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

messages listlengths 3 3
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John spent 3 years of his life exploring the jungle. He then spent half as much time writing up notes about ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Erica lives near a lake where most locals sell fish as their main source of income, earning $20 per kg of fis...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Elisa and her two friends went out to dinner. Each of them ordered a meal worth $10. Afterwards, they each ha...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What fraction of $\\frac{1}{2}$ is $\\frac{1}{7}$?" } ] }, { "role": "assistant", "cont...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Thirteen blue and six green hexagonal tiles were used to create the figure below. If a new figure is created ...
[ { "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": "Find the center of the circle with equation $x^2 - 2x + y^2 - 4y - 28 = 0$." } ] }, { "role...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At lunch, $60\\%$ of the students selected soda while $20\\%$ selected milk. If 72 students selected soda, ho...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Evaluate\n\\[\\begin{vmatrix} y + 1 & y & y \\\\ y & y + 1 & y \\\\ y & y & y + 1 \\end{vmatrix}.\\]" }...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $m$ and $n$ be any two odd numbers, with $n$ less than $m$. The largest integer which divides all possibl...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jim decides to buy mayo in bulk. He can buy 1 gallon of mayo at Costco for 8 dollars. At the normal store, ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Our club has 20 members, 10 boys and 10 girls. In how many ways can we choose a president and a vice-preside...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the greatest common divisor of 30 and 81 and the least common multiple of 36 and 12?" ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Marianne was 20 years old when Bella was 8 years old. How old will Marianne be when Bella turns 18?" } ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the squares of the coefficients of $4(x^4 + 3x^2 + 1)$?" } ] }, { "role"...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Solve for $m$: $(m-4)^3 = \\left(\\frac 18\\right)^{-1}$." } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the least three-digit positive integer that has 2, 5 and 7 as factors?" } ] }, { "r...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Irene earns $500 if she works for 40 hours a week and gets an extra $20 for every hour of overtime. If she wo...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A cleaning company produces two sanitizer sprays. One spray kills 50% of germs, and another spray kills 25% o...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "You can buy 4 apples or 1 watermelon for the same price. You bought 36 fruits evenly split between oranges, a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define the operation $a\\nabla b = 2 + b^a$. What is the value of $(1\\nabla 2) \\nabla 3$?" } ] ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Simplify $2y + 3y+4y$." } ] }, { "role": "assistant", "content": [ { "typ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Kenton watched 2000 adult men and women board a cruise ship. Half of the adults were women. If 20$\\%$ of the...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lulu has a quadratic of the form $x^2+bx+44$, where $b$ is a specific positive number. Using her knowledge of...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The area of the floor in a square room is 225 square feet. The homeowners plan to cover the floor with rows o...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A tree on a farm has 10 branches. Each branch has 40 sub-branches with 60 leaves each. If the total number of...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received ha...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The vertical drop of a roller coaster is the largest difference in height between any high point and the next...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the number of functions $f : \\mathbb{R} \\to \\mathbb{R}$ such that\n\\[f(x + f(y)) = x + y\\]for all r...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 2,000 kids in camp. If half of the kids are going to soccer camp, and 1/4 of the kids going to socc...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A particular novel contains $40,\\!000$ words. If the author completed the novel in $80$ hours, on average ho...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In how many ways can four people sit in a row of five chairs?" } ] }, { "role": "assistant"...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Natalie's sister had 8 small diaries in her locker. Last summer she bought double the number of diaries she h...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Hallie borrows a book from the library. She reads the entire book in four days. She read 63 pages the first d...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Rosie pays for a $.44 piece of candy with a $1 bill. If the cashier gives her the smallest number of coins po...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jeannie hikes the 12 miles to Mount Overlook at a pace of 4 miles per hour, and then returns at a pace of 6 m...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is $\\dbinom{n}{1}$ for any positive integer $n$?" } ] }, { "role": "assistant", "...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the distance between the points $(-5,-2)$ and $(7,3)$." } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that $a$ and $b$ are nonzero real numbers, and that the equation $x^2+ax+b=0$ has solutions $a$ and $...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The bacteria in a jar triple every 20 seconds. After three minutes, there are 275,562 bacteria in the jar. Ho...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are two babysitters named Mila and Agnes. Mila makes $10 an hour while Agnes makes $15 an hour. Agnes w...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many cheese balls are in a 35oz barrel if the 24oz barrel has 60 servings and each serving has 12 cheese ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Benjamin is tracking how many miles he walks in a week. He walks to work and home five days a week, walks his...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the diagram, the square has a perimeter of $48$ and the triangle has a height of $48.$ If the square and t...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Rodney has 35 dollars more than Ian. Ian has half as much money as Jessica has. If Jessica has 100 dollars, h...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The $\\$4.55$ in Carol's piggy bank consists of quarters and nickels. There are seven more nickels than quart...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many units long is a segment whose endpoints are (2,3) and (7,15)?" } ] }, { "role": "a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Adrian has the choice between two boxes of contacts. One has 50 contacts for $25, and the other has 99 conta...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Millie, Monica, and Marius are taking subjects for school. Millie takes three more subjects than Marius, who ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $f(x)=f(2-x)$ for all $x$, then what line is necessarily an axis of symmetry of the graph of $y=f(x)$? (Gi...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the intersection of the lines given by $2y=-x+3$ and $-y=5x+1$? Enter the answer as an ordered pair....
