StepControlled/MATH-GSM8K-Tool-81K · Datasets at Hugging Face

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[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John is working as an IT specialist. He repairs broken computers. One day he had to fix 20 computers. 20% of ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Expand the following expression: $3(8x^2-2x+1)$." } ] }, { "role": "assistant", "conten...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the cu...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Oliver is trying to decide between two different sized boxes of macaroni and cheese. He wants to know which i...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the positive factors of 48?" } ] }, { "role": "assistant", "content"...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The diameter, in inches, of a sphere with twice the volume of a sphere of radius 9 inches can be expressed in...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let \\[f(n) = \\left\\{\n\\begin{array}{cl}\nn^2-2 & \\text{ if }n<0, \\\\\n2n-20 & \\text{ if }n \\geq 0.\n\...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A coin is flipped eight times, and the sequence of heads and tails occurring is recorded. How many distinct s...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Balki is counting the number of raisins in boxes of cereal. He counted 437 total raisins in 5 boxes. In one b...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The ratio of measures of two complementary angles is 4 to 5. The smallest measure is increased by $10\\%$. By...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ioana has three ropes whose lengths are 39 inches, 52 inches and 65 inches. She wants to cut the ropes into e...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "To support the school outreach program, Einstein wants to raise $500 by selling snacks. One box of pizza sell...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define $E(a,b,c) = a \\times b^c$. What positive value of $r$ is the solution to the equation $E(r,r,3) = 625...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the matrix $\\mathbf{M},$ with real entries, such that\n\\[\\mathbf{M}^3 - 4 \\mathbf{M}^2 + 5 \\mathbf{...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the point on the line\n\\[y = \\frac{x + 5}{2}\\]that is closest to the point $(6,1).$" } ] ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Anne drops a mirror and breaks it into 60 pieces. She sweeps up half of them, then her cat steals 3 pieces an...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jolene wants to raise some money to buy a bicycle. She babysits for 4 families for $30 each. She also washe...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Fred spent half of his allowance going to the movies. He washed the family car and earned 6 dollars. What is ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If a regular polygon has a total of nine diagonals, how many sides does it have?" } ] }, { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Express as a fraction in lowest terms: $0.\\overline{1} + 0.\\overline{01}$" } ] }, { "role...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Paul lives in a 5th story apartment. He makes 3 trips out from and back to his apartment throughout the day ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Amy is collecting candy for the car pool. She has 5 chocolate bars, 7 times as many M&Ms as chocolate bars, a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tonya is in a hamburger eating contest. Each hamburger is 4 ounces. Last year the winner ate 84 ounces. How m...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John has a party and invites 30 people. Of the people he invited 20% didn't show up. 75% of the people who ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Johnny makes his signature crab dish 40 times a day. It uses 1.5 pounds of crab meat. Crab meat sells for $...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In triangle $ABC,$ $\\sin A = \\frac{3}{5}$ and $\\cos B = \\frac{5}{13}.$ Find $\\cos C.$" } ] ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the remainder when 1,234,567,890 is divided by 99?" } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Monica charges $25.00 per person when catering a dinner party. For repeat customers, she offers a 10% discou...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Quantities $r$ and $s$ vary inversely. When $r$ is $1200,$ $s$ is $0.35.$ What is the value of $s$ when $r$ i...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let \\begin{align}\nf(x) &= 2x + 5 \\\\\ng(x) &= \\sqrt{f(x)} - 2 \\\\\nh(x) &= f(g(x))\n\\end{align} What...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, an...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Solve for $c$: \\[\\frac{c-23}{2} = \\frac{2c +5}{7}.\\]" } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A valid license plate in Xanadu consists of two letters followed by three digits. How many valid license plat...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The base three number $12012_3$ is equal to which base ten number?" } ] }, { "role": "assis...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Matt's protein powder is 80% protein. He weighs 80 kg and wants to eat 2 grams of protein per kilogram of bo...