data_source stringclasses 8 values | prompt listlengths 2 2 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $\\lfloor x\\rfloor$ represent the greatest integer which is less than or equ... | math | {
"ground_truth": "4.25",
"style": "rule"
} | {
"index": 200,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A cube has edges of length $n$, where $n$ is an integer. Three faces, meeting at ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 201,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Thurka bought some stuffed goats and some toy helicopters. She paid a total of $\... | math | {
"ground_truth": "7,4",
"style": "rule"
} | {
"index": 202,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real values of $x$ for which $(x+8)^{4}=(2 x+16)^{2}$.",
"role"... | math | {
"ground_truth": "-6,-8,-10",
"style": "rule"
} | {
"index": 203,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $f(x)=2 x+1$ and $g(f(x))=4 x^{2}+1$, determine an expression for $g(x)$.",
... | math | {
"ground_truth": "$g(x)=x^2-2x+2$",
"style": "rule"
} | {
"index": 204,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A geometric sequence has 20 terms.\n\nThe sum of its first two terms is 40 .\n\nT... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 205,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real values of $x$ for which $3^{(x-1)} 9^{\\frac{3}{2 x^{2}}}=27$.... | math | {
"ground_truth": "$1$,$\\frac{3 + \\sqrt{21}}{2}$,$\\frac{3 - \\sqrt{21}}{2}$",
"style": "rule"
} | {
"index": 206,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all points $(x, y)$ where the two curves $y=\\log _{10}\\left(x^{4}\\ri... | math | {
"ground_truth": "$(1,0),(\\frac{1}{100},-8),(100,8)$",
"style": "rule"
} | {
"index": 207,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Oi-Lam tosses three fair coins and removes all of the coins that come up heads. G... | math | {
"ground_truth": "$\\frac{27}{64}$",
"style": "rule"
} | {
"index": 208,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Ross starts with an angle of measure $8^{\\circ}$ and doubles it 10 times until h... | math | {
"ground_truth": "$4^{\\circ}$",
"style": "rule"
} | {
"index": 209,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For each positive integer $n$, let $T(n)$ be the number of triangles with integer... | math | {
"ground_truth": "2,4,3",
"style": "rule"
} | {
"index": 210,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For each positive integer $n$, let $T(n)$ be the number of triangles with integer... | math | {
"ground_truth": "309",
"style": "rule"
} | {
"index": 211,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose $0^{\\circ}<x<90^{\\circ}$ and $2 \\sin ^{2} x+\\cos ^{2} x=\\frac{25}{16... | math | {
"ground_truth": "$\\frac{3}{4}$",
"style": "rule"
} | {
"index": 212,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The first term of a sequence is 2007. Each term, starting with the second, is the... | math | {
"ground_truth": "153",
"style": "rule"
} | {
"index": 213,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Sequence A has $n$th term $n^{2}-10 n+70$.\n\n(The first three terms of sequence ... | math | {
"ground_truth": "5,15",
"style": "rule"
} | {
"index": 214,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all values of $x$ for which $2+\\sqrt{x-2}=x-2$.",
"role": "user"
... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 215,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all values of $x$ for which $(\\sqrt{x})^{\\log _{10} x}=100$.",
"r... | math | {
"ground_truth": "$100,\\frac{1}{100}$",
"style": "rule"
} | {
"index": 216,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that $f(x)=x^{2}+(2 n-1) x+\\left(n^{2}-22\\right)$ for some integer $n$.... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"index": 217,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A bag contains 3 red marbles and 6 blue marbles. Akshan removes one marble at a t... | math | {
"ground_truth": "$\\frac{10}{21}$",
"style": "rule"
} | {
"index": 218,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine the number of quadruples of positive integers $(a, b, c, d)$ with $a<b<... | math | {
"ground_truth": "417",
"style": "rule"
} | {
"index": 219,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that $\\triangle A B C$ is right-angled at $B$ and has $A B=n(n+1)$ and $... | math | {
