GmatKiss wrote:If m and n are nonzero integers, is m/n an integer?
(1) 2m is divisible by n
(2) m is divisible by 2n

Let's rephrase this target question.
If m/n is an integer, then we know that m = nk where k is an integer.
So, let's rephrase this target question as: Does m = kn for some integer k?

Statement 1: 2m is divisible by n
This means that 2m = qn for some integer q.
Divide both sides by 2 to get: m = (q/2)n
Do we have enough information to answer the target question? In other words, Does m = kn for some integer k?
Since (q/2) may or may not be an integer, we do not have sufficient information.

Statement 2: m is divisible by 2n
This means that m = q(2n) for some integer q.
Or we can write: m = 2qn
Do we have enough information to answer the target question? In other words, Does m = kn for some integer k?
Yes! Since q is an integer, we know that (2q) must be an integer.
So, we can be certain that m = kn for some integer k?
As such, statement 2 is sufficient, and the answer is B.

Cheers,
Brent