245c946"
} |
math_dapo-Qwen-instruct | [
{
"content": "The sum of $49$ consecutive integers is $7^5$. What is their median? Provide your answer in the form of $7^x$, where $x$ is an integer. Please give the value of $x$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3e8d57ec-dc4a-49d1-b654-52a893896a49"
} |
math_dapo-Qwen-instruct | [
{
"content": "A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by $25\\%$ without altering the volume, by what percent must the height be decreased? Provide your answer as a percentage. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0f6da490-5edb-4888-8082-9493f0d37def"
} |
math_dapo-Qwen-instruct | [
{
"content": "Two eight-sided dice each have faces numbered $1$ through $8$. When the dice are rolled, each face has an equal probability of appearing on the top. Find the probability that the product of the two top numbers is greater than their sum. The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ced70077-bc87-448c-a5de-0c2c22bfdf51"
} |
math_dapo-Qwen-instruct | [
{
"content": "The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is $20$ cents. If she had one more quarter, the average value would be $21$ cents. How many dimes does she have in her purse? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "40a34d83-7cb3-48bc-b66b-1beee0af7ee5"
} |
math_dapo-Qwen-instruct | [
{
"content": "All the students in an algebra class took a $100$-point test. Five students scored $100$, each student scored at least $60$, and the mean score was $76$. What is the smallest possible number of students in the class? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fdc61bd5-53aa-42fb-957a-a8ccb400e847"
} |
math_dapo-Qwen-instruct | [
{
"content": "The numbers $-2, 4, 6, 9$ and $12$ are rearranged according to these rules: \n \n$1$. The largest isn't first, but it is in one of the first three places. \n$2$. The smallest isn't last, but it is in one of the last three places. \n$3$. The median isn't first or last. \n \nIf the average of the first and last numbers is $x$, what is the value of $10x$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "65",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7fb5fbd2-1982-4474-bb06-0e79e0bc6e87"
} |
math_dapo-Qwen-instruct | [
{
"content": "Henry's Hamburger Haven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties and any collection of condiments. How many different kinds of hamburgers can be ordered? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "768",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cb1b81c2-2ede-4d37-8b6a-ab7778345e52"
} |
math_dapo-Qwen-instruct | [
{
"content": "Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $24$ hours. If she is using it constantly, the battery will last for only $3$ hours. Since the last recharge, her phone has been on $9$ hours, and during that time she has used it for $60$ minutes. If she doesn’t use it any more but leaves the phone on, how many more hours will the battery last? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "86e5d626-dda0-45be-86a5-a93080a78d33"
} |
math_dapo-Qwen-instruct | [
{
"content": "In the United States, coins have the following thicknesses: penny, $1.55 \\, \\text{mm}$; nickel, $1.95 \\, \\text{mm}$; dime, $1.35 \\, \\text{mm}$; quarter, $1.75 \\, \\text{mm}$. If a stack of these coins is exactly $14 \\, \\text{mm}$ high, how many coins are in the stack? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e1043097-382c-4e3c-bbdf-beb8edd2fc2d"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $S$ be the set of points $(a,b)$ in the coordinate plane, where each of $a$ and $b$ may be $-1$, $0$, or $1$. Find the number of distinct lines that pass through at least two members of $S$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2f8bde4a-0249-48d6-8d5a-2e70cbc1f4ae"
} |
math_dapo-Qwen-instruct | [
{
"content": "If $f(x) = ax+b$ and $f^{-1}(x) = bx+a$ with $a$ and $b$ real, find the value of $a+b$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "46e78d90-e93f-4e61-ab93-2d32dada10be"
} |
math_dapo-Qwen-instruct | [
{
"content": "A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only \\(\\frac{1}{3}\\) of the marbles in the bag are blue. Then yellow marbles are added to the bag until only \\(\\frac{1}{5}\\) of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue? Express your answer in the form \\(\\frac{k}{m}\\) where the fraction is simplified, and find the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2abc31f7-4d3f-4466-87ca-79e78f78dd49"
