Data Sufficiency

Here's my issue:

Let's take, for example, the following problem

If m is an integer, is m odd?

(1) m/2 is not an even integer
(2) m-3 is an even integer

This is quite simple to answer:

(1) If m/2 is not an even integer then it's either not an integer or it's an odd integer so statement 1 is NOT sufficient
(2) If m-3 is even then m must be odd so statement 2 IS sufficient

So the answer is "B) Statement 2 alone is sufficient, but statement 1 is not"

But what if statement (2) would look like this:

(2) m-2 is an even integer

In this case m must be even for obvious reasons. The way I see it is that I have found out that m is NOT odd (the question being 'ís m odd?') but I don't know whether I should mark down the same answer as above (B) or E.