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the domain of the function $$j(x) = \\frac{1}{x+8} + \\frac{1}{x^2+8} + \\frac{1}{x^3+8}~?$$Express y...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A church has 120 members. 40% are adults. The rest are children. How many children more children are there th...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $\\cos 90^\\circ$." } ] }, { "role": "assistant", "content": [ { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the value of $x$ that satisfies $\\frac{\\sqrt{5x}}{\\sqrt{3(x-1)}}=2$. Express your answer in simplest ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute the sum of the geometric series $-1 -3-9-27 -81-243-729$." } ] }, { "role": "assist...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A dental office gives away 2 toothbrushes to every patient who visits. His 8 hour days are packed and each v...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tim has 30 toads. Jim has 20 more toads than Tim does. Sarah has twice as many toads as Jim does. How many to...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Simplify\n\\[\\frac{\\tan^3 75^\\circ + \\cot^3 75^\\circ}{\\tan 75^\\circ + \\cot 75^\\circ}.\\]" } ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Angela has a collection of 24 pieces of rare action figures. She sold off a quarter of them at the pawnshop a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "From a group of six students, how many different four-student committees can be chosen?" } ] }, ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The point $(1,1,1)$ is rotated $180^\\circ$ about the $y$-axis, then reflected through the $yz$-plane, reflec...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "8 years ago James was twice Janet's age. In 15 years James will turn 37. Susan was born when Janet turned 3...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the greatest common divisor of 9118, 12173, and 33182." } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Expand the product ${(x+2)(x+5)}$." } ] }, { "role": "assistant", "content": [ { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "While preparing for a meeting, Bill fills Dixie cups with water from out of a water cooler. The water cooler ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Consider the geometric sequence $3$, $\\dfrac{9}{2}$, $\\dfrac{27}{4}$, $\\dfrac{81}{8}$, $\\ldots$. Find the...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 3 math teams in the area, with 5, 7, and 8 students respectively. Each team has two co-captains. If...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the tw...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Mickey's age is 4 years less than $300\\%$ of Jerry's age. If Mickey is 14 years old, how old is Jerry?" ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Baking in batches of 65 cupcakes, Carla made 45 batches of cupcakes for her daughter's birthday party. She th...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The number $a+\\sqrt{b}$ and its radical conjugate have a sum of $-4$ and a product of $1$. Find $a+b$." ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Vincent's bookstore is divided into different kinds of books. His top-selling books are fantasy books. He als...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the smallest positive integer $b$ for which $x^2+bx+2008$ factors into a product of two binomials, each ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the product of $0.\\overline{6}$ and 6." } ] }, { "role": "assistant", "content": ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the cu...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The number $1000!$ has a long tail of zeroes. How many zeroes are there? (Reminder: The number $n!$ is the p...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On the planet Orbius-5, there are 250 days per year, and each year is equally divided into 5 seasons. If an a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There exist integers $a,$ $b,$ and $c$ such that\n\\[(x - a)(x - 10) + 1 = (x + b)(x + c).\\]Enter all possib...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sum of two numbers $x$ and $y$ is 399, and the value of the fraction $\\frac{x}{y}$ is 0.9. What is the v...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many prime numbers are between 20 and 30?" } ] }, { "role": "assistant", "content":...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Chuck can ride the merry-go-round 5 times longer than Dave who can only ride it for 10 minutes before getting...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "For every 5 people that attend a poetry class, the teacher gives one of the students a lollipop. If 45 people...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lola baked 13 mini cupcakes, 10 pop tarts, and 8 blueberry pies. Meanwhile, Lulu made 16 mini cupcakes, 12 po...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $99^3 + 3(99^2) + 3(99) + 1$?" } ] }, { "role": "assistant", "cont...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Joan collects rocks. In her collection of rock samples, she had half as many gemstones as minerals yesterday....
