A company has two types ofmachines, type R and type S. Operatingat a constant rate, a machine of type R does a certain job in 36 hours and amachine of type S does the same job in 18 hours. If the company used the same number of eachtype of machine to do the job in 2 hours, how many machines of type R wereused?

At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

Which of the following is equal to ~$x^{18}$~ for all positive values of x ?

At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 50 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?

If a quality control checkis made by inspecting a sample of 2 lightbulbs from a box of 12 lightbulbs, howmany different samples can be chosen?

If each term in the sum a1+ a2 + . . . + an is either 7 or 77 and the sum equals 350, which of thefollowing could be equal to n ?

If r and s areintegers, and rs + r is odd, which of the following must beeven?

A certain builder isselling five homes for the following prices: $157,000, $168,000, $195,000, $235,000, and $256,000. If the price of the most expensive home isincreased $10,000, which of the following statements best describes the changein the mean and the median of the home prices?

Froma bag containing 12 identical blue balls, y identical yellow balls, and noother balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball willbe blue, what is the least number of yellow balls that must be in the bag?

At a dinner party, 5 peopleare to be seated around a circular table. Two seating arrangements are considered different only when thepositions of the people are different relative to each other. What is the total number of different possibleseating arrangements for the group?