"ground_truth": "222",
"style": "rule"
} | {
"index": 220,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real values of $x$ for which\n\n$$\n\\sqrt{\\log _{2} x \\cdot \\lo... | math | {
"ground_truth": "$[\\frac{1}{2}, 8]$",
"style": "rule"
} | {
"index": 221,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For every real number $x$, define $\\lfloor x\\rfloor$ to be equal to the greates... | math | {
"ground_truth": "590",
"style": "rule"
} | {
"index": 222,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For every real number $x$, define $\\lfloor x\\rfloor$ to be equal to the greates... | math | {
"ground_truth": "$p(x)=\\frac{(x-1)(x-2)}{6}$",
"style": "rule"
} | {
"index": 223,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "One of the faces of a rectangular prism has area $27 \\mathrm{~cm}^{2}$. Another ... | math | {
"ground_truth": "$166$",
"style": "rule"
} | {
"index": 224,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The equations $y=a(x-2)(x+4)$ and $y=2(x-h)^{2}+k$ represent the same parabola. W... | math | {
"ground_truth": "$2,-1,-18$",
"style": "rule"
} | {
"index": 225,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In an arithmetic sequence with 5 terms, the sum of the squares of the first 3 ter... | math | {
"ground_truth": "-5,7",
"style": "rule"
} | {
"index": 226,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Dan was born in a year between 1300 and 1400. Steve was born in a year between 14... | math | {
"ground_truth": "1469",
"style": "rule"
} | {
"index": 227,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all values of $k$ for which the points $A(1,2), B(11,2)$ and $C(k, 6)$ ... | math | {
"ground_truth": "1,3,9,11",
"style": "rule"
} | {
"index": 228,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $\\cos \\theta=\\tan \\theta$, determine all possible values of $\\sin \\theta... | math | {
"ground_truth": "$\\frac{-1+\\sqrt{5}}{2}$",
"style": "rule"
} | {
"index": 229,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Linh is driving at $60 \\mathrm{~km} / \\mathrm{h}$ on a long straight highway pa... | math | {
"ground_truth": "$\\frac{600}{7}$",
"style": "rule"
} | {
"index": 230,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all pairs $(a, b)$ of real numbers that satisfy the following system of... | math | {
"ground_truth": "$(22+8 \\sqrt{6}, 22-8 \\sqrt{6})$,$(22-8 \\sqrt{6}, 22+8 \\sqrt{6})$",
"style": "rule"
} | {
"index": 231,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A permutation of a list of numbers is an ordered arrangement of the numbers in th... | math | {
"ground_truth": "$\\frac{10}{3}$",
"style": "rule"
} | {
"index": 232,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A permutation of a list of numbers is an ordered arrangement of the numbers in th... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 233,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A permutation of a list of numbers is an ordered arrangement of the numbers in th... | math | {
"ground_truth": "6700",
"style": "rule"
} | {
"index": 234,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $0^{\\circ}<x<90^{\\circ}$ and $3 \\sin (x)-\\cos \\left(15^{\\circ}\\right)=0... | math | {
"ground_truth": "$18.8^{\\circ}$",
"style": "rule"
} | {
"index": 235,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The function $f(x)$ has the property that $f(2 x+3)=2 f(x)+3$ for all $x$. If $f(... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"index": 236,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that the functions $f(x)$ and $g(x)$ satisfy the system of equations\n\n$... | math | {
"ground_truth": "$5,-2$",
"style": "rule"
} | {
"index": 237,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In a short-track speed skating event, there are five finalists including two Cana... | math | {
"ground_truth": "$\\frac{1}{10}$",
"style": "rule"
} | {
"index": 238,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine the number of positive integers less than or equal to 300 that are mult... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"index": 239,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In the series of odd numbers $1+3+5-7-9-11+13+15+17-19-21-23 \\ldots$ the signs a... | math | {
