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": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i...
math
{ "ground_truth": "3", "style": "rule" }
{ "index": 600, "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": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i...
math
{ "ground_truth": "76", "style": "rule" }
{ "index": 601, "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": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i...
math
{ "ground_truth": "5", "style": "rule" }
{ "index": 602, "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": "Elizabeth is in an \"escape room\" puzzle. She is in a room with one door which i...
math
{ "ground_truth": "0", "style": "rule" }
{ "index": 603, "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": "Regular tetrahedra $J A N E, J O H N$, and $J O A N$ have non-overlapping interio...
math
{ "ground_truth": "$\\frac{5 \\sqrt{2}}{2}$", "style": "rule" }
{ "index": 604, "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": "Each positive integer less than or equal to 2019 is written on a blank sheet of p...
math
{ "ground_truth": "976", "style": "rule" }
{ "index": 605, "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": "Compute the third least positive integer $n$ such that each of $n, n+1$, and $n+2...
math
{ "ground_truth": "93", "style": "rule" }
{ "index": 606, "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 points $(1,2,3)$ and $(3,3,2)$ are vertices of a cube. Compute the product of...
math
{ "ground_truth": "216", "style": "rule" }
{ "index": 607, "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": "Eight students attend a Harper Valley ARML practice. At the end of the practice, ...
math
{ "ground_truth": "12", "style": "rule" }
{ "index": 608, "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": "$\\quad$ Compute the least positive value of $t$ such that\n\n$$\n\\operatorname{...
math
{ "ground_truth": "$\\frac{3 \\pi}{4}$", "style": "rule" }
{ "index": 609, "split": "default" }
olympiad_bench
[ { "content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.", "role": "system" }, { "content": "In non-right triangle $A B C$, distinct points $P, Q, R$, and $S$ lie on $\\overl...
math
{ "ground_truth": "$\\frac{45}{2}$", "style": "rule" }
{ "index": 610, "split": "default" }
olympiad_bench
[ { "content": "You are Qwen, created by Alibaba Cloud. You are a helpful assistant. Solve the following math problem step by step. Put your final answer within <answer></answer> tags.", "role": "system" }, { "content": "Consider the system of equations\n\n$$\n\\begin{aligned}\n& \\log _{4} x+\\log _{...
math
{ "ground_truth": "$\\frac{66}{7}$", "style": "rule" }
{ "index": 611, "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 complex number $z$ is selected uniformly at random such that $|z|=1$. Compute t...
math
{ "ground_truth": "$\\frac{505}{8076}$", "style": "rule" }
{ "index": 612, "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": "Compute the least positive integer $n$ such that the sum of the digits of $n$ is ...
math
{ "ground_truth": "7986", "style": "rule" }
{ "index": 613, "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": "$\\quad$ Compute the greatest real number $K$ for which the graphs of\n\n$$\n(|x|...
math
{ "ground_truth": "29", "style": "rule" }
{ "index": 614, "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": "To morph a sequence means to replace two terms $a$ and $b$ with $a+1$ and $b-1$ i...
math
{ "ground_truth": "56", "style": "rule" }
{ "index": 615, "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 $A B C$ is inscribed in circle $\\omega$. The tangents to $\\omega$ at $...
math
{ "ground_truth": "$\\frac{800}{3}$", "style": "rule" }
{ "index": 616, "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": "Given that $a, b, c$, and $d$ are integers such that $a+b c=20$ and $-a+c d=19$, ...
math
{ "ground_truth": "39", "style": "rule" }
{ "index": 617, "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 $T$ = 39. Emile randomly chooses a set of $T$ cards from a standard deck of 5...
math
{ "ground_truth": "1", "style": "rule" }
{ "index": 618, "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 $T=1$. In parallelogram $A B C D, \\frac{A B}{B C}=T$. Given that $M$ is the ...
math
{ "ground_truth": "6", "style": "rule" }
{ "index": 619, "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 $T=6$. Compute the value of $x$ such that $\\log _{T} \\sqrt{x-7}+\\log _{T^{...
