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"content": "Return your final response within \\boxed{}. The operation $\\otimes$ is defined for all nonzero numbers by $a\\otimes b =\\frac{a^{2}}{b}$. Determine $[(1\\otimes 2)\\otimes 3]-[1\\otimes (2\\otimes 3)]$.\n$\\text{(A)}\\ -\\frac{2}{3}\\qquad\\text{(B)}\\ -\\frac{1}{4}\\qquad\\text{(C)}\\ 0\\qquad... |
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"content": "Return your final response within \\boxed{}. Doug constructs a square window using $8$ equal-size panes of glass, as shown. The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide. In inches, what is the side length of the square ... |
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"content": "Return your final response within \\boxed{}. $P(x)$ is a polynomial of degree $3n$ such that\n\\begin{eqnarray*} P(0) = P(3) = \\cdots &=& P(3n) = 2, \\\\ P(1) = P(4) = \\cdots &=& P(3n-2) = 1, \\\\ P(2) = P(5) = \\cdots &=& P(3n-1) = 0, \\quad\\text{ and }\\\\ && P(3n+1) = 730.\\end{eqnarray*}\nD... |
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"content": "Return your final response within \\boxed{}. Let $f$ be the function defined by $f(x)=ax^2-\\sqrt{2}$ for some positive $a$. If $f(f(\\sqrt{2}))=-\\sqrt{2}$ then $a=$\n$\\text{(A) } \\frac{2-\\sqrt{2}}{2}\\quad \\text{(B) } \\frac{1}{2}\\quad \\text{(C) } 2-\\sqrt{2}\\quad \\text{(D) } \\frac{\\sq... |
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"content": "Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May?",
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"content": "Natalia sold 48/2 = <<48/2=24>>24 clips in May.\nNatalia sold 48+24 = <<48+24=72>>72 clips altog... |
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"content": "Return your final response within \\boxed{}. The total in-store price for an appliance is $\\textdollar 99.99$. A television commercial advertises the same product for three easy payments of $\\textdollar 29.98$ and a one-time shipping and handling charge of $\\textdollar 9.98$. How many cents are... |
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"content": "Return your final response within \\boxed{}. Points $A,B,C,D,E$ and $F$ lie, in that order, on $\\overline{AF}$, dividing it into five segments, each of length 1. Point $G$ is not on line $AF$. Point $H$ lies on $\\overline{GD}$, and point $J$ lies on $\\overline{GF}$. The line segments $\\overlin... |
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"content": "Return your final response within \\boxed{}. During the softball season, Judy had $35$ hits. Among her hits were $1$ home run, $1$ triple and $5$ doubles. The rest of her hits were single. What percent of her hits were single?\n$\\text{(A)}\\ 28\\% \\qquad \\text{(B)}\\ 35\\% \\qquad \\text{(C)... |
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"content": "Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn?",
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"content": "Weng earns 12/60 = $<<12/60=0.2>>0.2 per minute.\nWorking 50 minutes, she earned 0.2 x 50 = $<<0.2*50=10>>10.\n#### 10",
"role": "assi... |
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"content": "Return your final response within \\boxed{}. The graph, $G$ of $y=\\log_{10}x$ is rotated $90^{\\circ}$ counter-clockwise about the origin to obtain a new graph $G'$. Which of the following is an equation for $G'$?\n(A) $y=\\log_{10}\\left(\\frac{x+90}{9}\\right)$ (B) $y=\\log_{x}10$ (C) $y=\\frac... |
[
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"content": "Betty is saving money for a new wallet which costs $100. Betty has only half of the money she needs. Her parents decided to give her $15 for that purpose, and her grandparents twice as much as her parents. How much more money does Betty need to buy the wallet?",
"role": "user"
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"co... |
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"content": "Return your final response within \\boxed{}. Jose, Thuy, and Kareem each start with the number 10. Jose subtracts 1 from the number 10, doubles his answer, and then adds 2. Thuy doubles the number 10, subtracts 1 from her answer, and then adds 2. Kareem subtracts 1 from the number 10, adds 2 to... |