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $p(x) = 2x - 7$ and $q(x) = 3x - b$. If $p(q(4)) = 7$, what is $b$?" } ] }, { "role": ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 28 students in a classroom. Half of them have 5 notebooks each and the other half have 3 notebooks ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John had $20. He spent 1/5 of his money on snacks and 3/4 of the remaining money on necessities. How much is ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "James wants to build a 16-foot by 20-foot quilt. He uses patches that are each 4 square feet. The first 10 ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tim is stuck in traffic for twice as long as he was driving. He drove 5 hours. How long was the trip?" ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jose invested $\\$50,\\!000$ for $2$ years at an annual interest rate of $4$ percent compounded yearly. Patri...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of $\\left(\\dfrac{1}{3}\\right) + \\left(\\dfrac{1}{3}\\right)^2 + \\left(\\dfrac{1}{3}\\rig...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At the pet shop, there were 3 birds, 5 dogs, 4 snakes, and 1 spider for sale. How many legs were there in tot...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If Patty's dress was $10 more than Ida's dress, and Ida's dress was $30 more than Jean's dress, and Jean's dr...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many digits does the smallest repeating block in the decimal expansion of $\\frac{5}{7}$ contain?" ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?" } ] }...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A divisor of a number is a proper divisor if it is not equal to the number. What is the sum of the proper div...
[ { "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": "For each positive integer $n$, let $f(n)$ be the sum of the digits in the base-four representation of $n$ and...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $f(x) = 5x-4$, what is $f(f(f(2)))$?" } ] }, { "role": "assistant", "content": [ ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red buttons...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Malcolm can run a race at a speed of 6 minutes per mile, while Joshua runs at 8 minutes per mile. In a 10-mil...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the largest divisor of 342 that is also a factor of 285?" } ] }, { "role": "assista...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define $A\\star B$ as $A\\star B = \\frac{(A+B)}{3}$. What is the value of $(2\\star 10) \\star 5$?" } ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Mark collects money for the homeless. He visits 20 households a day for 5 days and half of those households ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the sum of all positive integers $n$ such that $1.2n-4.4<5.2$." } ] }, { "role": "assi...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The electricity price in Coco's town is $0.10 per kW. Coco's new oven has a consumption rate of 2.4 kWh (kilo...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Elysse can carry 3 bags of groceries into her home with each trip from the car. Her brother can carry the sam...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $a\\ast b = 3a+4b-ab$, what is the value of $5\\ast2$?" } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the residue of $182\\cdot 12 - 15\\cdot 7 + 3\\pmod{14}$." } ] }, { "role": "assistant...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There's a Bobbit worm hiding in the bottom of James' aquarium. Every day it eats 2 fish. After two weeks, Jam...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Bill thought he bought 70 chihuahuas, but some of them turned out to be rats. If the number of rats was 6 tim...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "It will take Richard and Sarah 3 years to save enough for a down payment on a house at their current rates. I...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the minimum value of\n\\[\\sin^4 x + \\frac{3}{2} \\cos^4 x,\\]as $x$ varies over all real numbers." ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $\\begin{pmatrix} \\sqrt{3} & -1 \\\\ 1 & \\sqrt{3} \\end{pmatrix}^6.$" } ] }, { "r...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many factors of 8000 are perfect squares?" } ] }, { "role": "assistant", "content":...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Consider the given functions: $$\\begin{array}{ccc}\nf(x) & = & 5x^2 - \\frac{1}{x}+ 3\\\\\ng(x) & = & x^2-k\...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There were 180 apples in each crate. 12 such crates of apples were delivered to a factory. 160 apples were ro...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose $f(x) = \\frac{x}{5} + 3$ and $g(x) = 4-x$. If $f(g(a)) = 5$, find $a$." } ] }, { "...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $i^{600} + i^{599} + \\cdots + i + 1$, where $i^2=-1$." } ] }, { "role": "assistant...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Three cats sat on a fence, meowing at the moon. The first cat meowed 3 times per minute. The second cat meo...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The length of a rectangle is increased by $25\\%$, but the width of the rectangle is decreased to keep the ar...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jimmy wants to play in the inflatable swimming pool in his backyard. The swimming pool is empty and the garag...