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.

What is the total surface area of rectangular solid R ?

(1) The surface area of one of the faces of R is 48.
(2) The length of one of the edges of R is 3.

Is the positive integer n an odd integer?

(1) n + 4 is a prime number.
(2) n + 3 is not a prime number.

If y is an integer and y = |x| + x, is y = 0 ?

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

The symbol @ represents one of the four arithmetic operations: addition, subtraction, multiplication, and division.
Is (5 @ 6) @ 2 = 5 @ (6 @ 2) ?

(1) 5 @ 6 = 6 @ 5
(2) 2 @ 0 = 2