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"content": "Return your final response within \\boxed{}. A set of consecutive positive integers beginning with $1$ is written on a blackboard. One number is erased. The average (arithmetic mean) of the remaining numbers is $35\\frac{7}{17}$. What number was erased? \n$\\textbf{(A)}\\ 6\\qquad \\textbf{(B)}\\... |
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"content": "Return your final response within \\boxed{}. A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths $15$ and $25$ meters. What fraction of the yar... |
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"content": "Return your final response within \\boxed{}. What is the sum of all possible values of $t$ between $0$ and $360$ such that the triangle in the coordinate plane whose vertices are \\[(\\cos 40^\\circ,\\sin 40^\\circ), (\\cos 60^\\circ,\\sin 60^\\circ), \\text{ and } (\\cos t^\\circ,\\sin t^\\circ)\... |
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"content": "Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read?",
"role": "user"
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"content": "Maila read 12 x 2 = <<12*2=24>>2... |
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"content": "Return your final response within \\boxed{}. Given: $x > 0, y > 0, x > y$ and $z\\ne 0$. The inequality which is not always correct is:\n$\\textbf{(A)}\\ x + z > y + z \\qquad\\textbf{(B)}\\ x - z > y - z \\qquad\\textbf{(C)}\\ xz > yz$\n$\\textbf{(D)}\\ \\frac {x}{z^2} > \\frac {y}{z^2} \\qquad\\... |
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"content": "James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year?",
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"content": "He writes each friend 3*2=<<3*2=6>>6 pages a week\nSo he writes 6*2=<<6*2=12>>12 pages every week\nThat means he writes 12*52=<<12*52=624>>624 pages... |
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"content": "Return your final response within \\boxed{}. The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of $1$ and $2016$ is closest to which integer?\n$\\textbf{(A)}\\ 2 \\qquad \\textbf{(B)}\\ 45 \\qquad \\textbf{(C)}\\ 504 \\qquad \\textbf{... |
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"content": "Return your final response within \\boxed{}. The first three terms of an arithmetic progression are $x - 1, x + 1, 2x + 3$, in the order shown. The value of $x$ is: \n$\\textbf{(A)}\\ -2\\qquad\\textbf{(B)}\\ 0\\qquad\\textbf{(C)}\\ 2\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ \\text{undetermin... |
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"content": "Return your final response within \\boxed{}. Let a geometric progression with n terms have first term one, common ratio $r$ and sum $s$, where $r$ and $s$ are not zero. The sum of the geometric progression formed by replacing each term of the original progression by its reciprocal is\n$\\textbf{(A... |
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"content": "Mark has a garden with flowers. He planted plants of three different colors in it. Ten of them are yellow, and there are 80% more of those in purple. There are only 25% as many green flowers as there are yellow and purple flowers. How many flowers does Mark have in his garden?",
"role": "user"... |
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"content": "Return your final response within \\boxed{}. Alicia had two containers. The first was $\\tfrac{5}{6}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\\tfrac{3}{4}$ full of water. What is ... |
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"content": "Return your final response within \\boxed{}. Misha rolls a standard, fair six-sided die until she rolls $1-2-3$ in that order on three consecutive rolls. The probability that she will roll the die an odd number of times is $\\dfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. F... |
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"content": "Return your final response within \\boxed{}. An architect is building a structure that will place vertical pillars at the vertices of regular hexagon $ABCDEF$, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The he... |