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ryan is considering buying a new multivitamin brand. Each pill has 50 mg of Vitamin A in it. The recommende...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A circular garden is enlarged so that the new diameter is twice the old diameter. What is the ratio of the or...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "For a fundraiser, Nellie needs to sell 45 rolls of gift wrap. So far, she has sold 1 roll to her grandmother,...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $x$ for which $\|3x+5\|$ is not positive? Express your answer as a common fraction." ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The number of coronavirus cases in a certain country was 300 infections per day during the first wave. Howeve...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $p(x) = x^2 + bx + c,$ where $b$ and $c$ are integers. If $p(x)$ is factor of both $x^4 + 6x^2 + 25$ and...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the coordinate plane, the curve $xy = 1$ intersects a circle at four points, three of which are $\\left( 2...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A person borrowed an amount of money for a year at an interest rate of 12%. If the total interest is $1500, w...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Javier is selling donuts to raise money for a new game. He wants to raise $96. He buys each dozen donuts for ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John spent 3 years of his life exploring the jungle. He then spent half as much time writing up notes about ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Erica lives near a lake where most locals sell fish as their main source of income, earning $20 per kg of fis...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Elisa and her two friends went out to dinner. Each of them ordered a meal worth $10. Afterwards, they each ha...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What fraction of $\\frac{1}{2}$ is $\\frac{1}{7}$?" } ] }, { "role": "assistant", "cont...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Thirteen blue and six green hexagonal tiles were used to create the figure below. If a new figure is created ...

[ { "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": "Find the center of the circle with equation $x^2 - 2x + y^2 - 4y - 28 = 0$." } ] }, { "role...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At lunch, $60\\%$ of the students selected soda while $20\\%$ selected milk. If 72 students selected soda, ho...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Evaluate\n\\[\\begin{vmatrix} y + 1 & y & y \\\\ y & y + 1 & y \\\\ y & y & y + 1 \\end{vmatrix}.\\]" }...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $m$ and $n$ be any two odd numbers, with $n$ less than $m$. The largest integer which divides all possibl...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jim decides to buy mayo in bulk. He can buy 1 gallon of mayo at Costco for 8 dollars. At the normal store, ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Our club has 20 members, 10 boys and 10 girls. In how many ways can we choose a president and a vice-preside...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the greatest common divisor of 30 and 81 and the least common multiple of 36 and 12?" ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Marianne was 20 years old when Bella was 8 years old. How old will Marianne be when Bella turns 18?" } ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the squares of the coefficients of $4(x^4 + 3x^2 + 1)$?" } ] }, { "role"...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Solve for $m$: $(m-4)^3 = \\left(\\frac 18\\right)^{-1}$." } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the least three-digit positive integer that has 2, 5 and 7 as factors?" } ] }, { "r...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Irene earns $500 if she works for 40 hours a week and gets an extra $20 for every hour of overtime. If she wo...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A cleaning company produces two sanitizer sprays. One spray kills 50% of germs, and another spray kills 25% o...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "You can buy 4 apples or 1 watermelon for the same price. You bought 36 fruits evenly split between oranges, a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define the operation $a\\nabla b = 2 + b^a$. What is the value of $(1\\nabla 2) \\nabla 3$?" } ] ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Simplify $2y + 3y+4y$." } ] }, { "role": "assistant", "content": [ { "typ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Kenton watched 2000 adult men and women board a cruise ship. Half of the adults were women. If 20$\\%$ of the...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lulu has a quadratic of the form $x^2+bx+44$, where $b$ is a specific positive number. Using her knowledge of...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The area of the floor in a square room is 225 square feet. The homeowners plan to cover the floor with rows o...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A tree on a farm has 10 branches. Each branch has 40 sub-branches with 60 leaves each. If the total number of...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received ha...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The vertical drop of a roller coaster is the largest difference in height between any high point and the next...