"ground_truth": "-900",
"style": "rule"
} | {
"index": 240,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A two-digit number has the property that the square of its tens digit plus ten ti... | math | {
"ground_truth": "11,19,37,73",
"style": "rule"
} | {
"index": 241,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A lead box contains samples of two radioactive isotopes of iron. Isotope A decays... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 242,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Solve the system of equations:\n\n$$\n\\begin{aligned}\n& \\log _{10}\\left(x^{3}... | math | {
"ground_truth": "$10^{3},10$",
"style": "rule"
} | {
"index": 243,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A positive integer $n$ is called \"savage\" if the integers $\\{1,2,\\dots,n\\}$ ... | math | {
"ground_truth": "8,32,44,68,80",
"style": "rule"
} | {
"index": 244,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Tanner has two identical dice. Each die has six faces which are numbered 2, 3, 5,... | math | {
"ground_truth": "$\\frac{1}{6}$",
"style": "rule"
} | {
"index": 245,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $\\frac{1}{\\cos x}-\\tan x=3$, what is the numerical value of $\\sin x$ ?",
... | math | {
"ground_truth": "$-\\frac{4}{5}$",
"style": "rule"
} | {
"index": 246,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all linear functions $f(x)=a x+b$ such that if $g(x)=f^{-1}(x)$ for all... | math | {
"ground_truth": "$f(x)=x+22$",
"style": "rule"
} | {
"index": 247,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all pairs $(a, b)$ of positive integers for which $a^{3}+2 a b=2013$.",... | math | {
"ground_truth": "$(1,1006),(3,331),(11,31)$",
"style": "rule"
} | {
"index": 248,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real values of $x$ for which $\\log _{2}\\left(2^{x-1}+3^{x+1}\\rig... | math | {
"ground_truth": "$\\frac{\\log 2}{\\log 2-\\log 3}$",
"style": "rule"
} | {
"index": 249,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A multiplicative partition of a positive integer $n \\geq 2$ is a way of writing ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 250,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A multiplicative partition of a positive integer $n \\geq 2$ is a way of writing ... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"index": 251,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "What are all values of $x$ such that\n\n$$\n\\log _{5}(x+3)+\\log _{5}(x-1)=1 ?\n... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 252,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A chef aboard a luxury liner wants to cook a goose. The time $t$ in hours to cook... | math | {
"ground_truth": "$1.68,0.45$",
"style": "rule"
} | {
"index": 253,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A circle passes through the origin and the points of intersection of the parabola... | math | {
"ground_truth": "$(-\\frac{1}{2}, \\frac{7}{2})$",
"style": "rule"
} | {
"index": 254,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In a soccer league with 5 teams, each team plays 20 games(that is, 5 games with e... | math | {
"ground_truth": "19,0,1",
"style": "rule"
} | {
"index": 255,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Three thin metal rods of lengths 9,12 and 15 are welded together to form a right-... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 256,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Triangle $A B C$ has vertices $A(0,5), B(3,0)$ and $C(8,3)$. Determine the measur... | math | {
"ground_truth": "$45^{\\circ}$",
"style": "rule"
} | {
"index": 257,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Blaise and Pierre will play 6 games of squash. Since they are equally skilled, ea... | math | {
"ground_truth": "$\\frac{11}{32}$",
"style": "rule"
} | {
"index": 258,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real values of $x$ for which\n\n$$\n3^{x+2}+2^{x+2}+2^{x}=2^{x+5}+3... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 259,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real values of $x$ such that\n\n$$\n\\log _{5 x+9}\\left(x^{2}+6 x+... | math | {
"ground_truth": "$0,-1,-\\frac{3}{2}$",
"style": "rule"
} | {