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"content": "Albert is wondering how much pizza he can eat in one day. He buys 2 large pizzas and 2 small pizzas. A large pizza has 16 slices and a small pizza has 8 slices. If he eats it all, how many pieces does he eat that day?",
"role": "user"
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"content": "He eats 32 from the largest pizzas... |
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"content": "Return your final response within \\boxed{}. Diameter $AB$ of a circle has length a $2$-digit integer (base ten). Reversing the digits gives the length of the perpendicular chord $CD$. The distance from their intersection point $H$ to the center $O$ is a positive rational number. Determine the len... |
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"content": "Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of j... |
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"content": "Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, b... |
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"content": "Return your final response within \\boxed{}. Find the smallest positive number from the numbers below.\n$\\textbf{(A)} \\ 10-3\\sqrt{11} \\qquad \\textbf{(B)} \\ 3\\sqrt{11}-10 \\qquad \\textbf{(C)}\\ 18-5\\sqrt{13}\\qquad \\textbf{(D)}\\ 51-10\\sqrt{26}\\qquad \\textbf{(E)}\\ 10\\sqrt{26}-51$",... |
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"content": "Return your final response within \\boxed{}. The points $(2,-3)$, $(4,3)$, and $(5, k/2)$ are on the same straight line. The value(s) of $k$ is (are):\n$\\textbf{(A)}\\ 12\\qquad \\textbf{(B)}\\ -12\\qquad \\textbf{(C)}\\ \\pm 12\\qquad \\textbf{(D)}\\ {12}\\text{ or }{6}\\qquad \\textbf{(E)}\... |
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"content": "Return your final response within \\boxed{}. Suppose $q_1,q_2,...$ is an infinite sequence of integers satisfying the following two conditions:\n(a) $m - n$ divides $q_m - q_n$ for $m>n \\geq 0$\n(b) There is a polynomial $P$ such that $|q_n|<P(n)$ for all $n$.\nProve that there is a polynomial $Q... |
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"content": "Tina makes $18.00 an hour. If she works more than 8 hours per shift, she is eligible for overtime, which is paid by your hourly wage + 1/2 your hourly wage. If she works 10 hours every day for 5 days, how much money does she make?",
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"content": "She works 8 hours a... |
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"content": "A deep-sea monster rises from the waters once every hundred years to feast on a ship and sate its hunger. Over three hundred years, it has consumed 847 people. Ships have been built larger over time, so each new ship has twice as many people as the last ship. How many people were on the ship the m... |
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"content": "Return your final response within \\boxed{}. In a certain year the price of gasoline rose by $20\\%$ during January, fell by $20\\%$ during February, rose by $25\\%$ during March, and fell by $x\\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginnin... |
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"content": "Tobias is buying a new pair of shoes that costs $95. He has been saving up his money each month for the past three months. He gets a $5 allowance a month. He also mows lawns and shovels driveways. He charges $15 to mow a lawn and $7 to shovel. After buying the shoes, he has $15 in change. If he mo... |
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"content": "Randy has 60 mango trees on his farm. He also has 5 less than half as many coconut trees as mango trees. How many trees does Randy have in all on his farm?",
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"content": "Half of the number of Randy's mango trees is 60/2 = <<60/2=30>>30 trees.\nSo Randy has 30 - 5 = ... |
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"content": "Return your final response within \\boxed{}. Quadrilateral $ABCD$ satisfies $\\angle ABC = \\angle ACD = 90^{\\circ}, AC=20,$ and $CD=30.$ Diagonals $\\overline{AC}$ and $\\overline{BD}$ intersect at point $E,$ and $AE=5.$ What is the area of quadrilateral $ABCD?$\n$\\textbf{(A) } 330 \\qquad \\te... |
