Hi Needgmat,

This DS question is based on Number Properties - a group of specific math rules that the GMAT tends to test frequently.

We're told that R and S are positive integers. We're asked "Is R/S an integer?" This is a YES/NO question.

Fact 1: EVERY factor of S is also a factor of R

This means that EVERY number that divides evenly into S also divides evenly into R. By definition, R/S will be an integer. Here's why:

If S = 4, then we know that S is evenly divisible by 1, 2 and 4. According to Fact 1, those numbers must also divide into R...

R could = 4, 8, 12, 16, etc.
4/4 = 1 = YES
8/4 = 2 = YES
12/4 = 3 = YES
16/4 = 4 = YES

Since everything that divides into S must divide into R, we know that R is a MULTIPLE of S. By extension, R/S will be an integer.
Fact 1 is SUFFICIENT

Fact 2: Every PRIME factor of S is also a prime factor of R.

Here we have a different Number Property: All of the PRIME numbers that divide into S will also divide into R. The problem with this piece of information is that repetition of primes is something you have to account for.

If S = 4, then it has just one prime factor: 2. So, 2 must divide into R.

If R = 2, then R/S = 2/4 = NOT an integer = NO
If R = 4, then R/S = 1 = YES
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich