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GMAT Prep- 1

by akhilsuhag » Thu Sep 01, 2011 8:03 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 prime factor of r.

I marked that both are sufficient, but it is not so. What numbers can I choose for the second statement that makes it insufficient.
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by Anurag@Gurome » Thu Sep 01, 2011 8:26 am
akhilsuhag wrote: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 prime factor of r.
Statement 1: As every factor of s is also a factor of r, s itself is a factor of r. Hence, r/s is an integer.

Sufficient

Statement 2: Every prime factor of s is also a prime factor of r. But the same prime factors may be contained in s more than they are contained in r. For example, take r = 2 and s = 4. Both r ans s have the same prime factor 2 but r/s is not an integer.

Not sufficient

The correct answer is A.
Anurag Mairal, Ph.D., MBA
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