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"content": "Jasper will serve charcuterie at his dinner party. He buys 2 pounds of cheddar cheese for $10, a pound of cream cheese that cost half the price of the cheddar cheese, and a pack of cold cuts that cost twice the price of the cheddar cheese. How much does he spend on the ingredients?",
"role": "... |
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"content": "Return your final response within \\boxed{}. The angle bisector of the acute angle formed at the origin by the graphs of the lines $y = x$ and $y=3x$ has equation $y=kx.$ What is $k?$\n$\\textbf{(A)} \\ \\frac{1+\\sqrt{5}}{2} \\qquad \\textbf{(B)} \\ \\frac{1+\\sqrt{7}}{2} \\qquad \\textbf{(C)} \\... |
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"content": "Return your final response within \\boxed{}. A set $S$ of points in the $xy$-plane is symmetric about the origin, both coordinate axes, and the line $y=x$. If $(2,3)$ is in $S$, what is the smallest number of points in $S$?\n$\\mathrm{(A) \\ } 1\\qquad \\mathrm{(B) \\ } 2\\qquad \\mathrm{(C) \\ } ... |
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"content": "Return your final response within \\boxed{}. Five positive consecutive integers starting with $a$ have average $b$. What is the average of $5$ consecutive integers that start with $b$?\n$\\textbf{(A)}\\ a+3\\qquad\\textbf{(B)}\\ a+4\\qquad\\textbf{(C)}\\ a+5\\qquad\\textbf{(D)}\\ a+6\\qquad\\textb... |
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"content": "Return your final response within \\boxed{}. Which of the following is the negation of the statement: For all $x$ of a certain set, $x^2>0$?\n$\\textbf{(A)}\\ \\text{For all x}, x^2 < 0\\qquad \\textbf{(B)}\\ \\text{For all x}, x^2 \\le 0\\qquad \\textbf{(C)}\\ \\text{For no x}, x^2>0\\qquad \\\\ ... |
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"content": "Joy can read 8 pages of a book in 20 minutes. How many hours will it take her to read 120 pages?",
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"content": "In one hour, there are 3 sets of 20 minutes.\nSo, Joy can read 8 x 3 = <<8*3=24>>24 pages in an hour.\nIt will take her 120/24 = <<120/24=5>>5 hours to rea... |
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"content": "Return your final response within \\boxed{}. What is the greatest power of $2$ that is a factor of $10^{1002} - 4^{501}$?\n$\\textbf{(A) } 2^{1002} \\qquad\\textbf{(B) } 2^{1003} \\qquad\\textbf{(C) } 2^{1004} \\qquad\\textbf{(D) } 2^{1005} \\qquad\\textbf{(E) }2^{1006}$",
"role": "user"
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... |
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"content": "Return your final response within \\boxed{}. Consider all 1000-element subsets of the set $\\{1, 2, 3, ... , 2015\\}$. From each such subset choose the least element. The arithmetic mean of all of these least elements is $\\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. ... |
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"content": "James creates a media empire. He creates a movie for $2000. Each DVD cost $6 to make. He sells it for 2.5 times that much. He sells 500 movies a day for 5 days a week. How much profit does he make in 20 weeks?",
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"content": "He sold each DVD for 6*2.5=$<<6*2.5=1... |
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"content": "The profit from a business transaction is shared among 2 business partners, Mike and Johnson in the ratio 2:5 respectively. If Johnson got $2500, how much will Mike have after spending some of his share on a shirt that costs $200?",
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"content": "According to the rati... |
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"content": "Return your final response within \\boxed{}. A man on his way to dinner short after $6: 00$ p.m. observes that the hands of his watch form an angle of $110^{\\circ}$. Returning before $7: 00$ p.m. he notices that again the hands of his watch form an angle of $110^{\\circ}$. The number of minutes t... |
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"content": "In a truck, there are 26 pink hard hats, 15 green hard hats, and 24 yellow hard hats. If Carl takes away 4 pink hard hats, and John takes away 6 pink hard hats and twice as many green hard hats as the number of pink hard hats that he removed, then calculate the total number of hard hats that rema... |
