Concept: The question tests on the application of Number Properties in a DS format

Solution:

The terms can be rearranged and written as a2+a (b+ c) +b c

Statement 1: a is odd

We do not know about b and c, if they are odd or even.

For eg, if b and c are both even, we have O + O (E + E) + E = O + O *E + E = O + E + E = O + E = Odd

if b and c are both Odd, we have O + O(O + O) + O = O + O *E + O = O + E + O = Even

 Answer options could be B, C or E

Therefore Statement 1 Alone is Insufficient
 

Statement 2: b + c is Odd

This means that one of them has to be odd and the other even, so bc = Even

If a is Odd, then we get O + (O * O) + E = O + O + E = O + O = Even

If a is even, then we get E + (E * O) + E = E + E + E = Even

Therefore Statement 2 Alone is (Sufficient).
Option B