Problem Solving

A certain electronic component is sold in boxes of 54 for $16.20andinboxesof27for$13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable . Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes?

If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?

A union contract specifies a 6 percent salary increase plus a $450 bonus for each employee. For a certain employee, this is equivalent to an 8% salary increase. What was this employee's salary before the new contract?

If a positive integer n is divisible by both 5 and 7, the n must also be divisible by which of the following? I 12 II 35 III 70

Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750;eachofhisremainingpaycheckswas$30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

S represents the sum of the weights of n fish in pounds. Which of the following represents the average (arithmetic mean) of the n weights in ounces? (1pound = 16 ounces)

Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Sam, and Tina are all alive 4 years from today, which of the following must be true on that day? I. Rose is twice as old as Sam. II. Sam is 3 years younger than Tina. III. Rose is older than Tina.

AVERAGE COSTS OF OPERATING SUBCOMPACT, COMPACT, AND MIDSIZE CARS IN THE UNITED STATES, 1982~1986 For each of the years shown, the average cost per mile of operating a compact car minus the average cost per mile of operating a subcompact car was between

In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 20 miles per hour, how many miles did the car travel in the third 5-minute interval?

In a certain school, 40 more than 1/3 of all the students are taking a science course and 1/4 of those taking a science course are taking physics. If 1/8 of all the students in the school are taking physics, how many students are in the school ?

In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality 2 x − 3 y ≤ − 6 ?

If "basis points" are defined so that 1 percent is equal to 100 basis points, then 82.5 percent is how many basis points greater than 62.5 percent?

Envelopes can be purchased for $1.50perpackof100,$1.00 per pack of 50, or $0.03each.Whatisthegreatestnumberofenvelopesthatcanbepurchasedfor$7.30?

A group of store managers must assemble 280 displays for an upcoming sale. If they assemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will not have been assembled by the end of the second hour?

(1/5) 2 − 1 5 * 1 4 =

An athlete runs R miles in H hours, then rides a bike Q miles in the same number of hours. Which of the following represents the average speed, in miles per hour, for these two activities combined?

If positive integers x and y are not both odd, which of the following must be even?