Problem Solving

The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?

Of the following, which one is third greatest?

If x books cost $5eachandybookscost$8 each, then the average (arithmetic mean) cost, in dollars per book, is equal to

A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. Which of the following integers has length 3 ?

61.24 * 0.998 2 403 − − √ 61.24 * 0.998 2 403 The expression above is approximately equal to

If a = 7 and b = − 7 , what is the value of 2 a − 2 b + b 2 ?

Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

A certain pair of used shoes can be repaired for $12.50andwilllastfor1year.Apairofthesamekindofshoescanbepurchasednewfor$28.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?

If the perimeter of a rectangular garden plot is 34 feet and its area is 60 square feet, what is the length of each of the longer sides?

In square ABCD above, if DE = EB and DF = FC, then the area of the shaded region is what fraction of the area of square region ABCD?

If m is an integer such that (− 2) 2 m = 2 9 − m , then m=

If 1/2 of the money in a certain trust fund was invested in stocks, 1/4 in bonds, 1/5 in a mutual fund, and the remaining $10,000 in a government certificate, what was the total amount of the trust fund?

A restaurant buys fruit in cans containing 3 1 2 cups of fruit each. If the restaurant uses 1/2 cup of the fruit in each serving of its fruit compote, what is the least number of cans needed to prepare 60 servings of the compote ?

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?

Lloyd normally works 7.5 hours per day and earns $4.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?

AB x BA The product of the two-digit numbers above is the three-digit number ACA, where A, B and C are three different nonzero digits. If A x B <10, what is the two-digit number AB?

A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

During the four years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the remainder. The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total. If the only other expenses were taxes and license fees, then the cost of financing was how much more or less than the cost of taxes and license fees?