SajjadAhmad wrote:

If x is a factor of positive integer y, then which of the following must be positive?

A. x – y

B. y – x

C. 2x – y

D. x − 2y

E. y – x + 1

Dear

SajjadAhmad,

I'm happy to respond.

This is an interesting question.

Here, it's important to understand that, if P is a positive number, all the factors of P are less than P except for P itself.

Every positive integer is a factor of itself and a multiple of itself. That's very important to understand. Here's a blog article:

GMAT Math: FactorsHere's a free lesson:

Multiples For example, suppose y = 12. Then it could be true that x = 3 or that x = 12. Since the factor is sometimes smaller than the number, subtracting factor minus number would be negative. With the examples x = 3 and y = 12, we get

(A)

negative(B)

positive(C)

negative (D)

negative(E)

positiveWe eliminated three answer choices with that. Now, use x = 12 and y = 12.

(B)

negative(E)

positiveBy POE, the answer must be (E).

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)