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": "Let $a$ and $b$ be the roots of $k(x^2 - x) + x + 5 = 0.$ Let $k_1$ and $k_2$ be the values of $k$ for which...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "An archer needs to practice. He intends to shoot 200 shots 4 days a week. He is able to recover 20% of his ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Mr. McNeely takes a register of the total number of students present in class every day. On a particular week...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Barbie and Bruno have a pile of 144 coconuts that they need to move from one side of their yard to the other ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $\\frac{1}{x} + \\frac{1}{y} = 3$ and $\\frac{1}{x} - \\frac{1}{y} = -7$ what is the value of $x + y$? Exp...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the least common multiple of 6, 8, and 10?" } ] }, { "role": "assistant", "cont...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many paths are there from $A$ to $B$, if every step must be up or to the right?[asy]size(4cm,4cm);int w=6...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Yanna bought ten shirts at $5 each and three pairs of sandals at $3 each. How much change did she get back i...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A family had 10 eggs, but the mother used 5 of them to make an omelet. Then, 2 chickens laid 3 eggs each. How...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the equation of the oblique asymptote of the graph of $\\frac{2x^2+7x+10}{2x+3}$?\n\nEnter your answe...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Every 5 months, Hal has to replace the batteries in his calculator. He changed them the first time in May. In...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Zoe ate a snack of 12 strawberries and 6 ounces of yogurt. If strawberries have 4 calories each and yogurt ha...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A certain tree was 100 meters tall at the end of 2017. It will grow 10% more than its previous height each ye...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Given that $a$ and $b$ are positive integers and that $a+b=24$, what is the value of $ab$ if $2ab + 10a = 3b ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the quadratic polynomial $p(x)$ such that $p(-2) = 13,$ $p(1) = -2,$ and $p(3) = 8.$" } ] },...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The graphs of $2y + x + 3 = 0$ and $3y + ax + 2 = 0$ are perpendicular. Solve for $a.$" } ] }, ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tim does 100 tasks a day. They each pay $1.2. If he works 6 days a week how much does he make a week?" ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ryosuke is picking up his friend from work. The odometer reads 74,568 when he picks his friend up, and it rea...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the matrix $\\mathbf{M}$ such that\n\\[\\mathbf{M} \\begin{pmatrix} 1 & -4 \\\\ 3 & -2 \\end{pmatrix} = ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At Sunshine Orchard, there are 12 more than three times the number of pumpkins at Moonglow Orchard. If Moongl...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There were sweets on the table. Jack came and took half of all the candies and 4 more candies. Then Paul came...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The mayor commissioned two artists to paint 50 murals around the city. Once the work was completed, Celina wa...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lyka wants to buy a smartphone worth $160 but she only has $40 at the moment. She plans to save an equal amou...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Addilynn went to the grocery store and bought six dozen eggs for use in her house. After two weeks, she used ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Bert fills out the daily crossword puzzle in the newspaper every day. He uses up a pencil to fill out the puz...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On an indoor circular track of circumference 50 feet, Joneal starts at point $S$, runs in a counterclockwise ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If it takes 20 minutes to paint a house, how many houses can you paint in 3 hours?" } ] }, { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $\\frac{2013^3-2 \\cdot 2013^2 \\cdot 2014+3 \\cdot 2013 \\cdot 2014^2-2014^3+1}{2013 \\...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Janice's office is on the third floor, and she has to walk up 3 flights of stairs to get to her office. In a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "James earns $20 an hour while working at his main job. He earns 20% less while working his second job. He w...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $x^2+y^2-z^2+2xy$ when $x=-3$, $y=5$, and $z=-4$?" } ] }, { "role": "a...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find $325_{8}-237_{8}$. Express your answer in base $8$." } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The matrix for reflecting over a certain line $\\ell,$ which passes through the origin, is given by\n\\[\\beg...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A park has three colors of flowering crepe myrtle trees planted: red, white, and pink. When they bloom, a thi...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Brenda bakes 20 cakes a day. She does this for 9 days and then sells half of the cakes. How many cakes are le...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the units digit of $3^{2004}$?" } ] }, { "role": "assistant", "content": [ ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The graph shows the birth month of 100 famous Americans. What percent of these people have March as their bir...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The slant height of a cone is 13 cm, and the height from the vertex to the center of the base is 12 cm. What ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $C$ be the circle with equation $x^2+12y+57=-y^2-10x$. If $(a,b)$ is the center of $C$ and $r$ is its rad...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Five percent of the 300 senior students got a full merit college scholarship and ten percent of them got a ha...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lizzy has to ship 540 pounds of fish that are packed into 30-pound crates. If the shipping cost of each crate...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Dan's skateboarding helmet has ten more craters than Daniel's ski helmet. Rin's snorkel helmet has 15 more cr...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the smallest integer $b > 3$ for which the base $b$ number $23_b$ is a perfect square?" } ]...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define the operation $\\S$ as follows: $a\\,\\S\\, b=3a+5b$. What is the value of $7\\,\\S\\,2$?" } ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the domain of $y=\\dfrac{x^3-27}{x+27}$? (Express your answer using interval notation.)" } ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the product of all positive integral values of $n$ such that $n^2-35n+306= p$ for some prime number $p$....
