Data Sufficiency

Try TESTING VALUES here:

Question: is 4 a factor of p - q?

(1) 4 is a factor of p.
Case #1:
p = 12
q = 5
p - q = 7 --> No, 4 is not a factor of p - q.

Case #2:
p = 12
q = 8
p - q = 4 --> Yes, 4 is a factor of p - q.

We got one "no" and one "yes," so this is insufficient.

Pro tip: when you're testing cases w/ 2 variables, it's often easiest to hold one value constant (as I did with p = 12) and vary the other (q = 7, q = 8).

(2) 4 is a factor of q.
Case #1:
p = 12
q = 8
p - q = 4 --> Yes, 4 is a factor of p - q.
(recycling a case we used before)

Case #2:
p = 11
q = 8
p - q = 3 --> No, 4 is NOT a factor of p - q.

We got one "no" and one "yes," so this is insufficient.

Together:
If both p and q are multiples of 4, then p - q must also be a multiple of 4. Sufficient.

The answer is C.