} |
math_dapo-Qwen-instruct | [
{
"content": "In $\\triangle ABC$, $AB=13$, $AC=5$, and $BC=12$. Points $M$ and $N$ lie on $AC$ and $BC$, respectively, with $CM=CN=4$. Points $J$ and $K$ are on $AB$ so that $MJ$ and $NK$ are perpendicular to $AB$. Find the area of pentagon $CMJKN$. The original answer is in \\frac{m}{n} format, please give the value of m + n. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "253",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "315e8320-4bc4-4583-9747-9108cd805e18"
} |
math_dapo-Qwen-instruct | [
{
"content": "Given that $-4\\leq x\\leq-2$ and $2\\leq y\\leq4$, find the largest possible value of $\\frac{x+y}{x}$. The original answer is in \\frac{k}{m} format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9050aab1-78ac-42ed-9d97-0afaced81e87"
} |
math_dapo-Qwen-instruct | [
{
"content": "Patty has $20$ coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels, she would have $70$ cents more. How much are her coins worth in dollars? Provide your answer as a numerical value, and then multiply it by 100 to give your final answer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "115",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5c62714f-68e7-4391-b160-09c2d2d1d581"
} |
math_dapo-Qwen-instruct | [
{
"content": "Thirteen black and six white hexagonal tiles were used to create the figure below. If a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?\nProvide your answer as an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5ff88832-9dbd-45b7-ba40-aae2901ad763"
} |
math_dapo-Qwen-instruct | [
{
"content": "The $5\\times 5$ grid shown contains a collection of squares with sizes from $1\\times 1$ to $5\\times 5$. How many of these squares contain the black center square? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0b67c967-7493-4452-a349-3eebe54dbb5f"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three circles of radius \\(1\\) are externally tangent to each other and internally tangent to a larger circle. The radius of the large circle can be expressed in the form \\(\\frac{k + 2\\sqrt{m}}{n}\\), where the expression is in its simplest form. Find the value of \\(k + m + n\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "81f699df-1c84-45c7-8bf4-9432f88ef0d2"
} |
math_dapo-Qwen-instruct | [
{
"content": "The set of all real numbers \\(x\\) for which \n\\[\n\\log_{2004}(\\log_{2003}(\\log_{2002}(\\log_{2001}{x})))\n\\] \nis defined is \\(\\{x\\mid x > c\\}\\). The original answer is in the form \\(a^b\\). What is the value of \\(a+b\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "4003",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d63632dd-340d-4e33-b61e-4f346010a6a2"
} |
math_dapo-Qwen-instruct | [
{
"content": "In the right triangle $\\triangle ACE$, we have $AC=12$, $CE=16$, and $EA=20$. Points $B$, $D$, and $F$ are located on $AC$, $CE$, and $EA$, respectively, so that $AB=3$, $CD=4$, and $EF=5$. Find the ratio of the area of $\\triangle DBF$ to that of $\\triangle ACE$. The answer is in the form \\frac{k}{m}, please provide the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c39cd847-fee8-4466-a91a-9352ffa0b7b1"
} |
math_dapo-Qwen-instruct | [
{
"content": "Square $ABCD$ has side length $2$. A semicircle with diameter $\\overline{AB}$ is constructed inside the square, and the tangent to the semicircle from $C$ intersects side $\\overline{AD}$ at $E$. Find the length of $\\overline{CE}$. The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1c6bbbd0-e11d-4cff-96f4-8774e8d2a87e"
} |
math_dapo-Qwen-instruct | [
{
"content": "A white cylindrical silo has a diameter of $30$ feet and a height of $80$ feet. A red stripe with a horizontal width of $3$ feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "240",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b30d1a5d-f5f8-40d2-a601-a8bccdebacef"
} |
math_dapo-Qwen-instruct | [
{
"content": "In the sequence $2001$, $2002$, $2003$, $\\cdots$, each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is $2001 + 2002 - 2003 = 2000$. What is the $2004^{th}$ term in this sequence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d6a10521-1464-4f52-9eec-370752c04421"
} |
math_dapo-Qwen-instruct | [