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ray has 175 cents in nickels. Ray gives 30 cents to Peter, and he gives twice as many cents to Randi as he ga...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a_1 , a_2 , \\dots$ be a sequence for which $a_1=2$ , $a_2=3$, and $a_n=\\frac{a_{n-1}}{a_{n-2}}$ for e...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $\\left(1 - \\frac{1}{2}\\right)\\left(1-\\frac{1}{3}\\right)\\left(1-\\frac{1}{4}\\righ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the remainder when $1^3 + 2^3 + 3^3 + \\dots + 100^3$ is divided by 6." } ] }, { "role...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Determine the sum of all prime numbers $p$ for which there exists no integer solution in $x$ to the congruenc...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $13^{3n}=\\left(\\frac{1}{13}\\right)^{n-24}$, find $n$." } ] }, { "role": "assistant", ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A bowl contains 10 jellybeans (four red, one blue and five white). If you pick three jellybeans from the bowl...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $\\frac{6! + 7!}{5!}$" } ] }, { "role": "assistant", "content": [ { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jessica was trying to win a gift card to her favorite store. To win, she had to guess the total number of re...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Determine the value of\n\\[2002 + \\frac{1}{2} \\left( 2001 + \\frac{1}{2} \\left( 2000 + \\dots + \\frac{1}{...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is $(5^{-2})^0 + (5^0)^3$?" } ] }, { "role": "assistant", "content": [ { ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the first ten positive multiples of $13$?" } ] }, { "role": "assistant",...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Two fair, six-sided dice are rolled. What is the probability that the sum of the two numbers showing is less...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A set of three numbers has both a mean and median equal to 4. If the smallest number in the set is 1, what is...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the complex plane, the line segment with end-points $-11 + 3i$ and $3 - 7i$ is plotted in the complex plan...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The expression $\\cos x + \\cos 3x + \\cos 7x + \\cos 9x$ can be written in the equivalent form\n\\[a \\cos b...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At the family reunion, everyone ate too much food and gained weight. Orlando gained 5 pounds. Jose gained t...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The average of the numbers 23 and $x$ is 27. What is the positive difference between 23 and $x$? (Recall that...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is r...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "One and a half increase in the productivity in Tutuwanas saw-mill this year was due to the Albaszu machine's ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In regular pentagon $ABCDE$, diagonal $AC$ is drawn, as shown. Given that each interior angle of a regular pe...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Oleg is an event organizer. He is organizing an event with 80 guests where 40 of them are men, half the numbe...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In right triangle $PQR$, we have $\\angle Q = \\angle R$ and $QR = 6\\sqrt{2}$. What is the area of $\\trian...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The matrix\n\\[\\begin{pmatrix} a & 3 \\\\ -8 & d \\end{pmatrix}\\]is its own inverse, for some real numbers ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Rene has three times as many dolls as her sister, while her sister has two more dolls than their grandmother....
