Carcass wrote:
If x > y and y > z, which of the following represents the greatest number?
(A) x − z
(B) x − y
(C) y − x
(D) z − y
(E) z − x
The key here is to recognize that there is only ONE correct answer.
So, as long as we find values that satisfy the given conditions (x > y and y > z), we can simply test the answer choices.
If x > y and y > z, then it could be the case that x = 1, y = 0, and z = -1
We'll now plug these values into the five answer choices....
(A) x − z = 1 - (-1) =
2(B) x − y = 1 - 0 = 1
(C) y − x = 0 - 1 = -1
(D) z − y = (-1) - 0 = -1
(E) z − x = (-1) - 1 = -2
Answer: A