Is ~$y< \frac{x+z}{2}$~ ?

(1) y - x < z - y
(2) ~$z-y> \frac{z-x}{2}$~

If ~$\frac{2}{5}$~ of the students at College C are business majors, what is the number of female students at College C ?

(1) ~$\frac{2}{5}$~ of the male students at College C are business majors.
(2) 200 of the female students at College C are business majors.

If r and t are positive integers, is rt even?

(1) r + t is odd.
(2) r^t is odd.

If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 @ k ?

(1) 2 @ k = 3
(2) 1 @ 0 = k

A certain motel has a total of 540 units, each of which has a 1-person, 2-person, or 4-person capacity. How many people stayed in the motel's 4-person units yesterday?

(1) At this motel, ~$\frac{1}{3}$~ of the units are 4-person units.
(2) Yesterday, 80 percent of the 4-person units in the motel were filled to capacity, and the rest of the 4-person units were empty.

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15 ?

(1) n - 2 is divisible by 5.
(2) t is divisible by 3.

If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) 2 is not a factor of n.
(2) 3 is not a factor of n.

If n and s are each 2-digit positive integers, is n greater than s ?

(1) The units digit of n is greater than the units digit of s.
(2) The tens digit of n is greater than the tens digit of s.

If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n ?

(1) The greatest of the 6 consecutive integers is 20.
(2) The average (arithmetic mean) of the 6 consecutive integers is 17.5.

At a two-candidate election for mayor, ~$\frac{3}{4}$~ of the registered voters cast ballots. How many registered voters cast ballots for the winning candidate?

(1) 25,000 registered voters did not cast ballots in the election.
(2) Of the registered voters who cast ballots, 55 percent cast ballots for the winning candidate.