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Another approach-
S1: c= b+1
If c and b were integers, then this statement tells c and b are consecutive integers, so d, which lies between them has to be non-integer. Then our answer to the question would be a NO. But since it is not given that c and b are integers, we have to consider the case if c and b are both non-integers with a difference of 1 (e.g.. 1.5 and 0.5), then it is possible that d is an integer and answer to question would be YES.
Thus Statement 1 is INSUFFICIENT.

S2: d = (b+c)/2

If sum of b and c is even, then d will be integer, so answer to question will be YES.
If sum of b and c is odd, then d is not an integer. So answer to question is NO.
Thus, statement 2 is INSUFFICIENT.

Combine (1) and (2), it says:
d = (2b+1)/2

One may falter here thinking, 2b+1 has to be ODD, so d is definitely not integer. However, one should not forget that b can be non-integer e.g. 1.5, and then d will be an integer. So both statements combined are INSUFFICIENT.

Answer: E

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