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{
"content": "It takes Roque two hours to walk to work and one hour to ride his bike to work. Roque walks to and from work three times a week and rides his bike to and from work twice a week. How many hours in total does he take to get to and from work a week with walking and biking?",
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... |
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"content": "Tim rides his bike back and forth to work for each of his 5 workdays. His work is 20 miles away. He also goes for a weekend bike ride of 200 miles. If he can bike at 25 mph how much time does he spend biking a week?",
"role": "user"
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"content": "He bikes 20*2=<<20*2=40>>40 mil... |
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"content": "Return your final response within \\boxed{}. A 3x3x3 cube is made of $27$ normal dice. Each die's opposite sides sum to $7$. What is the smallest possible sum of all of the values visible on the $6$ faces of the large cube?\n$\\text{(A)}\\ 60 \\qquad \\text{(B)}\\ 72 \\qquad \\text{(C)}\\ 84 \\qqu... |
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"content": "Return your final response within \\boxed{}. In the multiplication problem below $A$, $B$, $C$, $D$ are different digits. What is $A+B$? \n\\[\\begin{array}{cccc}& A & B & A\\\\ \\times & & C & D\\\\ \\hline C & D & C & D\\\\ \\end{array}\\]\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 2\\qquad\\text... |
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"content": "Return your final response within \\boxed{}. Let $\\, a =(m^{m+1} + n^{n+1})/(m^m + n^n), \\,$ where $\\,m\\,$ and $\\,n\\,$ are positive integers. Prove that $\\,a^m + a^n \\geq m^m + n^n$.\n[You may wish to analyze the ratio $\\,(a^N - N^N)/(a-N),$ for real $\\, a \\geq 0 \\,$ and integer $\\, ... |
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"content": "Return your final response within \\boxed{}. The sum of two natural numbers is $17{,}402$. One of the two numbers is divisible by $10$. If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?\n$\\textbf{(A)} ~10{,}272\\qquad\\textbf{(... |
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"content": "Return your final response within \\boxed{}. What is the value of \\[2^{\\left(0^{\\left(1^9\\right)}\\right)}+\\left(\\left(2^0\\right)^1\\right)^9?\\]\n$\\textbf{(A) } 0 \\qquad\\textbf{(B) } 1 \\qquad\\textbf{(C) } 2 \\qquad\\textbf{(D) } 3 \\qquad\\textbf{(E) } 4$",
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{... |
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"content": "Return your final response within \\boxed{}. Which of the following describes the graph of the equation $(x+y)^2=x^2+y^2$?\n$\\textbf{(A) } \\text{the\\,empty\\,set}\\qquad \\textbf{(B) } \\textrm{one\\,point}\\qquad \\textbf{(C) } \\textrm{two\\,lines} \\qquad \\textbf{(D) } \\textrm{a\\,circle} ... |
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"content": "Bella bought stamps at the post office. Some of the stamps had a snowflake design, some had a truck design, and some had a rose design. Bella bought 11 snowflake stamps. She bought 9 more truck stamps than snowflake stamps, and 13 fewer rose stamps than truck stamps. How many stamps did Bella buy ... |
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"content": "Each bird eats 12 beetles per day, each snake eats 3 birds per day, and each jaguar eats 5 snakes per day. If there are 6 jaguars in a forest, how many beetles are eaten each day?",
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"content": "First find the total number of snakes eaten: 5 snakes/jaguar * 6 jaguars... |
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"content": "Return your final response within \\boxed{}. If $\\texttt{a}$ and $\\texttt{b}$ are digits for which\n$\\begin{array}{ccc}& 2 & a\\\\ \\times & b & 3\\\\ \\hline & 6 & 9\\\\ 9 & 2\\\\ \\hline 9 & 8 & 9\\end{array}$\nthen $\\texttt{a+b =}$\n$\\mathrm{(A)\\ } 3 \\qquad \\mathrm{(B) \\ }4 \\qquad \\m... |