"index": 260,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For each positive integer $N$, an Eden sequence from $\\{1,2,3, \\ldots, N\\}$ is... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 261,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For each positive integer $N$, an Eden sequence from $\\{1,2,3, \\ldots, N\\}$ is... | math | {
"ground_truth": "$6764$,$10945$",
"style": "rule"
} | {
"index": 262,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $a$ is chosen randomly from the set $\\{1,2,3,4,5\\}$ and $b$ is chosen random... | math | {
"ground_truth": "$\\frac{2}{5}$",
"style": "rule"
} | {
"index": 263,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A bag contains some blue and some green hats. On each turn, Julia removes one hat... | math | {
"ground_truth": "$\\frac{11}{18}$",
"style": "rule"
} | {
"index": 264,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that, for some angles $x$ and $y$,\n\n$$\n\\begin{aligned}\n& \\sin ^{2} ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 265,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The sequence $2,5,10,50,500, \\ldots$ is formed so that each term after the secon... | math | {
"ground_truth": "233",
"style": "rule"
} | {
"index": 266,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $\\log _{2} x-2 \\log _{2} y=2$, determine $y$, as a function of $x$",
"ro... | math | {
"ground_truth": "$\\frac{1}{2},\\sqrt{x}$",
"style": "rule"
} | {
"index": 267,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Define $f(x)=\\sin ^{6} x+\\cos ^{6} x+k\\left(\\sin ^{4} x+\\cos ^{4} x\\right)$... | math | {
"ground_truth": "$-\\frac{3}{2}$",
"style": "rule"
} | {
"index": 268,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Define $f(x)=\\sin ^{6} x+\\cos ^{6} x+k\\left(\\sin ^{4} x+\\cos ^{4} x\\right)$... | math | {
"ground_truth": "$x=\\frac{1}{6} \\pi+\\pi k, \\frac{1}{3} \\pi+\\pi k, \\frac{2}{3} \\pi+\\pi k, \\frac{5}{6} \\pi+\\pi k$",
"style": "rule"
} | {
"index": 269,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Define $f(x)=\\sin ^{6} x+\\cos ^{6} x+k\\left(\\sin ^{4} x+\\cos ^{4} x\\right)$... | math | {
"ground_truth": "$[-1,-\\frac{1}{2}]$",
"style": "rule"
} | {
"index": 270,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Hexagon $A B C D E F$ has vertices $A(0,0), B(4,0), C(7,2), D(7,5), E(3,5)$, $F(0... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"index": 271,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A list $a_{1}, a_{2}, a_{3}, a_{4}$ of rational numbers is defined so that if one... | math | {
"ground_truth": "$\\frac{7}{5}$",
"style": "rule"
} | {
"index": 272,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A hollow cylindrical tube has a radius of $10 \\mathrm{~mm}$ and a height of $100... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"index": 273,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A function $f$ has the property that $f\\left(\\frac{2 x+1}{x}\\right)=x+6$ for a... | math | {
"ground_truth": "$\\frac{13}{2}$",
"style": "rule"
} | {
"index": 274,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real numbers $a, b$ and $c$ for which the graph of the function $y=... | math | {
"ground_truth": "$\\frac{1}{3},-2,5$",
"style": "rule"
} | {
"index": 275,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "A computer is programmed to choose an integer between 1 and 99, inclusive, so tha... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 276,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "What is the smallest positive integer $x$ for which $\\frac{1}{32}=\\frac{x}{10^{... | math | {
"ground_truth": "3125",
"style": "rule"
} | {
"index": 277,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all possible values for the area of a right-angled triangle with one si... | math | {
"ground_truth": "2400, 1350, 864",
"style": "rule"
} | {
"index": 278,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Amrita and Zhang cross a lake in a straight line with the help of a one-seat kaya... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 279,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all pairs $(x, y)$ of real numbers that satisfy the system of equations... | math | {
"ground_truth": "$(0,0),(0, \\frac{5}{2}),(\\frac{1}{2}, 0),(-\\frac{1}{2}, 0),(\\frac{3}{2}, 4),(-1, \\frac{3}{2})$",