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Hannah is trying to figure out how much she'll get paid this week. She makes $30/hour and works 18 hours per ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Nancy and Rose are making bracelets, and there are eight beads in each bracelet. Nancy has 40 metal beads an...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sequence $\\{a_n\\}$ satisfies $a_1 = 1$ and $5^{a_{n + 1} - a_n} - 1 = \\frac {1}{n + \\frac {2}{3}}$ fo...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Janina spends $30 each day for rent and uses $12 worth of supplies daily to run her pancake stand. If she sel...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There is a unique polynomial $P(x)$ of degree $4$ with rational coefficients and leading coefficient $1$ whic...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the cross product of $\\begin{pmatrix} 5 \\\\ 2 \\\\ -6 \\end{pmatrix}$ and $\\begin{pmatrix} 1 \\\\ 1 \...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the coefficient of $x^{70}$ in the expansion of\n\\[(x - 1)(x^2 - 2)(x^3 - 3) \\dotsm (x^{11} - 11)(x^{1...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get?" ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jake and Penny are hunting snakes. Jake's snake is 12 inches longer than Jenny's snake. If the two snakes hav...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Abigail thinks she has some lost some money out of her purse. She had $11 in her purse at the start of the da...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Given that $2^x+ 2^x+ 2^x+ 2^x= 512$, what is the value of $x$?" } ] }, { "role": "assistan...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Taylor and his friends decide to bring their pets together for a walk. 3 of his friends come first, each havi...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Andrew works in a company that provides a generous vacation allotment: for every 10 days worked, you get 1 va...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "To transmit a positive integer less than 1000, the Networked Number Node offers two options.\n\nOption 1. Pay...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sum of all the positive factors of integer $x$ is 24. If one of the factors is 3, what is the value of $x...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A zoo is arranging the layout of its animal enclosures. There are 4 tiger enclosures in a row and behind each...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 285 sweets in the bowl. If 49 of the sweets are red and 59 of the sweets are green, how many of the...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $\\theta$ be an angle such that $\\sin 2 \\theta = \\frac{1}{3}.$ Compute $\\sin^6 \\theta + \\cos^6 \\t...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In Ms. Smith's class, each student averages one day absent out of thirty. What is the probability that out of...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a,$ $b,$ $c$ be a three-term arithmetic series where all the terms are positive, such that $abc = 64.$ ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many integers (positive and negative) are divisors of 20?" } ] }, { "role": "assistant"...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John reels in 3 crab baskets a week. Each basket holds 4 crabs. He collects crabs twice a week. Each crab ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the diagram, $D$ and $E$ are the midpoints of $\\overline{AB}$ and $\\overline{BC}$ respectively. Determi...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A bottled water company has designed a new cup for its dispenser. The cup will be a right circular cone with ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Nicole has 4 fish tanks. The first two tanks need 8 gallons of water each and the other two need 2 fewer gall...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Two athletes decided to compete to see who had the best jumping ability. They were each going to do the long ...
[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Vanessa has decided to sell some of her clothes to make pocket money, offering a standard price for each type...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a$ and $b$ be the roots of $k(x^2 - x) + x + 5 = 0.$ Let $k_1$ and $k_2$ be the values of $k$ for which...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "An archer needs to practice. He intends to shoot 200 shots 4 days a week. He is able to recover 20% of his ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Mr. McNeely takes a register of the total number of students present in class every day. On a particular week...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Barbie and Bruno have a pile of 144 coconuts that they need to move from one side of their yard to the other ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $\\frac{1}{x} + \\frac{1}{y} = 3$ and $\\frac{1}{x} - \\frac{1}{y} = -7$ what is the value of $x + y$? Exp...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the least common multiple of 6, 8, and 10?" } ] }, { "role": "assistant", "cont...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many paths are there from $A$ to $B$, if every step must be up or to the right?[asy]size(4cm,4cm);int w=6...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Yanna bought ten shirts at $5 each and three pairs of sandals at $3 each. How much change did she get back i...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A family had 10 eggs, but the mother used 5 of them to make an omelet. Then, 2 chickens laid 3 eggs each. How...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the equation of the oblique asymptote of the graph of $\\frac{2x^2+7x+10}{2x+3}$?\n\nEnter your answe...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Every 5 months, Hal has to replace the batteries in his calculator. He changed them the first time in May. In...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Zoe ate a snack of 12 strawberries and 6 ounces of yogurt. If strawberries have 4 calories each and yogurt ha...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A certain tree was 100 meters tall at the end of 2017. It will grow 10% more than its previous height each ye...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Given that $a$ and $b$ are positive integers and that $a+b=24$, what is the value of $ab$ if $2ab + 10a = 3b ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the quadratic polynomial $p(x)$ such that $p(-2) = 13,$ $p(1) = -2,$ and $p(3) = 8.$" } ] },...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The graphs of $2y + x + 3 = 0$ and $3y + ax + 2 = 0$ are perpendicular. Solve for $a.$" } ] }, ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Tim does 100 tasks a day. They each pay $1.2. If he works 6 days a week how much does he make a week?" ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ryosuke is picking up his friend from work. The odometer reads 74,568 when he picks his friend up, and it rea...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the matrix $\\mathbf{M}$ such that\n\\[\\mathbf{M} \\begin{pmatrix} 1 & -4 \\\\ 3 & -2 \\end{pmatrix} = ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At Sunshine Orchard, there are 12 more than three times the number of pumpkins at Moonglow Orchard. If Moongl...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There were sweets on the table. Jack came and took half of all the candies and 4 more candies. Then Paul came...