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"content": "Return your final response within \\boxed{}. At $2: 15$ o'clock, the hour and minute hands of a clock form an angle of:\n$\\textbf{(A)}\\ 30^{\\circ} \\qquad\\textbf{(B)}\\ 5^{\\circ} \\qquad\\textbf{(C)}\\ 22\\frac {1}{2}^{\\circ} \\qquad\\textbf{(D)}\\ 7\\frac {1}{2} ^{\\circ} \\qquad\\textbf{(E... |
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"content": "Return your final response within \\boxed{}. In [right triangle](https://artofproblemsolving.com/wiki/index.php/Right_triangle) $ABC$ with [right angle](https://artofproblemsolving.com/wiki/index.php/Right_angle) $C$, $CA = 30$ and $CB = 16$. Its legs $CA$ and $CB$ are extended beyond $A$ and $B$... |
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"content": "Return your final response within \\boxed{}. A finite [sequence](https://artofproblemsolving.com/wiki/index.php/Sequence) of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units di... |
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"content": "Return your final response within \\boxed{}. What time was it $2011$ minutes after midnight on January 1, 2011? \n$\\textbf{(A)}\\ \\text{January 1 at 9:31PM}$\n$\\textbf{(B)}\\ \\text{January 1 at 11:51PM}$\n$\\textbf{(C)}\\ \\text{January 2 at 3:11AM}$\n$\\textbf{(D)}\\ \\text{January 2 at 9:31A... |
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"content": "Return your final response within \\boxed{}. A basketball player made $5$ baskets during a game. Each basket was worth either $2$ or $3$ points. How many different numbers could represent the total points scored by the player?\n$\\textbf{(A)}\\ 2 \\qquad \\textbf{(B)}\\ 3 \\qquad \\textbf{(C)}\\ 4... |
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"content": "Return your final response within \\boxed{}. Square $EFGH$ has one vertex on each side of square $ABCD$. Point $E$ is on $AB$ with $AE=7\\cdot EB$. What is the ratio of the area of $EFGH$ to the area of $ABCD$?\n$\\text{(A)}\\,\\frac{49}{64} \\qquad\\text{(B)}\\,\\frac{25}{32} \\qquad\\t... |
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"content": "Samantha’s last name has three fewer letters than Bobbie’s last name. If Bobbie took two letters off her last name, she would have a last name twice the length of Jamie’s. Jamie’s full name is Jamie Grey. How many letters are in Samantha’s last name?",
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"content": "T... |
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"content": "Ann's favorite store was having a summer clearance. For $75 she bought 5 pairs of shorts for $7 each and 2 pairs of shoes for $10 each. She also bought 4 tops, all at the same price. How much did each top cost?",
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"content": "She bought 5 shorts at $7 each so 5*7=$<<... |
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"content": "Return your final response within \\boxed{}. A house worth $ $9000$ is sold by Mr. A to Mr. B at a $10$ % loss. Mr. B sells the house back to Mr. A at a $10$ % gain. \nThe result of the two transactions is: \n$\\textbf{(A)}\\ \\text{Mr. A breaks even} \\qquad \\textbf{(B)}\\ \\text{Mr. B gains }$9... |
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"content": "Mary does her grocery shopping on Saturday. She does her shopping only at a specific store where she is allowed a credit of $100, which must be paid in full before her next shopping trip. That week she spent the full credit limit and paid $15 of it on Tuesday and $23 of it on Thursday. How much cr... |
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"content": "Return your final response within \\boxed{}. Chandler wants to buy a $500$ dollar mountain bike. For his birthday, his grandparents\nsend him $50$ dollars, his aunt sends him $35$ dollars and his cousin gives him $15$ dollars. He earns\n$16$ dollars per week for his paper route. He will use all of... |
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"content": "Return your final response within \\boxed{}. The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?\n$\\textbf{(A) }\\frac{3}{7}\\qquad\\textbf{(B) }\\frac{7}{12}\\qquad\\textbf{(C) }\\frac{12}{7}... |
