Problem Solving

Most Manhattan GMAT students are trying to break the 700 barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level problem (I'll post the solution next Monday).

Question: Give or Take a Little

If r – s = 3p , is p an integer?

(1) r is divisible by 735

(2) r + s is divisible by 3
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Answer is C.
if (r-s) is divisible by 3 then p is an integer.
If r is divisible by 735 then r is divisible by 3.
and if r+s is divisible by 3 then s is factor of 3. which means subtracting s from r would also keep it divisible by 3, hence r-s is divisible by 3.

Am i right?

If r is divisible by 735, then it has to be a multiple of 3 because 735 is a multiple of 3; but this is not sufficient for p to be an integer since it does not tell us anything about s
r+s divisible by three indicates that r+s is a multiple of 3. E.g.
r=5, s=4
Therefore, r+s=9 which is divisible by 3 but r-s=1 which is not divisible by 3. Therefore statement 2 is insufficient on its own.
But if r is divisible by 3 then for r+s to be divisible by 3, s has to be divisible by 3.
Therefore both statements are sufficient together but not individually

what is the OA??