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If x is a factor of positive integer y, then which of the following mu

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If x is a factor of positive integer y, then which of the following mu [#permalink]

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New post 17 Mar 2017, 01:35
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A
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C
D
E

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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
[Reveal] Spoiler: OA

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Re: If x is a factor of positive integer y, then which of the following mu [#permalink]

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New post 17 Mar 2017, 10:05
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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: Factors
Here'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) positive

We eliminated three answer choices with that. Now, use x = 12 and y = 12.
(B) negative
(E) positive

By POE, the answer must be (E).

Does all this make sense?
Mike :-)
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Magoosh Test Prep

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Re: If x is a factor of positive integer y, then which of the following mu [#permalink]

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New post 02 Apr 2017, 23:27
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(1) There is no mention in the question that the two integers are DISTINCT. That means they can be equal and thus resulting in zero (such as in option A and B) which is neither positive nor negative.

(2) This is true because every integer is a factor of itself and a multiple of itself (e.g. 2 is a factor of 2 and 2 is a multiple of 2 (2*1)).

(3) Also 1 is a factor of every integer and thus would yield a negative result in option C and D.

Thus the answer is option E.
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Re: If x is a factor of positive integer y, then which of the following mu   [#permalink] 02 Apr 2017, 23:27
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