{
"content": "In \\(\\triangle ABC\\), points \\(D\\) and \\(E\\) lie on \\(BC\\) and \\(AC\\), respectively. If \\(AD\\) and \\(BE\\) intersect at \\(T\\) so that \\(\\frac{AT}{DT}=3\\) and \\(\\frac{BT}{ET}=4\\), find the value of \\(\\frac{CD}{BD}\\). The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "83f7b0e5-f064-4543-9724-d53388c08395"
} |
math_dapo-Qwen-instruct | [
{
"content": "Select numbers $a$ and $b$ between $0$ and $1$ independently and at random, and let $c$ be their sum. Let $A, B$ and $C$ be the results when $a, b$ and $c$, respectively, are rounded to the nearest integer. Find the probability that $A + B = C$. The original answer is in \\frac{k}{m} format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8323190a-244d-4c3e-a0c3-bd75728f87aa"
} |
math_dapo-Qwen-instruct | [
{
"content": "Each face of a cube is painted either red or blue, each with probability $1/2$. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color? The original answer is in \\frac{k}{m} format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "00fc2a3c-09b6-4f8c-9b5d-8782a4d24ca5"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $1; 4; 7; \\cdots$ and $9; 16; 23; \\cdots$ be two arithmetic progressions. The set $S$ is the union of the first $2004$ terms of each sequence. How many distinct numbers are in $S$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3722",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8d0f7ee7-dbf1-4e3f-b54b-82c2b0e77863"
} |
math_dapo-Qwen-instruct | [
{
"content": "Square $ABCD$ has side length $2$. A semicircle with diameter $\\overline{AB}$ is constructed inside the square, and the tangent to the semicircle from $C$ intersects side $\\overline{AD}$ at $E$. What is the length of $\\overline{CE}$? The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "22ed5c2f-0b12-493e-aca5-17ddf7e6bbd0"
} |
math_dapo-Qwen-instruct | [
{
"content": "A triangle with sides of \\(5, 12,\\) and \\(13\\) has both an inscribed and a circumscribed circle. What is the distance between the centers of those circles? Provide your answer in the form \\(\\frac{\\sqrt{k}}{m}\\), and calculate the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "67",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a4c8aec2-3ce9-4c81-894a-1cc871542a18"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three mutually tangent spheres of radius \\(1\\) rest on a horizontal plane. A sphere of radius \\(2\\) rests on them. Find the distance from the plane to the top of the larger sphere, expressed in the form \\(3 + \\frac{\\sqrt{x}}{y}\\). Please find the value of \\(x + y\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "53ef16dd-7b1e-48a4-ad88-dd5a0101eefe"
} |
math_dapo-Qwen-instruct | [
{
"content": "The square \n$$ \n\\begin{array}{|c|c|c|}\\hline50&b&c\\\\\\hline d&e&f\\\\\\hline g&h&2\\\\\\hline\\end{array}\n$$ \nis a multiplicative magic square. That is, the product of the numbers in each row, column, and diagonal is the same. If all the entries are positive integers, find the sum of the possible values of $g$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "32d56da6-b580-4848-b7ab-e4d0aa17201c"
} |
math_dapo-Qwen-instruct | [
{
"content": "Each face of a cube is painted either red or blue, each with probability \\( \\frac{1}{2} \\). The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color? The original answer is in the form \\(\\frac{k}{m}\\), where the fraction is in simplest form. Please provide the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "94e89a5a-5f28-425d-b298-82348e2ee9db"
} |
math_dapo-Qwen-instruct | [
{
"content": "The polynomial $x^3 - 2004 x^2 + mx + n$ has integer coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the sum of the other two. If the number of possible values of $n$ is denoted as $k$, find the value of $k$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "250500",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "29a384bd-d8d4-40cc-a25f-cb6ab843cac7"
} |
math_dapo-Qwen-instruct | [
{
"content": "In triangle \\(ABC\\) we have \\(AB=7\\), \\(AC=8\\), \\(BC=9\\). Point \\(D\\) is on the circumscribed circle of the triangle so that \\(AD\\) bisects angle \\(BAC\\). The value of \\(\\frac{AD}{CD}\\) is given in the form \\(\\frac{k}{m}\\), where k and m are coprime integers. Please find the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3ebb9433-2da2-430f-a966-186456d58fe6"
