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$$\frac{1}{{\frac{1}{3}}+\frac{1}{6}}=$$
What is the greatest prime number that is a divisor of both 380 and 570?
Horace bought 6 dozen donuts and 6 dozen eggs for $45.00. If the donuts cost $0.50 each, how much did Horace pay for a dozen eggs?
The value of the product of u and v is equal to twenty times the ratio of the value obtained by subtracting v from u to the value of v. If v equals 4,what is the value of u?
How many three-digit numbers begin with a digit which represents an odd number that is a prime, have a prime number as a second digit, and end with a digit that represents an odd number?
Jack, Tom, Beth, and Ruth are each competing to paint one side of a square fence. The fastest, Jack, painted his side in 13 hours, the slowest, Tom, painted his side in 14 hours. Which of the following could NOT be the average of the times that each of the four competitors spent painting his or her side of the fence?
A distributor sells a product through an on-line store, which takes a commission of 20 percent off the price set by the distributor. The distributor obtains the product from a producer at the price of 15 dollars per item. What is the price that a buyer observes on-line if the distributor wants to maintain a 20 percent profit on the cost of the item?
In the figure above, two circles with radii equal to 10 units of length overlap such that their centres, $${O}_{1}$$ and $${O}_{2}$$, are 16 units apart. What is the distance between the line joining the centres of the circles and the line drawn through point P parallel to the line connecting the centres?
Gaby, Dimitri, and Marat played a game of poker. At the end of the game, Gaby had 12 dollars more than Dimitri, but only one-half of what Marat had. If each player brought 20 dollars to the game, what were Gaby's total dollar winnings?
A certain retailer gets a shipment of items the day after his inventory drops below $$\frac{y}{4}$$ items. Each shipment replenishes the retailer's inventory up to the level y, and it is estimated that the retailer, on average, maintains $$\frac{y}{2}$$ in inventory every month throughout the year. The cost of keeping an item in inventory is $0.5 per month. What is the retailer's annual inventory cost.
A factory worker produced one lot of connecting clips, and initial quality control found that $$\frac{5}{7}$$ of clips in the lot could be used. An assembly plant purchased this lot of clips valuing the lot at $3 per each usable clip. During assembly, it became known that only $$\frac{3}{5}$$ of the clips in the lot were usable. What was price per usable clip that the assembly plant paid for the lot?
If the water level rises 20 percent from m meters to 12 meters, then 12 - m = ?
A tank with an isosceles-triangular cross section with sides 4,4,and 6 meters, has a length of 10 meters, and is currently resting on the 6 meter by 10 meter face. The tank is filled with water to the depth of 1 meter. If the tank is placed on a triangular face, what would be the depth of the water in the tank?
How many integers between 250 and 300, inclusive, can be evenly divided by NEITHER 3 NOR 5?
Two secretaries, Sally and Lisa, type at even but difference paces. Sally is more experienced and types 80 characters per minute. Lisa, a beginner, can type only 30 characters per minute. On one day, Lisa starts typing before Sally. At some point, both have typed the same number of characters. Then both continue typing and Sally types 800 more characters until her computer breaks down. Assuming Lisa does not take any break, how long, in hours, will it take her to finish typing the same number of characters?
The cost of 150 erasers and 300 pencils is $75. At the same rate, what is the cost of 50 erasers and 100 pencils?
The cost of operating an aircraft consists of landing and take-off costs of 1 thousand dollars per one landing and take-off and fuel costs of f dollars per mile flown. How much, in thousands of dollars, does it cost per week to operate an aircraft which makes one landing and take-off per day and flies m miles per week?
A certain MBA class had twice as many men as women. In a fund-raising event for a local school, each member of the class bought 10 raffle tickets at $5 per ticket. If the raffle ticket sales for the class totaled $3150,how many men were there in the class?
From 1997 to 2003, the number of the U.S. produced motion pictures which did not use computer generated special effects decreased from 1,750 to 1,050. What was the percent decrease in the number of the U.S. produced motion pictures which are not using computer generated special effects over this period?
PREP07 Test 1
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is
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