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Given that $a > 0$, if $f(g(a)) = 8$, where $f(x) = x^2 + 8$ and $g(x) = x^2 - 4$, what is the value of $a$?"...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $a,b,c$ satisfy the system of equations \\begin{align*}b + c &= 12-3a \\\\\na+c &= -14 - 3b \\\\\na+b &= ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of all values of $y$ for which the expression $\\frac{y+6}{y^2-5y+4}$ is undefined?" } ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Convert $1011001_2$ to base 4." } ] }, { "role": "assistant", "content": [ { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jimmy's father receives 20 emails a day. Halfway through April, he subscribed to a news channel that sent 5 m...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Reynald is the head of the varsity department, and he bought 145 balls. Twenty were soccer balls. There were ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Henry, John and Leo collected some seashells from the beach. Henry collected 11, Paul 24. If they initially c...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A number $n$ has $3$ divisors. How many divisors does $n^2$ have?" } ] }, { "role": "assist...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A triangular region is bounded by the two coordinate axes and the line given by the equation $2x + y = 6$. Wh...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $f(x) = ax+b$, where $a$ and $b$ are real constants, and $g(x) = 2x - 5$. Suppose that for all $x$, it is...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In a single-elimination tournament, each game is between two players. Only the winner of each game advances t...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a,$ $b,$ $c$ be distinct integers, and let $\\omega$ be a complex number such that $\\omega^3 = 1$ and $...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The ratio of boys to girls in a classroom is 3:5. If there are 4 more girls than boys, how many students are ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Felicity and Adhira took separate trips. Felicity used 5 less gallons of gas than four times the number of ga...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tom and Elizabeth have a competition to climb a hill. Elizabeth takes 30 minutes to climb the hill. Tom takes...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find an ordered pair $(u,v)$ that solves the system: \\begin{align*} 5u &= -7 - 2v,\\\\ 3u &= 4v - 25 \\end{a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On a Sunday morning, Josephine sold milk in the farm stall. The buyers brought their containers. She filled t...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At the Boisjoli farm, there is a chicken coop where 270 hens and 3 roosters live. Every morning, around 8 a.m...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On a $12$-hour clock, an elapsed time of four hours looks the same as an elapsed time of $16$ hours. Because ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Evaluate $(x-a+3)$ if the value of $x$ is $(a+7)$." } ] }, { "role": "assistant", "cont...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that $f(x)=\\frac{1}{2x+b}$. For what value of $b$ does $f^{-1}(x)=\\frac{1-2x}{2x}$?" } ] ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that the number $\\sqrt{2700} - 37$ can be expressed in the form $(\\sqrt a - b)^3,$ where $a$ and $b...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There were 10 snowflakes at first. It snowed an additional 4 snowflakes every 5 minutes. How many minutes pas...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the equation $\|x-7\| -3 = -2$, what is the product of all possible values of $x$?" } ] }, { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A piece of cheese is located at $(12,10)$ in a coordinate plane. A mouse is at $(4,-2)$ and is running up ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A garden store sells packages of pumpkin seeds for $2.50, tomato seeds for $1.50, and chili pepper seeds for ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Edward the plumber is replacing a pipe in a bathroom wall. He needs to use 40 feet of copper pipe to complet...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sum of the first and third of three consecutive integers is 118. What is the value of the second integer?...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that $wz = 12-8i$, and $\|w\| = \\sqrt{13}$. What is $\|z\|$?" } ] }, { "role": "assis...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Steve is 5'6\". He grows 6 inches. How tall is he in inches?" } ] }, { "role": "assistant...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John is working as an IT specialist. He repairs broken computers. One day he had to fix 20 computers. 20% of ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Expand the following expression: $3(8x^2-2x+1)$." } ] }, { "role": "assistant", "conten...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the cu...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Oliver is trying to decide between two different sized boxes of macaroni and cheese. He wants to know which i...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the positive factors of 48?" } ] }, { "role": "assistant", "content"...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The diameter, in inches, of a sphere with twice the volume of a sphere of radius 9 inches can be expressed in...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let \\[f(n) = \\left\\{\n\\begin{array}{cl}\nn^2-2 & \\text{ if }n<0, \\\\\n2n-20 & \\text{ if }n \\geq 0.\n\...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A coin is flipped eight times, and the sequence of heads and tails occurring is recorded. How many distinct s...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Balki is counting the number of raisins in boxes of cereal. He counted 437 total raisins in 5 boxes. In one b...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The ratio of measures of two complementary angles is 4 to 5. The smallest measure is increased by $10\\%$. By...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ioana has three ropes whose lengths are 39 inches, 52 inches and 65 inches. She wants to cut the ropes into e...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "To support the school outreach program, Einstein wants to raise $500 by selling snacks. One box of pizza sell...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define $E(a,b,c) = a \\times b^c$. What positive value of $r$ is the solution to the equation $E(r,r,3) = 625...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the matrix $\\mathbf{M},$ with real entries, such that\n\\[\\mathbf{M}^3 - 4 \\mathbf{M}^2 + 5 \\mathbf{...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the point on the line\n\\[y = \\frac{x + 5}{2}\\]that is closest to the point $(6,1).$" } ] ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Anne drops a mirror and breaks it into 60 pieces. She sweeps up half of them, then her cat steals 3 pieces an...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jolene wants to raise some money to buy a bicycle. She babysits for 4 families for $30 each. She also washe...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Fred spent half of his allowance going to the movies. He washed the family car and earned 6 dollars. What is ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If a regular polygon has a total of nine diagonals, how many sides does it have?" } ] }, { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Express as a fraction in lowest terms: $0.