} |
math_dapo-Qwen-instruct | [
{
"content": "In \\(\\triangle ABC\\), \\(AB = BC\\), and \\(\\overline{BD}\\) is an altitude. Point \\(E\\) is on the extension of \\(\\overline{AC}\\) such that \\(BE = 10\\). The values of \\(\\tan \\angle CBE\\), \\(\\tan \\angle DBE\\), and \\(\\tan \\angle ABE\\) form a geometric progression, and the values of \\(\\cot \\angle DBE,\\) \\(\\cot \\angle CBE,\\) \\(\\cot \\angle DBC\\) form an arithmetic progression. The area of \\(\\triangle ABC\\) is in the form \\(\\frac{m}{n}\\). Please calculate the value of \\(m+n\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b41cbcb9-a488-488b-bec7-84b0ff1fc55e"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three mutually tangent spheres of radius \\(1\\) rest on a horizontal plane. A sphere of radius \\(2\\) rests on them. Find the distance from the plane to the top of the larger sphere. The answer is in the form \\(k + \\frac{\\sqrt{m}}{n}\\), where \\(n\\) is not divisible by any square number other than \\(1\\). Please calculate the value of \\(k + m + n\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "75",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cdbc6217-2a5a-4618-9556-bf50662f6fcf"
} |
math_dapo-Qwen-instruct | [
{
"content": "A circle of radius \\(1\\) is internally tangent to two circles of radius \\(2\\) at points \\(A\\) and \\(B\\), where \\(AB\\) is a diameter of the smaller circle. Find the area of the region, shaded in the picture, that is outside the smaller circle and inside each of the two larger circles. The original answer is in the form \\(\\frac{k}{m} \\pi - n\\sqrt{p}\\), where \\(\\frac{k}{m}\\) and \\(n\\sqrt{p}\\) are in their simplest forms. Please provide the value of k + m + n + p. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ca31f6e3-c4c4-464b-a70b-2cabc0e7e1db"
} |
math_dapo-Qwen-instruct | [
{
"content": "Given that $2^{2004}$ is a $604$-digit number whose first digit is $1$, find how many elements of the set $S = \\{2^0,2^1,2^2,\\cdots ,2^{2003}\\}$ have a first digit of $4$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "195",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4a23d90a-9953-44b6-bce7-7516d5a27e68"
} |
math_dapo-Qwen-instruct | [
{
"content": "Two \\(4 \\times 4\\) squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. Find the area of the shaded region created by removing the circle from the squares. The answer is in the form \\(k - m\\pi\\), please provide the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5f3f31a6-fb27-44b3-beb1-bde8b4c220f4"
} |
math_dapo-Qwen-instruct | [
{
"content": "Let $f(t) = \\frac{t}{1-t}$, where $t \\neq 1$. If $y = f(x)$, express $x$ in terms of $y$. The original answer is in the form \\frac{m}{n}, please give the value of m + n. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9c4285ed-b401-4947-9522-643f455df96c"
} |
math_dapo-Qwen-instruct | [
{
"content": "Brianna is using part of the money she earned on her weekend job to buy several equally-priced CDs. She used one fifth of her money to buy one third of the CDs. What fraction of her money will she have left after she buys all the CDs? Provide your answer in the form of \\(\\frac{k}{m}\\), where the fraction is in simplest form, and find the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "83a53890-2fd2-4d9d-bf64-30a0a6232f0e"
} |
math_dapo-Qwen-instruct | [
{
"content": "A store normally sells windows at $100$ each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a7e1c852-ca8b-4b32-b0ee-b04500b0b333"
} |
math_dapo-Qwen-instruct | [
{
"content": "In $\\triangle ABC$, we have $AC=BC=7$ and $AB=2$. Suppose that $D$ is a point on line $AB$ such that $B$ lies between $A$ and $D$ and $CD=8$. What is the length of $BD$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9729b267-36cc-4a2f-81a5-515ef883d81e"
} |
math_dapo-Qwen-instruct | [
{
"content": "Suppose $d$ is a digit. For how many values of $d$ is $2.00d5 > 2.005$? Provide your answer as an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8a4191c6-0dd7-4bae-a12b-83a00cb6a94b"
} |
math_dapo-Qwen-instruct | [
{
"content": "A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. Find the ratio of the area of the smallest circle to the area of the largest square. The original answer is in \\(\\frac{k\\pi}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7ee6e437-cbe8-4364-9238-c6c35d25ec2d"
