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GMAT Prep integer question (r and s)

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GMAT Prep integer question (r and s)

by Baldini » Tue Apr 07, 2009 5:37 am
If r and s are positive integers, is r/s an integer?

1. Every factor of s is also a factor of r
2. Every prime factor of s is also a factor of r

OA is A .

Can someone please explain why, especially with reference to the second statement?

thanks in advance
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by mjjking » Tue Apr 07, 2009 5:48 am
Just try testing some numbers.

From 1. we know that r and s share the all the factors of s. Hence, if r is 70 (7x2x5) it means that s is either 2, 5, 7, 2x7, 2x5, 2x5x7. Hence sufficient.

From 2 I think it helps to plug in numbers to see this:

let r = 18 (has prime factors 2, 3, 3)
let s = 6 (has prime factors 2,3)

Since the prime factors of 6 (2, 3) are also the prime factors of 18, we can say in this case that r/s is an integer

let r = 18 (has prime factors 2, 3, 3)
let s = 8 (has prime factors 2, 2, 2)

All of the prime factors of s (2, 2, 2) are not the prime factors of 18, so we can say that r/s is not an integer in this case.

So statement 2 is insufficient.
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