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The mayor commissioned two artists to paint 50 murals around the city. Once the work was completed, Celina wa...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lyka wants to buy a smartphone worth $160 but she only has $40 at the moment. She plans to save an equal amou...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Addilynn went to the grocery store and bought six dozen eggs for use in her house. After two weeks, she used ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Bert fills out the daily crossword puzzle in the newspaper every day. He uses up a pencil to fill out the puz...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "On an indoor circular track of circumference 50 feet, Joneal starts at point $S$, runs in a counterclockwise ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If it takes 20 minutes to paint a house, how many houses can you paint in 3 hours?" } ] }, { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $\\frac{2013^3-2 \\cdot 2013^2 \\cdot 2014+3 \\cdot 2013 \\cdot 2014^2-2014^3+1}{2013 \\...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Janice's office is on the third floor, and she has to walk up 3 flights of stairs to get to her office. In a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "James earns $20 an hour while working at his main job. He earns 20% less while working his second job. He w...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $x^2+y^2-z^2+2xy$ when $x=-3$, $y=5$, and $z=-4$?" } ] }, { "role": "a...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find $325_{8}-237_{8}$. Express your answer in base $8$." } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The matrix for reflecting over a certain line $\\ell,$ which passes through the origin, is given by\n\\[\\beg...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A park has three colors of flowering crepe myrtle trees planted: red, white, and pink. When they bloom, a thi...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Brenda bakes 20 cakes a day. She does this for 9 days and then sells half of the cakes. How many cakes are le...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the units digit of $3^{2004}$?" } ] }, { "role": "assistant", "content": [ ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The graph shows the birth month of 100 famous Americans. What percent of these people have March as their bir...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The slant height of a cone is 13 cm, and the height from the vertex to the center of the base is 12 cm. What ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $C$ be the circle with equation $x^2+12y+57=-y^2-10x$. If $(a,b)$ is the center of $C$ and $r$ is its rad...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Five percent of the 300 senior students got a full merit college scholarship and ten percent of them got a ha...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Lizzy has to ship 540 pounds of fish that are packed into 30-pound crates. If the shipping cost of each crate...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Dan's skateboarding helmet has ten more craters than Daniel's ski helmet. Rin's snorkel helmet has 15 more cr...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the smallest integer $b > 3$ for which the base $b$ number $23_b$ is a perfect square?" } ]...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Define the operation $\\S$ as follows: $a\\,\\S\\, b=3a+5b$. What is the value of $7\\,\\S\\,2$?" } ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the domain of $y=\\dfrac{x^3-27}{x+27}$? (Express your answer using interval notation.)" } ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the product of all positive integral values of $n$ such that $n^2-35n+306= p$ for some prime number $p$....

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Ray has 175 cents in nickels. Ray gives 30 cents to Peter, and he gives twice as many cents to Randi as he ga...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a_1 , a_2 , \\dots$ be a sequence for which $a_1=2$ , $a_2=3$, and $a_n=\\frac{a_{n-1}}{a_{n-2}}$ for e...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the value of $\\left(1 - \\frac{1}{2}\\right)\\left(1-\\frac{1}{3}\\right)\\left(1-\\frac{1}{4}\\righ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the remainder when $1^3 + 2^3 + 3^3 + \\dots + 100^3$ is divided by 6." } ] }, { "role...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Determine the sum of all prime numbers $p$ for which there exists no integer solution in $x$ to the congruenc...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "If $13^{3n}=\\left(\\frac{1}{13}\\right)^{n-24}$, find $n$." } ] }, { "role": "assistant", ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A bowl contains 10 jellybeans (four red, one blue and five white). If you pick three jellybeans from the bowl...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Compute $\\frac{6! + 7!}{5!}$" } ] }, { "role": "assistant", "content": [ { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jessica was trying to win a gift card to her favorite store. To win, she had to guess the total number of re...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Determine the value of\n\\[2002 + \\frac{1}{2} \\left( 2001 + \\frac{1}{2} \\left( 2000 + \\dots + \\frac{1}{...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is $(5^{-2})^0 + (5^0)^3$?" } ] }, { "role": "assistant", "content": [ { ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the sum of the first ten positive multiples of $13$?" } ] }, { "role": "assistant",...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Two fair, six-sided dice are rolled. What is the probability that the sum of the two numbers showing is less...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A set of three numbers has both a mean and median equal to 4. If the smallest number in the set is 1, what is...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the complex plane, the line segment with end-points $-11 + 3i$ and $3 - 7i$ is plotted in the complex plan...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The expression $\\cos x + \\cos 3x + \\cos 7x + \\cos 9x$ can be written in the equivalent form\n\\[a \\cos b...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "At the family reunion, everyone ate too much food and gained weight. Orlando gained 5 pounds. Jose gained t...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The average of the numbers 23 and $x$ is 27. What is the positive difference between 23 and $x$? (Recall that...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is r...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "One and a half increase in the productivity in Tutuwanas saw-mill this year was due to the Albaszu machine's ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In regular pentagon $ABCDE$, diagonal $AC$ is drawn, as shown. Given that each interior angle of a regular pe...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Oleg is an event organizer. He is organizing an event with 80 guests where 40 of them are men, half the numbe...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In right triangle $PQR$, we have $\\angle Q = \\angle R$ and $QR = 6\\sqrt{2}$. What is the area of $\\trian...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The matrix\n\\[\\begin{pmatrix} a & 3 \\\\ -8 & d \\end{pmatrix}\\]is its own inverse, for some real numbers ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Rene has three times as many dolls as her sister, while her sister has two more dolls than their grandmother....

