If m is an integer…
We are given that m is an integer and we must determine whether it is odd.
Statement One Alone:
m/2 is not an even integer.
The information in statement one is not enough to determine whether m is odd since m can be odd or even. For example, if m = 3 (an odd number), m/2 = 3/2 = 1.5 is not an even integer. On the other hand, if m = 2 (an even number), m/2 = 2/2 = 1 is not an even integer also.
Thus, statement one is not sufficient to determine whether m is odd. We can eliminate answer choices A and D.
Statement Two Alone:
m – 3 is an even integer.
Since m – 3 is an even integer, we can say m – 3 = even. That is, m = even + 3. Since 3 is odd and we know that even + odd = odd, we know that m must be an odd integer.
Statement two is sufficient to answer the question.