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"content": "Ralph is going to practice playing tennis with a tennis ball machine that shoots out tennis balls for Ralph to hit. He loads up the machine with 175 tennis balls to start with. Out of the first 100 balls, he manages to hit 2/5 of them. Of the next 75 tennis balls, he manages to hit 1/3 of them. Ou... |
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"content": "Jack is stranded on a desert island. He wants some salt to season his fish. He collects 2 liters of seawater in an old bucket. If the water is 20% salt, how many ml of salt will Jack get when all the water evaporates?",
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"content": "First find how many liters of the ... |
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"content": "Brennan was researching his school project and had to download files from the internet to his computer to use for reference. After downloading 800 files, he deleted 70% of them because they were not helpful. He downloaded 400 more files but again realized that 3/5 of them were irrelevant. How many... |
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"content": "There are 5 houses on a street, and each of the first four houses has 3 gnomes in the garden. If there are a total of 20 gnomes on the street, how many gnomes does the fifth house have?",
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"content": "In the first four houses, there are a total of 4 houses * 3 gnomes... |
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"content": "Return your final response within \\boxed{}. Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, which of the following number of words would be ... |
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"content": "Return your final response within \\boxed{}. If the following instructions are carried out by a computer, which value of $X$ will be printed because of instruction $5$?\n\n1. START $X$ AT $3$ AND $S$ AT $0$. \n2. INCREASE THE VALUE OF $X$ BY $2$. \n3. INCREASE THE VALUE OF $S$ BY THE VALUE OF $... |
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"content": "Return your final response within \\boxed{}. Which of the following is equivalent to \"If P is true, then Q is false.\"?",
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"content": "<think>\n\nOkay, let's tackle this logic problem. The question is asking which of the following is equivalent to \"If P is true, th... |
[
{
"content": "Return your final response within \\boxed{}. Let $m$ be the least positive integer divisible by $17$ whose digits sum to $17$. Find $m$.",
"role": "user"
},
{
"content": "<think>\n\nOkay, let's see. I need to find the smallest positive integer that's divisible by 17 and whose digits ad... |
[
{
"content": "Return your final response within \\boxed{}. A shopper plans to purchase an item that has a listed price greater than $\\textdollar 100$ and can use any one of the three coupons. Coupon A gives $15\\%$ off the listed price, Coupon B gives $\\textdollar 30$ off the listed price, and Coupon C gives ... |
[
{
"content": "Return your final response within \\boxed{}. In $\\triangle ABC$, $\\angle ABC=45^\\circ$. Point $D$ is on $\\overline{BC}$ so that $2\\cdot BD=CD$ and $\\angle DAB=15^\\circ$. Find $\\angle ACB.$\n$\\text{(A) }54^\\circ \\qquad \\text{(B) }60^\\circ \\qquad \\text{(C) }72^\\circ \\qquad \\text{(D... |
[
{
"content": "Mrs. Snyder used to spend 40% of her monthly income on rent and utilities. Her salary was recently increased by $600 so now her rent and utilities only amount to 25% of her monthly income. How much was her previous monthly income?",
"role": "user"
},
{
"content": "Let her previous mont... |
[
{
"content": "Ann, Bill, Cate, and Dale each buy personal pan pizzas cut into 4 pieces. If Bill and Dale eat 50% of their pizzas and Ann and Cate eat 75% of the pizzas, how many pizza pieces are left uneaten?",
"role": "user"
},
{
"content": "In total, there are 4 x 4 = <<4*4=16>>16 pizza pieces.\nB... |
[
{
"content": "Noah is a painter. He paints pictures and sells them at the park. He charges $60 for a large painting and $30 for a small painting. Last month he sold eight large paintings and four small paintings. If he sold twice as much this month, how much is his sales for this month?",
"role": "user"
}... |
[
{
