Q. if m is an integer, is m odd?

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

Ans: Correct B
explaination
(1) since m could be either the odd integer 3 or the even integer 10 and still satisfy this condition, there is no information to definately show where m is odd or even, NOT sufficient

My question:
While substituting values for m, if m = 3, 3/2 = NOT an INTEGER, why does the solution refers to value of m = 3 as a good value for m? I was only substituting values for m such that m/2 would not be even AND would be an integer?
So I had values of m that qualify as 2, 5, 10, 14.. etc and I said stat (1) is sufficient! Can someone please help? What I am I missing here?

You're currently reading the answer choice incorrectly. As an analogy, take the following:

(1) X is not a blonde woman

I satisfy this criterion, because I'm a man and I have dark hair. If you substitute 'integer' for 'woman' and 'even' for 'blonde', you'll see the fallacy in your logic: you'd be saying that I don't satisfy (1), 'not a blonde woman', because I'm not a woman. Not so: if EITHER I'm a man OR I have dark hair, then I'm included in this description.

To satisfy (1) it is enough EITHER that m/2 is not even, OR that m/2 is not an integer at all. So values like m = 3, 5, ... are fine.