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If x and y are positive integers, is x/y an integer? (1) [#permalink]
09 Sep 2007, 19:34

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct
0% (00:00) wrong based on 1 sessions

If x and y are positive integers, is x/y an integer?

(1) every factor of y is also a factor of x
(2) every prime factor of y is also a prime factor of x

I have OA but cannot understand the explanation, was wondering if anyone could explain in different words?

Specifically, what confuses me is OA explanation's claim that if you test x/y = 18/8, it will satisfy criteria for (2). How can this be? As I see it:

Prime factors of 18 = (2)(3)(3)
Prime factors of 8 = (2)(2)(2)

Hence ONE prime factor of y is also a prime factor of x, but it's false that EVERY prime factor of y is also a prime factor of x. I would think you'd need three 2s, i.e. (2)(2)(2), i.e. 2^3 in x for this to be the case.

St1:
If every factor of y is also a factor of x, then x must be a multiple of y and so x/y = integer. Sufficient.

St2:
If x = 15 and it has primes 5,3 and y = 75 which has primes 5 and 3, then x/y = non-integer. However, if x = 15 and y = 5, then x/y = integer. INsufficient.

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