If x is a positive integer, is 108/(x-2) an integer?

Render, You are combining both statements A and B and saying that x as 20 is not required. But, we need to validate each statement individually.

Asked: If x is a positive integer, is 108/(x-2) an integer?
108 = 2^2*3^3

I. x is non-prime number less than 9
x = {1,4,6,8}
x-2 = {-1,2,4,6}
108/(x-2) = {-108,54,27,18}
108/(x-2) is an integer
SUFFICIENT

II. x is a multiple of 4 and a factor of 20.
x = {4,20}
x-2 = {2,18}
108/(x-2) = {54,6}
108/(x-2) is an integer
SUFFICIENT

IMO D

Question stem:

This is asking me whether x-2 is a factor of 108. My first thought is that 108 doesn't have all that many factors, and listing the factors out will probably make it easier to work with the statements once I get there.

Create a factor table to list all of the factors (don't confuse this with a factor tree, which you would use for PRIME factors):

1 x 108
2 x 54
3 x 36
4 x 27
6 x 18
9 x 12

Is x-2 one of those numbers? (We're going to have to be careful to distinguish x versus x-2 - that makes this problem trickier!)

I. x is non-prime number less than 9

This tells you that x = 1, 4, 6, or 8. I'm going to assume that x can't equal 1, because that would make this problem a bit weird with regards to factors and negative numbers. On the GMAT, they'd probably tell you clearly that x isn't equal to 1.

So, x = 4, 6, or 8.

Then, x-2 = 2, 4, or 6.

Those three numbers are all on our list. Therefore, the answer to the question ("is x-2 one of these numbers?") is YES. This statement is sufficient.

II. x is a multiple of 4 and a factor of 20.

This tells you that x = 4 or 20.

Therefore, x-2 = 2 or 18.

Both of those numbers are on the list. Therefore, the answer to the question ("is x-2 one of these numbers?") is YES. This statement is sufficient.

The correct answer is D.