\\overline{1} + 0.\\overline{01}$" } ] }, { "role...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Paul lives in a 5th story apartment. He makes 3 trips out from and back to his apartment throughout the day ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Amy is collecting candy for the car pool. She has 5 chocolate bars, 7 times as many M&Ms as chocolate bars, a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tonya is in a hamburger eating contest. Each hamburger is 4 ounces. Last year the winner ate 84 ounces. How m...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John has a party and invites 30 people. Of the people he invited 20% didn't show up. 75% of the people who ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Johnny makes his signature crab dish 40 times a day. It uses 1.5 pounds of crab meat. Crab meat sells for $...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In triangle $ABC,$ $\\sin A = \\frac{3}{5}$ and $\\cos B = \\frac{5}{13}.$ Find $\\cos C.$" } ] ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the remainder when 1,234,567,890 is divided by 99?" } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Monica charges $25.00 per person when catering a dinner party. For repeat customers, she offers a 10% discou...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Quantities $r$ and $s$ vary inversely. When $r$ is $1200,$ $s$ is $0.35.$ What is the value of $s$ when $r$ i...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let \\begin{align*}\nf(x) &= 2x + 5 \\\\\ng(x) &= \\sqrt{f(x)} - 2 \\\\\nh(x) &= f(g(x))\n\\end{align*} What...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, an...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Solve for $c$: \\[\\frac{c-23}{2} = \\frac{2c +5}{7}.\\]" } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A valid license plate in Xanadu consists of two letters followed by three digits. How many valid license plat...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The base three number $12012_3$ is equal to which base ten number?" } ] }, { "role": "assis...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Matt's protein powder is 80% protein. He weighs 80 kg and wants to eat 2 grams of protein per kilogram of bo...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the domain of the function $$j(x) = \\frac{1}{x+8} + \\frac{1}{x^2+8} + \\frac{1}{x^3+8}~?$$Express y...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A church has 120 members. 40% are adults. The rest are children. How many children more children are there th...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $\\cos 90^\\circ$." } ] }, { "role": "assistant", "content": [ { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the value of $x$ that satisfies $\\frac{\\sqrt{5x}}{\\sqrt{3(x-1)}}=2$. Express your answer in simplest ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute the sum of the geometric series $-1 -3-9-27 -81-243-729$." } ] }, { "role": "assist...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A dental office gives away 2 toothbrushes to every patient who visits. His 8 hour days are packed and each v...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tim has 30 toads. Jim has 20 more toads than Tim does. Sarah has twice as many toads as Jim does. How many to...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Simplify\n\\[\\frac{\\tan^3 75^\\circ + \\cot^3 75^\\circ}{\\tan 75^\\circ + \\cot 75^\\circ}.\\]" } ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Angela has a collection of 24 pieces of rare action figures. She sold off a quarter of them at the pawnshop a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "From a group of six students, how many different four-student committees can be chosen?" } ] }, ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The point $(1,1,1)$ is rotated $180^\\circ$ about the $y$-axis, then reflected through the $yz$-plane, reflec...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "8 years ago James was twice Janet's age. In 15 years James will turn 37. Susan was born when Janet turned 3...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the greatest common divisor of 9118, 12173, and 33182." } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Expand the product ${(x+2)(x+5)}$." } ] }, { "role": "assistant", "content": [ { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "While preparing for a meeting, Bill fills Dixie cups with water from out of a water cooler. The water cooler ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Consider the geometric sequence $3$, $\\dfrac{9}{2}$, $\\dfrac{27}{4}$, $\\dfrac{81}{8}$, $\\ldots$. Find the...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 3 math teams in the area, with 5, 7, and 8 students respectively. Each team has two co-captains. If...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The average of two 2-digit positive integers is equal to the decimal number obtained by writing one of the tw...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Mickey's age is 4 years less than $300\\%$ of Jerry's age. If Mickey is 14 years old, how old is Jerry?" ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Baking in batches of 65 cupcakes, Carla made 45 batches of cupcakes for her daughter's birthday party. She th...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The number $a+\\sqrt{b}$ and its radical conjugate have a sum of $-4$ and a product of $1$. Find $a+b$." ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Vincent's bookstore is divided into different kinds of books. His top-selling books are fantasy books. He als...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the smallest positive integer $b$ for which $x^2+bx+2008$ factors into a product of two binomials, each ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the product of $0.\\overline{6}$ and 6." } ] }, { "role": "assistant", "content": ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the cu...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The number $1000!$ has a long tail of zeroes. How many zeroes are there? (Reminder: The number $n!$ is the p...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On the planet Orbius-5, there are 250 days per year, and each year is equally divided into 5 seasons. If an a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There exist integers $a,$ $b,$ and $c$ such that\n\\[(x - a)(x - 10) + 1 = (x + b)(x + c).\\]Enter all possib...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sum of two numbers $x$ and $y$ is 399, and the value of the fraction $\\frac{x}{y}$ is 0.9. What is the v...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many prime numbers are between 20 and 30?" } ] }, { "role": "assistant", "content":...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Chuck can ride the merry-go-round 5 times longer than Dave who can only ride it for 10 minutes before getting...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "For every 5 people that attend a poetry class, the teacher gives one of the students a lollipop. If 45 people...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lola baked 13 mini cupcakes, 10 pop tarts, and 8 blueberry pies. Meanwhile, Lulu made 16 mini cupcakes, 12 po...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $99^3 + 3(99^2) + 3(99) + 1$?" } ] }, { "role": "assistant", "cont...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Joan collects rocks. In her collection of rock samples, she had half as many gemstones as minerals yesterday....

