Hi vishugogo,

In these types of DS questions, TESTing values is a great way to prove what's possible.

Here we're told that R and S are positive integers (which is really restrictive) and we're asked "Is R/S is an integer?" This is a Yes/No question

Fact 1 tells us that EVERY factor of S is a factor of R

In math, if every number that divides into a number divides into another number, then the second number is a multiple of the first. Here's the proof:

Let's set S = 2
2 is divisible by 1 and 2
Based on what we're told, we'd have to pick a number that was divisible by 1 and 2....
So R could be = 2, 4, 6, 8, 10 etc.
R/S could be:
2/2 = 1 and the answer to the question is YES
4/2 = 2 and the answer to the question is YES
6/2 = 3 and the answer to the question is YES
etc.

Now, let's try an odd number
Let's set S = 3
3 is divisible by 1 and 3
So R could be, 3, 6, 9, 12, 15, etc.
R/S could be:
3/3 = 1 YES
6/3 = 2 YES
9/3 = 3 YES
etc.
Since the results are consistent, Fact 1 is SUFFICIENT

Fact 2 tells us that every PRIME factor of S is a PRIME factor of R
This language makes me suspicious; why the focus on the word "prime?" Be cynical when you do your TESTs...
We could use:
S = 2
The only prime factor is 2
R coud be 2, 4, 6, 8 etc.
2/2 = Yes
4/2 = Yes
6/2 = Yes
etc.

BUT if S = 8
The only prime factor is 2
R could be 2, 4, 6, 8
2/8 = 1/4 = NO
8/8 = 1 = YES
Inconsistent = INSUFFICIENT

Final Answer: A

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