} |
math_dapo-Qwen-instruct | [
{
"content": "Square $EFGH$ is inside the square $ABCD$ so that each side of $EFGH$ can be extended to pass through a vertex of $ABCD$. Square $ABCD$ has side length $\\sqrt{50}$ and $BE = 1$. What is the area of the inner square $EFGH$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "584ed9e5-fc2a-4cbf-b013-d1b67b490886"
} |
math_dapo-Qwen-instruct | [
{
"content": "What is the area enclosed by the graph of $|3x|+|4y|=12$? Provide your answer as an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9460cf40-44c3-4e78-b9ca-29c34e8459b4"
} |
math_dapo-Qwen-instruct | [
{
"content": "Three tiles are marked \\(X\\) and two other tiles are marked \\(O\\). The five tiles are randomly arranged in a row. Find the probability that the arrangement reads \\(XOXOX\\). The original answer is in \\(\\frac{k}{m}\\) format, please give the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4025891f-8420-4bc9-930c-14d1153bf4d4"
} |
math_dapo-Qwen-instruct | [
{
"content": "One fair die has faces \\(1, 1, 2, 2, 3, 3\\) and another has faces \\(4, 4, 5, 5, 6, 6\\). The dice are rolled and the numbers on the top faces are added. Find the probability that the sum will be odd. The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "53c837fe-b6b9-4533-a6c7-9448c50b2f2e"
} |
math_dapo-Qwen-instruct | [
{
"content": "There are two values of \\(a\\) for which the equation \\(4x^2 + ax + 8x + 9 = 0\\) has only one solution for \\(x\\). The discriminant of the quadratic equation can be expressed in the form \\(m + n = 0\\). Please find the sum of these values of \\(m\\) and \\(n\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c5eca0f6-4491-4aee-91b9-5737656762c5"
} |
math_dapo-Qwen-instruct | [
{
"content": "On a certain math exam, $10\\%$ of the students got $70$ points, $25\\%$ got $80$ points, $20\\%$ got $85$ points, $15\\%$ got $90$ points, and the rest got $95$ points. Find the difference between the mean and the median score on this exam. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c7be822f-8c24-4c3e-ad96-57f02a14c38e"
} |
math_dapo-Qwen-instruct | [
{
"content": "An envelope contains eight bills: $2$ ones, $2$ fives, $2$ tens, and $2$ twenties. Two bills are drawn at random without replacement. What is the probability that their sum is $＄$ $20$ or more? Express your answer in the form of a simplified fraction \\(\\frac{k}{m}\\), and provide the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fb53d9fc-dd62-43de-8f41-75881286da7d"
} |
math_dapo-Qwen-instruct | [
{
"content": "The sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up $90.00 and adds $6%$ sales tax, then subtracts $20%$ from this total. Jill rings up $90.00$, subtracts $20%$ of the price, then adds $6%$ of the discounted price for sales tax. What is the value of Jack's total minus Jill's total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "030c203d-9fa5-4621-ad8d-7a9d1167dd7f"
} |
math_dapo-Qwen-instruct | [
{
"content": "Twelve fair dice are rolled. Find the probability that the product of the numbers on the top faces is prime. If the probability can be expressed as \\(\\left(\\frac{1}{6}\\right)^n\\), what is the value of \\(n\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c26bcd9f-956f-4699-84f5-3df1a8b88855"
} |
math_dapo-Qwen-instruct | [
{
"content": "A line passes through $A\\ (1,1)$ and $B\\ (100,1000)$. How many other points with integer coordinates are on the line and strictly between $A$ and $B$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cdd50847-7504-4c70-9bce-0be0f1673f58"
} |
math_dapo-Qwen-instruct | [
{
"content": "How many numbers between $1$ and $2005$ are integer multiples of $3$ or $4$ but not $12$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "835",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ffe65ccb-afc4-4540-9312-29503d94639b"
} |
math_dapo-Qwen-instruct | [
{
"content": "Suppose that \\(4^{x_1}=5\\), \\(5^{x_2}=6\\), \\(6^{x_3}=7\\), ... , \\(127^{x_{124}}=128\\). The original answer is in the form \\(\\frac{k}{m}\\), where \\(k\\) and \\(m\\) are integers. Please find the value of \\(k + m\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6499f882-782e-4d09-a71a-673cf3684892"
} |
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