Data Sufficiency

p is an integer; n is an integer; and p/n is an integer. Is p/n odd?
(1) p is divisible by 4.
(2) n is divisible by 4.

Try using examples.

(1) Nothing is mentioned about n, so it is insufficient. Let's say p = 12, n could be anything (2,4 for example). p/n is an integer, but it could be 12/2 = 6 (even), or 12/4 = 3 (odd). Insufficient.
(2) Same thing as 1. n could be 4 (which is divisible by 4), but p could be 12, or 24, which would make p/n 3 or 6 respectively. Insufficient.

(1) + (2): let's say p = n = 4, then p/n = 1 which is odd. what if p = 8 and n = 4 (both of these are divisible by 4), then p/n = 2, which is even. Still insufficient.

You're left with choice E.