math
{ "ground_truth": "11", "style": "rule" }
{ "index": 620, "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 $T=11$. Let $p$ be an odd prime and let $x, y$, and $z$ be positive integers ...
math
{ "ground_truth": "55", "style": "rule" }
{ "index": 621, "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 $T=55$. Compute the value of $K$ such that $20, T-5, K$ is an increasing geom...
math
{ "ground_truth": "125", "style": "rule" }
{ "index": 622, "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 $T=125$. Cube $\\mathcal{C}_{1}$ has volume $T$ and sphere $\\mathcal{S}_{1}$...
math
{ "ground_truth": "15", "style": "rule" }
{ "index": 623, "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": "Square $K E N T$ has side length 20 . Point $M$ lies in the interior of $K E N T$...
math
{ "ground_truth": "400", "style": "rule" }
{ "index": 624, "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 $T$ be a rational number. Let $a, b$, and $c$ be the three solutions of the e...
math
{ "ground_truth": "362", "style": "rule" }
{ "index": 625, "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 $T=362$ and let $K=\\sqrt{T-1}$. Compute $\\left|(K-20)(K+1)+19 K-K^{2}\\righ...
math
{ "ground_truth": "20", "style": "rule" }
{ "index": 626, "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 $T=20$. In $\\triangle L E O, \\sin \\angle L E O=\\frac{1}{T}$. If $L E=\\fr...
math
{ "ground_truth": "$\\frac{1}{40}$", "style": "rule" }
{ "index": 627, "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 $T=\\frac{1}{40}$. Given that $x, y$, and $z$ are real numbers such that $x+y...
math
{ "ground_truth": "20", "style": "rule" }
{ "index": 628, "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 $T=20$. The product of all positive divisors of $2^{T}$ can be written in the...
math
{ "ground_truth": "210", "style": "rule" }
{ "index": 629, "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 $T=210$. At the Westward House of Supper (\"WHS\"), a dinner special consists...
math
{ "ground_truth": "10", "style": "rule" }
{ "index": 630, "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 $S=15$ and let $M=10$ . Sam and Marty each ride a bicycle at a constant speed...
math
{ "ground_truth": "60", "style": "rule" }
{ "index": 631, "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": "Compute the $2011^{\\text {th }}$ smallest positive integer $N$ that gains an ext...
math
{ "ground_truth": "6455", "style": "rule" }
{ "index": 632, "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 triangle $A B C, C$ is a right angle and $M$ is on $\\overline{A C}$. A circle...
math
{ "ground_truth": "$\\frac{12}{5}$", "style": "rule" }
{ "index": 633, "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 product of the first five terms of a geometric progression is 32 . If the fou...
math
{ "ground_truth": "$\\frac{4}{17}$", "style": "rule" }
{ "index": 634, "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": "Polygon $A_{1} A_{2} \\ldots A_{n}$ is a regular $n$-gon. For some integer $k<n$,...
math
{ "ground_truth": "40", "style": "rule" }
{ "index": 635, "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 20 lavender marbles, 12 emerald marbles, and some number of orange...
math
{ "ground_truth": "69", "style": "rule" }
{ "index": 636, "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": "Compute the number of ordered quadruples of integers $(a, b, c, d)$ satisfying th...
math
{ "ground_truth": "12", "style": "rule" }
{ "index": 637, "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 $n$ be a positive integer such that $\\frac{3+4+\\cdots+3 n}{5+6+\\cdots+5 n}...
math
{ "ground_truth": "$\\frac{27}{106}$", "style": "rule" }
{ "index": 638, "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 quadratic polynomial $f(x)$ has a zero at $x=2$. The polynomial $f(f(x))$ has...
math
{ "ground_truth": "$-\\frac{32}{9}$", "style": "rule" }
{ "index": 639, "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 Local Area Inspirational Math Exam comprises 15 questions. All answers are in...
