If m and n are integers, is m odd?

(1) n + m is odd.
(2) n + m = n² + 5

What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the ~$\frac{n}{3}$~ tallest people n the group is 6 feet ~$2\frac{1}{2}$~ inches, and the average height of the rest of the people n the group is 5 feet 10 inches.
(2) The sum of the heights of the n people is 178 feet 9 inches.

If the drama club and music club are combined, what percent of the combined membership will be male?

(1) Of the 16 members of the drama club, 15 are male.
(2) Of the 20 members of the music club, 10 are male.

If w + x < 0, is w - y > 0 ?

(1) x + y < 0
(2) y < x < w

Set S consists of 20 different positive integers. How many of the integers in S are odd?

(1) 10 of the integers in S are even.
(2) 10 of the integers in S are multiples of 4.

If t is a positive integer and r is the remainder when ~$t^2 + 5t + 6$~ is divided by 7, what is the value of r ?

(1) When t is divided by 7, the remainder is 6.
(2) When t2 is divided by 7, the remainder is 1.

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