Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $165,000.

II. At least one of the homes was sold for more than $130,0000 and less than $150,000

III. At least one of the homes was sold for less than $130,000.

Is x<y?

(1) 3^x<2^y
(2) x>0 and y>0

In the sequence above, each term after the first is one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?

The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line.

(2) 23 people in the line are behind Adam.

If x and y are each randomly chosen from the integers 1, 2, 3, 4, and 5, what is the probability that the product xy will be greater than 10 ?

List L consists of the integers from 1 to 99 and two integers c and d such that c + d = 100 and cd <0. Which of the following statements must be true?

I. The average (arithmetic mean) of the numbers in L is equal to the median of the numbers in L .

II. The range of the numbers in L is greater than 100.

III. The range of the numbers in L is an odd number.

If x is a real number and , which of the following is the value of ?

k is a positive integer. When k⁴ is divided by 32, the remainder is 0. Which of the following could be the remainder when k is divided by 32?

I. 2

II. 4

III. 6

Last Year a company gave bonuses to a number of employees, but only in the three amounts of $750, $1500, and $7,350. If the total amount of the bonuses was $64800 and each of the three amounts was given to at least one employee, what is the fewest number of bonuses that the company could have given to employees last year?­