Problem Solving

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

If √ 3 − 2 x = √ 2 x + 1 3 − 2 x − − − √ = 2 x − √ + 1 , then 4 x 2 =

The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments, how many of the parents volunteered to bring refreshments?

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid $3.99foreachadditionalcompactdiscpurchased.Ifapreferredcustomerpurchasedatotalof6compactdiscsandpaid$15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

The sequence a 1 , a 2 , a 3 , ... , a n , ... is such that a n = a n − 1 + a n − 2 2 for all n ≥ 3 . If a 3 = 4 and a 5 = 20 , what is the value of a 6 ?

John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened?

If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

Positive integer y is 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?

If n = 16 81 − √ n = 16 81 , what is the value of n √ n ?

Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A closed cylindrical tank contains 36 π cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

When the figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines, the result is a model of a geometric solid. This geometric solid consists of 2 pyramids each with a square base that they share. What is the sum of number of edges and number of faces of this geometric solid?

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

4.8 * 10 9 − − − − √ 4.8 * 10 9 is closest in value to

In the figure shown, what is the value of v+x+y+z+w?

Solution X is 15% salt and solution Y is 50% salt. If the two solutions are combined to form 7 gallons of a 30% solution, how many gallons of solution X must be used?