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Hannah is trying to figure out how much she'll get paid this week. She makes $30/hour and works 18 hours per ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Nancy and Rose are making bracelets, and there are eight beads in each bracelet. Nancy has 40 metal beads an...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sequence $\\{a_n\\}$ satisfies $a_1 = 1$ and $5^{a_{n + 1} - a_n} - 1 = \\frac {1}{n + \\frac {2}{3}}$ fo...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Janina spends $30 each day for rent and uses $12 worth of supplies daily to run her pancake stand. If she sel...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There is a unique polynomial $P(x)$ of degree $4$ with rational coefficients and leading coefficient $1$ whic...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the cross product of $\\begin{pmatrix} 5 \\\\ 2 \\\\ -6 \\end{pmatrix}$ and $\\begin{pmatrix} 1 \\\\ 1 \...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Find the coefficient of $x^{70}$ in the expansion of\n\\[(x - 1)(x^2 - 2)(x^3 - 3) \\dotsm (x^{11} - 11)(x^{1...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get?" ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Jake and Penny are hunting snakes. Jake's snake is 12 inches longer than Jenny's snake. If the two snakes hav...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Abigail thinks she has some lost some money out of her purse. She had $11 in her purse at the start of the da...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Given that $2^x+ 2^x+ 2^x+ 2^x= 512$, what is the value of $x$?" } ] }, { "role": "assistan...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Taylor and his friends decide to bring their pets together for a walk. 3 of his friends come first, each havi...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Andrew works in a company that provides a generous vacation allotment: for every 10 days worked, you get 1 va...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "To transmit a positive integer less than 1000, the Networked Number Node offers two options.\n\nOption 1. Pay...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "The sum of all the positive factors of integer $x$ is 24. If one of the factors is 3, what is the value of $x...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A zoo is arranging the layout of its animal enclosures. There are 4 tiger enclosures in a row and behind each...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "There are 285 sweets in the bowl. If 49 of the sweets are red and 59 of the sweets are green, how many of the...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $\\theta$ be an angle such that $\\sin 2 \\theta = \\frac{1}{3}.$ Compute $\\sin^6 \\theta + \\cos^6 \\t...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In Ms. Smith's class, each student averages one day absent out of thirty. What is the probability that out of...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Let $a,$ $b,$ $c$ be a three-term arithmetic series where all the terms are positive, such that $abc = 64.$ ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "How many integers (positive and negative) are divisors of 20?" } ] }, { "role": "assistant"...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "John reels in 3 crab baskets a week. Each basket holds 4 crabs. He collects crabs twice a week. Each crab ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "In the diagram, $D$ and $E$ are the midpoints of $\\overline{AB}$ and $\\overline{BC}$ respectively. Determi...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "A bottled water company has designed a new cup for its dispenser. The cup will be a right circular cone with ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Nicole has 4 fish tanks. The first two tanks need 8 gallons of water each and the other two need 2 fewer gall...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Two athletes decided to compete to see who had the best jumping ability. They were each going to do the long ...

[ { "role": "system", "content": [ { "type": "text", "content": "" } ] }, { "role": "user", "content": [ { "type": "text", "content": "Vanessa has decided to sell some of her clothes to make pocket money, offering a standard price for each type...