math
{ "ground_truth": "7530", "style": "rule" }
{ "index": 640, "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": "Circle $\\omega_{1}$ has center $O$, which is on circle $\\omega_{2}$. The circle...
math
{ "ground_truth": "$548 \\pi$", "style": "rule" }
{ "index": 641, "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": "Compute the number of integers $n$ for which $2^{4}<8^{n}<16^{32}$.", "role":...
math
{ "ground_truth": "41", "style": "rule" }
{ "index": 642, "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 $T=41$. Compute the number of positive integers $b$ such that the number $T$ ...
math
{ "ground_truth": "35", "style": "rule" }
{ "index": 643, "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 $T=35$. Triangle $A B C$ has a right angle at $C$, and $A B=40$. If $A C-B C=...
math
{ "ground_truth": "111", "style": "rule" }
{ "index": 644, "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 $x$ be a positive real number such that $\\log _{\\sqrt{2}} x=20$. Compute $\...
math
{ "ground_truth": "5", "style": "rule" }
{ "index": 645, "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 $T=5$. Hannah flips two fair coins, while Otto flips $T$ fair coins. Let $p$ ...
math
{ "ground_truth": "17", "style": "rule" }
{ "index": 646, "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 $T=17$. In ARMLovia, the unit of currency is the edwah. Janet's wallet contai...
math
{ "ground_truth": "1020", "style": "rule" }
{ "index": 647, "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": "Spheres centered at points $P, Q, R$ are externally tangent to each other, and ar...
math
{ "ground_truth": "$18 \\sqrt{6}$", "style": "rule" }
{ "index": 648, "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 $f(x)=x^{1}+x^{2}+x^{4}+x^{8}+x^{16}+x^{32}+\\cdots$. Compute the coefficient...
math
{ "ground_truth": "40", "style": "rule" }
{ "index": 649, "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": "Compute $\\left\\lfloor 100000(1.002)^{10}\\right\\rfloor$.", "role": "user" ...
math
{ "ground_truth": "102018", "style": "rule" }
{ "index": 650, "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 $1, x, y$ is a geometric sequence and $x, y, 3$ is an arithmetic sequence, com...
math
{ "ground_truth": "$\\frac{15}{4}$", "style": "rule" }
{ "index": 651, "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 the sequence of positive integers $\\left\\{a_{n}\\right\\}$ as follows:\n...
math
{ "ground_truth": "253", "style": "rule" }
{ "index": 652, "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": "Compute the base $b$ for which $253_{b} \\cdot 341_{b}=\\underline{7} \\underline...
math
{ "ground_truth": "20", "style": "rule" }
{ "index": 653, "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": "Some portions of the line $y=4 x$ lie below the curve $y=10 \\pi \\sin ^{2} x$, a...
math
{ "ground_truth": "$\\frac{5 \\pi}{4} \\sqrt{17}$", "style": "rule" }
{ "index": 654, "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 equilateral hexagon $A B C D E F, \\mathrm{~m} \\angle A=2 \\mathrm{~m} \\angl...
math
{ "ground_truth": "$\\frac{9}{2}$", "style": "rule" }
{ "index": 655, "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 taxicab distance between points $A=\\left(x_{A}, y_{A}\\right)$ and $B=\\left...
math
{ "ground_truth": "96", "style": "rule" }
{ "index": 656, "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 $f$ satisfies the relation $f(n)=f(n-1) f(n-2)$ for all integers $n$...
math
{ "ground_truth": "4096", "style": "rule" }
{ "index": 657, "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": "Frank Narf accidentally read a degree $n$ polynomial with integer coefficients ba...
math
{ "ground_truth": "70", "style": "rule" }
{ "index": 658, "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": "Given a regular 16-gon, extend three of its sides to form a triangle none of whos...
math
{ "ground_truth": "11", "style": "rule" }
{ "index": 659, "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": "Two square tiles of area 9 are placed with one directly on top of the other. The ...
math
{ "ground_truth": "$\\frac{5}{4}$", "style": "rule" }
{ "index": 660, "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 neither of the three-digit numbers $M=\\underline{4} \\underline{A} ...