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the number of functions $f : \\mathbb{R} \\to \\mathbb{R}$ such that\n\\[f(x + f(y)) = x + y\\]for all r...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 2,000 kids in camp. If half of the kids are going to soccer camp, and 1/4 of the kids going to socc...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A particular novel contains $40,\\!000$ words. If the author completed the novel in $80$ hours, on average ho...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In how many ways can four people sit in a row of five chairs?" } ] }, { "role": "assistant"...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Natalie's sister had 8 small diaries in her locker. Last summer she bought double the number of diaries she h...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Hallie borrows a book from the library. She reads the entire book in four days. She read 63 pages the first d...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Rosie pays for a $.44 piece of candy with a $1 bill. If the cashier gives her the smallest number of coins po...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jeannie hikes the 12 miles to Mount Overlook at a pace of 4 miles per hour, and then returns at a pace of 6 m...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is $\\dbinom{n}{1}$ for any positive integer $n$?" } ] }, { "role": "assistant", "...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the distance between the points $(-5,-2)$ and $(7,3)$." } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose that $a$ and $b$ are nonzero real numbers, and that the equation $x^2+ax+b=0$ has solutions $a$ and $...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The bacteria in a jar triple every 20 seconds. After three minutes, there are 275,562 bacteria in the jar. Ho...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are two babysitters named Mila and Agnes. Mila makes $10 an hour while Agnes makes $15 an hour. Agnes w...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many cheese balls are in a 35oz barrel if the 24oz barrel has 60 servings and each serving has 12 cheese ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Benjamin is tracking how many miles he walks in a week. He walks to work and home five days a week, walks his...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the diagram, the square has a perimeter of $48$ and the triangle has a height of $48.$ If the square and t...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Rodney has 35 dollars more than Ian. Ian has half as much money as Jessica has. If Jessica has 100 dollars, h...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The $\\$4.55$ in Carol's piggy bank consists of quarters and nickels. There are seven more nickels than quart...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many units long is a segment whose endpoints are (2,3) and (7,15)?" } ] }, { "role": "a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Adrian has the choice between two boxes of contacts. One has 50 contacts for $25, and the other has 99 conta...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Millie, Monica, and Marius are taking subjects for school. Millie takes three more subjects than Marius, who ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $f(x)=f(2-x)$ for all $x$, then what line is necessarily an axis of symmetry of the graph of $y=f(x)$? (Gi...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the intersection of the lines given by $2y=-x+3$ and $-y=5x+1$? Enter the answer as an ordered pair....

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $p(x) = 2x - 7$ and $q(x) = 3x - b$. If $p(q(4)) = 7$, what is $b$?" } ] }, { "role": ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 28 students in a classroom. Half of them have 5 notebooks each and the other half have 3 notebooks ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John had $20. He spent 1/5 of his money on snacks and 3/4 of the remaining money on necessities. How much is ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "James wants to build a 16-foot by 20-foot quilt. He uses patches that are each 4 square feet. The first 10 ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tim is stuck in traffic for twice as long as he was driving. He drove 5 hours. How long was the trip?" ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jose invested $\\$50,\\!000$ for $2$ years at an annual interest rate of $4$ percent compounded yearly. Patri...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of $\\left(\\dfrac{1}{3}\\right) + \\left(\\dfrac{1}{3}\\right)^2 + \\left(\\dfrac{1}{3}\\rig...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At the pet shop, there were 3 birds, 5 dogs, 4 snakes, and 1 spider for sale. How many legs were there in tot...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If Patty's dress was $10 more than Ida's dress, and Ida's dress was $30 more than Jean's dress, and Jean's dr...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many digits does the smallest repeating block in the decimal expansion of $\\frac{5}{7}$ contain?" ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $x$ satisfies $\\frac{1}{2}-\\frac{1}{3}=\\frac{3}{x}$, then what is the value of $x$ ?" } ] }...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A divisor of a number is a proper divisor if it is not equal to the number. What is the sum of the proper div...

