If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r ?

(1) q > 10
(2) q = 2^k, where k is a positive integer.

If ab ≠ 0 and points (-a, b) and (-b, a) are in the same quadrant of the xy-plane, is point (-x, y) in this same quadrant?

(1) xy > 0
(2) ax > 0

If a < y < z < b, is |y - a| < |y - b| ?

(1) |z - a| < |z - b|
(2) |y - a| < |z - b|

If m is a positive odd integer, what is the average (arithmetic mean) of a certain set of m integers?

(1) The integers in the set are consecutive multiples of 3.
(2) The median of the set of integers is 33.

If ~$y\geq0$~ , what is the value of x ?

(1)~$\left | x-3 \right |\geq y$~
(2)~$\left | x-3 \right |\leq -y$~

When the positive integer n is divided by 25, the remainder is 13. What is the value of n ?

(1) n < 100
(2) When n is divided by 20, the remainder is 3.

Does the integer k have a factor p such that 1 < p < k ?

(1) ~$k> 4!$~
(2) ~$13!+2\leq k\leq 13!+13$~

If k ~$\neq $~ 0, 1, or -1, is ~$\frac{1}{k}> 0$~ ?

(1) ~$\frac{1}{k-1}> 0$~

(2) ~$\frac{1}{k+1}> 0$~

A certain store sells chairs individually or in sets of 6. The store charges less for purchasing a set of 6 chairs than for purchasing 6 chairs individually. How much does the store charge for purchasing a set of 6 chairs?

(1) The charge for purchasing a set of 6 chairs is 10 percent less than the charge for purchasing the 6 chairs individually.
(2) The charge for purchasing a set of 6 chairs is $20 more than the charge for purchasing 5 chairs individually.

A certain list consists of several different integers. Is the product of all the integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.