math
{ "ground_truth": "12", "style": "rule" }
{ "index": 661, "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 $T=12$. Each interior angle of a regular $T$-gon has measure $d^{\\circ}$. Co...
math
{ "ground_truth": "150", "style": "rule" }
{ "index": 662, "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 $r$ and $s$ are the two roots of the equation $F_{k} x^{2}+F_{k+1} x...
math
{ "ground_truth": "2", "style": "rule" }
{ "index": 663, "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 $T=2$. Compute the product of $-T-i$ and $i-T$, where $i=\\sqrt{-1}$.", "...
math
{ "ground_truth": "5", "style": "rule" }
{ "index": 664, "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 $T=5$. Compute the number of positive divisors of the number $20^{4} \\cdot 1...
math
{ "ground_truth": "12", "style": "rule" }
{ "index": 665, "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 $T=72 \\sqrt{2}$, and let $K=\\left(\\frac{T}{12}\\right)^{2}$. In the sequen...
math
{ "ground_truth": "414", "style": "rule" }
{ "index": 666, "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 $A$ be the sum of the digits of the number you will receive from position 7 ,...
math
{ "ground_truth": "$\\frac{79}{128}$", "style": "rule" }
{ "index": 667, "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 $T=9.5$. If $\\log _{2} x^{T}-\\log _{4} x=\\log _{8} x^{k}$ is an identity f...
math
{ "ground_truth": "27", "style": "rule" }
{ "index": 668, "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 $T=16$. An isosceles trapezoid has an area of $T+1$, a height of 2 , and the ...
math
{ "ground_truth": "9.5", "style": "rule" }
{ "index": 669, "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 $T=10$. Susan flips a fair coin $T$ times. Leo has an unfair coin such that t...
math
{ "ground_truth": "16", "style": "rule" }
{ "index": 670, "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 $T=1$. Dennis and Edward each take 48 minutes to mow a lawn, and Shawn takes ...
math
{ "ground_truth": "10", "style": "rule" }
{ "index": 671, "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 T be a rational number. Compute $\\sin ^{2} \\frac{T \\pi}{2}+\\sin ^{2} \\fr...
math
{ "ground_truth": "1", "style": "rule" }
{ "index": 672, "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 $T=11$. Compute the value of $x$ that satisfies $\\sqrt{20+\\sqrt{T+x}}=5$.",...
math
{ "ground_truth": "14", "style": "rule" }
{ "index": 673, "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 sum of the interior angles of an $n$-gon equals the sum of the interior angle...
math
{ "ground_truth": "11", "style": "rule" }
{ "index": 674, "split": "default" }
minerva
[ { "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": "Each of the two Magellan telescopes has a diameter of $6.5 \\mathrm{~m}$. In one ...
math
{ "ground_truth": "1.6", "style": "rule" }
{ "index": 0, "split": "default" }
minerva
[ { "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 white dwarf star has an effective temperature, $T_{e}=50,000$ degrees Kelvin, b...
math
{ "ground_truth": "4.5e33", "style": "rule" }
{ "index": 1, "split": "default" }
minerva
[ { "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": "Preamble: A prism is constructed from glass and has sides that form a right trian...
math
{ "ground_truth": "41.8", "style": "rule" }
{ "index": 2, "split": "default" }
minerva
[ { "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 particular star has an absolute magnitude $M=-7$. If this star is observed in a...
math
{ "ground_truth": "20.39", "style": "rule" }
{ "index": 3, "split": "default" }
minerva
[ { "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": "Find the gravitational acceleration due to the Sun at the location of the Earth's...
math
{ "ground_truth": "0.006", "style": "rule" }
{ "index": 4, "split": "default" }
minerva
[ { "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": "Preamble: A collimated light beam propagating in water is incident on the surface...
math
{ "ground_truth": "np.arcsin(10/13)", "style": "rule" }
{ "index": 5, "split": "default" }
minerva
[ { "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": "Find the theoretical limiting angular resolution (in arcsec) of a commercial 8-in...
