Source: GMAT 10'th edition ( DS #65. pg 308)

If m is an integer, is m odd?

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

I am coming up with D but the explanation says B. I used the CLA method:

for statament 1:
Criteria= integer, m/2 is odd

2, 6, 10, 14, 18

So to me statement 1 is sufficient i.e. m is not ODD. But the answer is saying that it is NOT sufficient.

The problem here is that "NOT an even integer" is not the same as "IS an odd integer." Instead, "NOT an even integer" encompasses two possibilities:
* odd integer
* not an integer at all (in this case, an integer-and-a-half)

The second possibility admits odd integers (all of them, in fact), thus spoiling the fun.