Question

If a number y has a positive integer factors then y and 2z integer factors. Is it true? how?

Answer 1

Given:

x is a factor of y --> , for some non-zero integer ;

y is a factor of z --> , for some non-zero integer ;

So, .

Question: is z even? Note that will be even if either or is even

(1) even --> either even, so the answer is directly YES or is even (or both). But if is even and as then z must be even too (one of the multiples of z is even, so z is even too). Sufficient.

(2) even --> as then as one of the multiples of z even --> z even. Sufficient.

Answer: D.