math
{ "ground_truth": "0.49", "style": "rule" }
{ "index": 6, "split": "default" }
minerva
[ { "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 star has a measured parallax of $0.01^{\\prime \\prime}$, that is, $0.01$ arcse...
math
{ "ground_truth": "100", "style": "rule" }
{ "index": 7, "split": "default" }
minerva
[ { "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 extrasolar planet has been observed which passes in front of (i.e., transits) ...
math
{ "ground_truth": "0.022", "style": "rule" }
{ "index": 8, "split": "default" }
minerva
[ { "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 the Bohr energy levels scale as $Z^{2}$, where $Z$ is the atomic number of the...
math
{ "ground_truth": "9.6", "style": "rule" }
{ "index": 9, "split": "default" }
minerva
[ { "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 the Sun's absolute magnitude is $+5$, find the luminosity of a star of magnitu...
math
{ "ground_truth": "3.83e35", "style": "rule" }
{ "index": 10, "split": "default" }
minerva
[ { "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": "Preamble: A spectrum is taken of a single star (i.e., one not in a binary). Among...
math
{ "ground_truth": "300", "style": "rule" }
{ "index": 11, "split": "default" }
minerva
[ { "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 differential luminosity from a star, $\\Delta L$, with an approximate blackbo...
math
{ "ground_truth": "\\frac{2 \\pi c^{2} R^{2}}{\\lambda^{5}\\left[e^{h c /(\\lambda k T)}-1\\right] d^{2}}", "style": "rule" }
{ "index": 12, "split": "default" }
minerva
[ { "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": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of ...
math
{ "ground_truth": "8.7e8", "style": "rule" }
{ "index": 13, "split": "default" }
minerva
[ { "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 star is at a distance from the Earth of $300 \\mathrm{pc}$. Find its parallax a...
math
{ "ground_truth": "0.003", "style": "rule" }
{ "index": 14, "split": "default" }
minerva
[ { "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 Sun's effective temperature, $T_{e}$, is 5800 Kelvin, and its radius is $7 \\...
math
{ "ground_truth": "4e33", "style": "rule" }
{ "index": 15, "split": "default" }
minerva
[ { "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": "Use the Bohr model of the atom to compute the wavelength of the transition from t...
math
{ "ground_truth": "4.49", "style": "rule" }
{ "index": 16, "split": "default" }
minerva
[ { "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": "Preamble: A radio interferometer, operating at a wavelength of $1 \\mathrm{~cm}$,...
math
{ "ground_truth": "0.01", "style": "rule" }
{ "index": 17, "split": "default" }
minerva
[ { "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": "Preamble: Orbital Dynamics: A binary system consists of two stars in circular orb...
math
{ "ground_truth": "3.3e12", "style": "rule" }
{ "index": 18, "split": "default" }
minerva
[ { "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 star cluster is made up of $10^{4}$ stars, each of whose absolute magnitude ...
math
{ "ground_truth": "10", "style": "rule" }
{ "index": 19, "split": "default" }
minerva
[ { "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 galaxy moves directly away from us with a speed of $3000 \\mathrm{~km} \\mathrm...
math
{ "ground_truth": "6630", "style": "rule" }
{ "index": 20, "split": "default" }
minerva
[ { "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 Spitzer Space Telescope has an effective diameter of $85 \\mathrm{cm}$, and a...
math
{ "ground_truth": "1.2", "style": "rule" }
{ "index": 21, "split": "default" }
minerva
[ { "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": "It has long been suspected that there is a massive black hole near the center of ...
math
{ "ground_truth": "3e6", "style": "rule" }
{ "index": 22, "split": "default" }
minerva
[ { "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": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of ...
math
{ "ground_truth": "7e37", "style": "rule" }
{ "index": 23, "split": "default" }
minerva
[ { "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 large ground-based telescope has an effective focal length of 10 meters. Two as...
math
{ "ground_truth": "50", "style": "rule" }
{ "index": 24, "split": "default" }