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A number of eggs dyed various colors were hidden for an egg hunt. How many eggs in total were hidden?(1) The number of red eggs hidden is the square of an integer, while the total number of eggs hidden is 24 times that integer.(2) Exactly 143 of the eggs hidden were not red.
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The three-digit positive integer n can be written as ABC, in which A, B, and C stand for the unknown digits of n. What is the remainder when n is divided by 37?(1)$$A+\frac{B}{10}+\frac{C}{100}=B+\frac{C}{10}+\frac{A}{100}$$
(2)$$A+\frac{B}{10}+\frac{C}{100}=C+\frac{A}{10}+\frac{B}{100}$$
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If r, s, and t are nonzero numbers, is rt= 14?1.$${（r^{2}）st}=14rs$$2.$$\frac{t}{2}=\frac{7}{r}$$
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At a certain circus, every child was given either two or three balloons. How many children received three balloons? 1. At the circus, 40 percent of the children received two balloons.2. A total of 360 balloons were given out to children at the circus.
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What is the value of x + y ?1. xy+ wz + xz+ wy= 82. y + z = 4
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While motorcycling through the countryside, did Corrine ever exceed the posted 65-kilometer-per-hour speed limit?1. Corrine motorcycled for 3 hours through the countryside.2. Corrine motorcycled 180 kilometers through the countryside.
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If the average (arithmetic mean) of six different numbers is 25, how many of the numbers are greater than 25?1. None of the six numbers is greater than 50.2. Three of the six numbers are 7, 8, and 9, respectively.
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If p, q, x, and y are positive integers, is $${q^{y}}\over{p^{x}}$$ an integer?1. q is evenly divisible by p.2. $$y\ge{qx}$$
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Xander, Yolanda, and Zelda each have at least one hat. Zelda has more hats than Yolanda, who has more than Xander. Together, the total number of hats the three people have is 12. How many hats does Yolanda have?(1) Zelda has no more than 5 hats more than Xander.(2) The product of the numbers of hats that Xander, Yolanda, and Zelda have is less than 36.
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How many factors does x have, if x is a positive integer?(1) $$x=p^{n}$$, where p is a prime number.(2) $$n^{2}=n+n$$, where x is a positive integer.
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Several friends in a dinner group decide to contribute equally to the purchase of a $36 gift. How many people are in the group?(1) The number of people in the group is equal to the size of each person's contribution, in dollars.(2) If three more people joined the group, each person's individual contribution would fall by $2.
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The consumer price index in Zeropia in 2009 relative to the year 2000 was 1.75, meaning that for every Zeropian dollar spent on consumer goods in 2000, $1.75 on average had to be spent in 2009. In Zeropian dollars, what was the increase in the price of Brand Z running shoes from 2000 to 2009, if these shoes' price increased precisely according to the consumer price index?(1) The price of Brand Z running shoes was $91 in 2009.(2) The ratio of the dollar increase in the price of Brand Z running shoes to the price of the shoes in 2009 was 3:7.
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A triple of positive integers is defined to be a Pythagorean triple if and only if the sum of squares of the two of them equals the square of the third. If triangle S has sides whose lengths form a Pythagorean triple and triangle R has sides whose lengths are integers, do the side lengths of triangle R form a Pythagorean triple?1. R has area which is a multiple of the area of S.2. R and S are similar triangles.
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If the ratio of job applicants with a doctorate degree to job applicants with an MBA degree for positions at Company G in 1999 was $$\frac{1}{5}$$ what was the ratio of applicants with a doctorate to applicants with an MBA for positions at company G in 2003?1. Company G received 20,000 more MBA applicants in 2003 than in 1999.2. Company G received 2,000 more Ph.D. applicants in 2003 than in 1999.
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Because of economies of scale, the cost of production of the second gadget is half the first one which costs c dollars to produce. The production of the third gadget costs half of the second, etc. What is the value of c?1. The sum of the costs of the third and fourth gadgets is $9.2. The sum of the costs of the second and the ninth gadget is $${24}\cdot\frac{2^7+1}{2^8}$$ dollars.
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A direct flight from Lima to Cuzco was diverted to Arequipa due to unexpected bad weather. 163 passengers were on the flight when it finally arrived at Cuzco. How many passengers boarded the flight in Arequipa?1. When the plane took off from Lima, 184 people were on board.2. 30 people chose to disembark at Arequipa and did not re-board the flight.
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A retailer buys t-shirts from a wholesaler in lots of 25 t-shirts each. What is the wholesale price of a lot of t-shirts?1. The retailer sells a single t-shirt for $4.80.2. The retailer sells t-shirts at 20 percent above the wholesale price.
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What is the area of triangle R?1. The base of triangle R is 15.2. The ratio of the altitude dropped from the vertex opposite the base is related to the base of R is 5 to 1.
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A pharmacy offers customers both a patented and a generic version of a certain drug. The pharmacy makes a profit of 20 percent of the cost on every box of the patented version, and it makes a profit of 5 percent of the cost on every box of the generic version. During a certain time period, which version of the drug yields a greater dollar profit to the pharmacy?1. The pharmacy pays more to the wholesaler per box for the patented version than for the generic version.2. The pharmacy sells 30 percent more of the generic version of the drug by weight than the patented version.
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How many seconds long is time period U if U can be no longer than a day?1. Time period U lasts from 13:59:00 until 14:02:00.2. Time period U lasts from 1:59:00 pm until 2:02:00 pm.
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