"style": "rule"
} | {
"index": 280,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real numbers $x>0$ for which\n\n$$\n\\log _{4} x-\\log _{x} 16=\\fr... | math | {
"ground_truth": "$2^{-2 / 3}$, $8$",
"style": "rule"
} | {
"index": 281,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The string $A A A B B B A A B B$ is a string of ten letters, each of which is $A$... | math | {
"ground_truth": "631",
"style": "rule"
} | {
"index": 282,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Let $k$ be a positive integer with $k \\geq 2$. Two bags each contain $k$ balls, ... | math | {
"ground_truth": "$\\frac{27}{100}$",
"style": "rule"
} | {
"index": 283,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "In an arithmetic sequence, the first term is 1 and the last term is 19 . The sum ... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 284,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that $a(x+b(x+3))=2(x+6)$ for all values of $x$. Determine $a$ and $b$.",... | math | {
"ground_truth": "-2,-2",
"style": "rule"
} | {
"index": 285,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "An integer $n$, with $100 \\leq n \\leq 999$, is chosen at random. What is the pr... | math | {
"ground_truth": "$\\frac{1}{90}$",
"style": "rule"
} | {
"index": 286,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The parabola $y=x^{2}-2 x+4$ is translated $p$ units to the right and $q$ units d... | math | {
"ground_truth": "3,4",
"style": "rule"
} | {
"index": 287,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $\\log _{2} x,\\left(1+\\log _{4} x\\right)$, and $\\log _{8} 4 x$ are consecu... | math | {
"ground_truth": "$64,\\frac{1}{4}$",
"style": "rule"
} | {
"index": 288,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine the two pairs of positive integers $(a, b)$ with $a<b$ that satisfy the... | math | {
"ground_truth": "(2,32), (8,18)",
"style": "rule"
} | {
"index": 289,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Consider the system of equations:\n\n$$\n\\begin{aligned}\nc+d & =2000 \\\\\n\\fr... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 290,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Determine all real numbers $x$ for which $2 \\log _{2}(x-1)=1-\\log _{2}(x+2)$.",... | math | {
"ground_truth": "$\\sqrt{3}$",
"style": "rule"
} | {
"index": 291,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Consider the function $f(x)=x^{2}-2 x$. Determine all real numbers $x$ that satis... | math | {
"ground_truth": "$3,1,-1,1+\\sqrt{2}, 1-\\sqrt{2}$",
"style": "rule"
} | {
"index": 292,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Suppose that $x$ satisfies $0<x<\\frac{\\pi}{2}$ and $\\cos \\left(\\frac{3}{2} \... | math | {
"ground_truth": "$\\frac{\\pi^{2}-9}{9}$",
"style": "rule"
} | {
"index": 293,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For positive integers $a$ and $b$, define $f(a, b)=\\frac{a}{b}+\\frac{b}{a}+\\fr... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 294,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "For positive integers $a$ and $b$, define $f(a, b)=\\frac{a}{b}+\\frac{b}{a}+\\fr... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 295,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Amir and Brigitte play a card game. Amir starts with a hand of 6 cards: 2 red, 2 ... | math | {
"ground_truth": "$\\frac{7}{15}$",
"style": "rule"
} | {
"index": 296,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "Consider the sequence $t_{1}=1, t_{2}=-1$ and $t_{n}=\\left(\\frac{n-3}{n-1}\\rig... | math | {
"ground_truth": "$\\frac{-1}{1997}$",
"style": "rule"
} | {
"index": 297,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "The $n$th term of an arithmetic sequence is given by $t_{n}=555-7 n$.\n\nIf $S_{n... | math | {
"ground_truth": "158",
"style": "rule"
} | {
"index": 298,
"split": "default"
} |
olympiad_bench | [
{
"content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.",
"role": "system"
},
{
"content": "If $x$ and $y$ are real numbers, determine all solutions $(x, y)$ of the system o... | math | {
"ground_truth": "$(-1,-9),(4+2 \\sqrt{2}, 8),(4-2 \\sqrt{2}, 8)$",
"style": "rule"
} | {
"index": 299,
"split": "default"
} |
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