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Given that $a > 0$, if $f(g(a)) = 8$, where $f(x) = x^2 + 8$ and $g(x) = x^2 - 4$, what is the value of $a$?"...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $a,b,c$ satisfy the system of equations \\begin{align*}b + c &= 12-3a \\\\\na+c &= -14 - 3b \\\\\na+b &= ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of all values of $y$ for which the expression $\\frac{y+6}{y^2-5y+4}$ is undefined?" } ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Convert $1011001_2$ to base 4." } ] }, { "role": "assistant", "content": [ { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jimmy's father receives 20 emails a day. Halfway through April, he subscribed to a news channel that sent 5 m...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Reynald is the head of the varsity department, and he bought 145 balls. Twenty were soccer balls. There were ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Henry, John and Leo collected some seashells from the beach. Henry collected 11, Paul 24. If they initially c...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A number $n$ has $3$ divisors. How many divisors does $n^2$ have?" } ] }, { "role": "assist...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A triangular region is bounded by the two coordinate axes and the line given by the equation $2x + y = 6$. Wh...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $f(x) = ax+b$, where $a$ and $b$ are real constants, and $g(x) = 2x - 5$. Suppose that for all $x$, it is...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In a single-elimination tournament, each game is between two players. Only the winner of each game advances t...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a,$ $b,$ $c$ be distinct integers, and let $\\omega$ be a complex number such that $\\omega^3 = 1$ and $...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The ratio of boys to girls in a classroom is 3:5. If there are 4 more girls than boys, how many students are ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Felicity and Adhira took separate trips. Felicity used 5 less gallons of gas than four times the number of ga...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tom and Elizabeth have a competition to climb a hill. Elizabeth takes 30 minutes to climb the hill. Tom takes...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find an ordered pair $(u,v)$ that solves the system: \\begin{align*} 5u &= -7 - 2v,\\\\ 3u &= 4v - 25 \\end{a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On a Sunday morning, Josephine sold milk in the farm stall. The buyers brought their containers. She filled t...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At the Boisjoli farm, there is a chicken coop where 270 hens and 3 roosters live. Every morning, around 8 a.m...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On a $12$-hour clock, an elapsed time of four hours looks the same as an elapsed time of $16$ hours. Because ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Evaluate $(x-a+3)$ if the value of $x$ is $(a+7)$." } ] }, { "role": "assistant", "cont...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that $f(x)=\\frac{1}{2x+b}$. For what value of $b$ does $f^{-1}(x)=\\frac{1-2x}{2x}$?" } ] ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that the number $\\sqrt{2700} - 37$ can be expressed in the form $(\\sqrt a - b)^3,$ where $a$ and $b...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There were 10 snowflakes at first. It snowed an additional 4 snowflakes every 5 minutes. How many minutes pas...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the equation $|x-7| -3 = -2$, what is the product of all possible values of $x$?" } ] }, { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A piece of cheese is located at $(12,10)$ in a coordinate plane. A mouse is at $(4,-2)$ and is running up ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A garden store sells packages of pumpkin seeds for $2.50, tomato seeds for $1.50, and chili pepper seeds for ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Edward the plumber is replacing a pipe in a bathroom wall. He needs to use 40 feet of copper pipe to complet...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sum of the first and third of three consecutive integers is 118. What is the value of the second integer?...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that $wz = 12-8i$, and $|w| = \\sqrt{13}$. What is $|z|$?" } ] }, { "role": "assis...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Steve is 5'6\". He grows 6 inches. How tall is he in inches?" } ] }, { "role": "assistant...