I thought I'd throw in an example to illustrate Mom4MBA's explanation.

Statement 1: Neither c nor d is an integer.
Certainly not sufficient

Statement 2: c - d = 3
If we could be certain that c and d are both integers, this statement would be sufficient. However, since we cannot be certain of this, there are different cases to consider. The two cases I'll mention are:

Case a) c and d are both integers
For example, if c=4 and d=1, then there are 2 integers between c and d (they are 2 and 3)

Case b) c and d are not both integers
For example, if c=4.5 and d=1.5, then there are 3 integers between c and d (they are 2, 3 and 4)

So, statement 2 is not sufficient.


Statements 1 & 2:
Statement 1 guarantees that case b (above) is the only case, in which case we have sufficient information and the answer is C

Cheers,
Brent