[ { "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": "For each positive integer $n$, let $f(n)$ be the sum of the digits in the base-four representation of $n$ and...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $f(x) = 5x-4$, what is $f(f(f(2)))$?" } ] }, { "role": "assistant", "content": [ ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red buttons...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Malcolm can run a race at a speed of 6 minutes per mile, while Joshua runs at 8 minutes per mile. In a 10-mil...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the largest divisor of 342 that is also a factor of 285?" } ] }, { "role": "assista...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define $A\\star B$ as $A\\star B = \\frac{(A+B)}{3}$. What is the value of $(2\\star 10) \\star 5$?" } ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Mark collects money for the homeless. He visits 20 households a day for 5 days and half of those households ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the sum of all positive integers $n$ such that $1.2n-4.4<5.2$." } ] }, { "role": "assi...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The electricity price in Coco's town is $0.10 per kW. Coco's new oven has a consumption rate of 2.4 kWh (kilo...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Elysse can carry 3 bags of groceries into her home with each trip from the car. Her brother can carry the sam...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $a\\ast b = 3a+4b-ab$, what is the value of $5\\ast2$?" } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the residue of $182\\cdot 12 - 15\\cdot 7 + 3\\pmod{14}$." } ] }, { "role": "assistant...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There's a Bobbit worm hiding in the bottom of James' aquarium. Every day it eats 2 fish. After two weeks, Jam...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Bill thought he bought 70 chihuahuas, but some of them turned out to be rats. If the number of rats was 6 tim...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "It will take Richard and Sarah 3 years to save enough for a down payment on a house at their current rates. I...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the minimum value of\n\\[\\sin^4 x + \\frac{3}{2} \\cos^4 x,\\]as $x$ varies over all real numbers." ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $\\begin{pmatrix} \\sqrt{3} & -1 \\\\ 1 & \\sqrt{3} \\end{pmatrix}^6.$" } ] }, { "r...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many factors of 8000 are perfect squares?" } ] }, { "role": "assistant", "content":...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Consider the given functions: $$\\begin{array}{ccc}\nf(x) & = & 5x^2 - \\frac{1}{x}+ 3\\\\\ng(x) & = & x^2-k\...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There were 180 apples in each crate. 12 such crates of apples were delivered to a factory. 160 apples were ro...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Suppose $f(x) = \\frac{x}{5} + 3$ and $g(x) = 4-x$. If $f(g(a)) = 5$, find $a$." } ] }, { "...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $i^{600} + i^{599} + \\cdots + i + 1$, where $i^2=-1$." } ] }, { "role": "assistant...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Three cats sat on a fence, meowing at the moon. The first cat meowed 3 times per minute. The second cat meo...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The length of a rectangle is increased by $25\\%$, but the width of the rectangle is decreased to keep the ar...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jimmy wants to play in the inflatable swimming pool in his backyard. The swimming pool is empty and the garag...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ryan is considering buying a new multivitamin brand. Each pill has 50 mg of Vitamin A in it. The recommende...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A circular garden is enlarged so that the new diameter is twice the old diameter. What is the ratio of the or...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "For a fundraiser, Nellie needs to sell 45 rolls of gift wrap. So far, she has sold 1 roll to her grandmother,...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $x$ for which $|3x+5|$ is not positive? Express your answer as a common fraction." ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The number of coronavirus cases in a certain country was 300 infections per day during the first wave. Howeve...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $p(x) = x^2 + bx + c,$ where $b$ and $c$ are integers. If $p(x)$ is factor of both $x^4 + 6x^2 + 25$ and...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the coordinate plane, the curve $xy = 1$ intersects a circle at four points, three of which are $\\left( 2...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A person borrowed an amount of money for a year at an interest rate of 12%. If the total interest is $1500, w...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Javier is selling donuts to raise money for a new game. He wants to raise $96. He buys each dozen donuts for ...