If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x, y, and y - 2 is x.

(2) The average (arithmetic mean) of x and y is not an integer.

If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > ~$\frac{1}{2}$~ ?

(1) More than ~$\frac{1}{2}$~ of the 10 employees are women.

(2) The probability that both representatives selected will be men is less than ~$\frac{1}{10}$~

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?

I. 1

II. 3

III. 4

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce ~$5 \over 4$~ w widgets in 3 days, how many days would it take Machine X alone to produce 2W widgets?

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

If n is a positive integer and n² is divisible by 72, then the largest positive integer that must divide n is

An airline passenger is planning a trip that involves three connecting flights that leave from Airports A, B, and C, respectively. The first flight leaves Airport A every hour, beginning at 8:00 a.m., and arrives at Airport B 2~$1 \over 2$~ hours later. The second flight leaves Airport B every 20 minutes, beginning at 8:00 a.m.,and arrives at Airport C 1~$1 \over 6$~ hours later. The third flight leaves Airport C every hour, beginning at 8:45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?

In the figure above, point O is the center of the circle and OC = AC = AB. What is the value of x ?