Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Since both x and y are restricted to positive integers, we should start with low positive integers. If x = 1 and y = 1, then we have which is true. Thus, x – y could equal 1 – 1 = 0. However, 0 is not among our answer choices, so we must keep looking.
If x = 1, then raised to any power is 1. Thus, no other values of y (besides 1) could equal that result, and we should look at other possible values of x and y.
If x = 2, then we have two possible values of y:
y = 2:
y = 4:
In the first case, we have x – y = 2 – 2 = 0 again. However, in the second case, we have x – y = 2 – 4 = -2.
As it turns out, there are no other possible combinations of x and y, but we don’t need to prove that; we can stop here.
The correct answer is (A).