"content": "Return your final response within \\boxed{}. Mary's top book shelf holds five books with the following widths, in centimeters: $6$, $\\dfrac{1}{2}$, $1$, $2.5$, and $10$. What is the average book width, in centimeters?\n$\\mathrm{(A)}\\ 1 \\qquad \\mathrm{(B)}\\ 2 \\qquad \\mathrm{(C)}\\ 3 \\qquad... |
[
{
"content": "Return your final response within \\boxed{}. The equation $2^{2x}-8\\cdot 2^x+12=0$ is satisfied by:\n$\\text{(A) } log(3)\\quad \\text{(B) } \\tfrac{1}{2}log(6)\\quad \\text{(C) } 1+log(\\tfrac{3}{2})\\quad \\text{(D) } 1+\\frac{log(3)}{log(2)}\\quad \\text{(E) none of these}$",
"role": "user... |
[
{
"content": "A car is driving through a tunnel with many turns. After a while, the car must travel through a ring that requires a total of 4 right-hand turns. After the 1st turn, it travels 5 meters. After the 2nd turn, it travels 8 meters. After the 3rd turn, it travels a little further and at the 4th turn, i... |
[
{
"content": "Return your final response within \\boxed{}. The sum of the greatest integer less than or equal to $x$ and the least integer greater than or equal to $x$ is $5$. The solution set for $x$ is\n$\\textbf{(A)}\\ \\Big\\{\\frac{5}{2}\\Big\\}\\qquad \\textbf{(B)}\\ \\big\\{x\\ |\\ 2 \\le x \\le 3\\big\\... |
[
{
"content": "To make pizza, together with other ingredients, Kimber needs 10 cups of water, 16 cups of flour, and 1/2 times as many teaspoons of salt as the number of cups of flour. Calculate the combined total number of cups of water, flour, and teaspoons of salt that she needs to make the pizza.",
"role"... |
[
{
"content": "Return your final response within \\boxed{}. A powderman set a fuse for a blast to take place in $30$ seconds. He ran away at a rate of $8$ yards per second. Sound travels at the rate of $1080$ feet per second. When the powderman heard the blast, he had run approximately:\n$\\textbf{(A)}\\ \\text{... |
[
{
"content": "Return your final response within \\boxed{}. A student council must select a two-person welcoming committee and a three-person planning committee from among its members. There are exactly $10$ ways to select a two-person team for the welcoming committee. It is possible for students to serve on bot... |
[
{
"content": "Mr. Sam shared a certain amount of money between his two sons, Ken and Tony. If Ken got $1750, and Tony got twice as much as Ken, how much was the money shared?",
"role": "user"
},
{
"content": "Tony got twice $1750 which is 2*$1750 = $<<2*1750=3500>>3500\nThe total amount shared was $... |
[
{
"content": "Mr. Sanchez found out that 40% of his Grade 5 students got a final grade below B. How many of his students got a final grade of B and above if he has 60 students in Grade 5?",
"role": "user"
},
{
"content": "Since 40% of his students got below B, 100% - 40% = 60% of Mr. Sanchez's stud... |
[
{
"content": "Return your final response within \\boxed{}. Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be $2$ : $1$ ?\n$\\textbf{(A)}\\ 2 \\qquad\\textbf{(B)} \\ 4 \\qquad\\textbf{(C)}... |
[
{
"content": "Lisa, Jack, and Tommy earned $60 from washing cars all week. However, half of the $60 was earned by Lisa. Tommy earned half of what Lisa earned. How much more money did Lisa earn than Tommy?",
"role": "user"
},
{
"content": "Lisa earned $60 * 1/2 = $<<60*1/2=30>>30.\nTommy earned $30 *... |
[
{
"content": "Five friends eat at a fast-food chain and order the following: 5 pieces of hamburger that cost $3 each; 4 sets of French fries that cost $1.20; 5 cups of soda that cost $0.5 each; and 1 platter of spaghetti that cost $2.7. How much will each of them pay if they will split the bill equally?",
"... |
[
{
"content": "Artemis is making tea for a party. She knows her mom drinks an 8-ounce cup of tea and uses one ounce of tea. She will use this same ratio for the party. The party has 12 people there and each of them wants a 6-ounce cup of tea. How many ounces of tea does she need?",
"role": "user"
},
{
... |
[
{
"content": "Return your final response within \\boxed{}. If $\\theta$ is a constant such that $0 < \\theta < \\pi$ and $x + \\dfrac{1}{x} = 2\\cos{\\theta}$, then for each positive integer $n$, $x^n + \\dfrac{1}{x^n}$ equals\n$\\textbf{(A)}\\ 2\\cos\\theta\\qquad \\textbf{(B)}\\ 2^n\\cos\\theta\\qquad \\textb... |
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