**Concept: The question tests on the application of exponents and equation in a DS format.**

**Solution:**

2^{x+y} = (2^{2})^{8} = 2^{16}

x +y = 16

St (1) x2^{ }= 81 and thus x = 9, - 9

Hence y = 7, 25

No unique value of y is obtained. **Insufficient**

St (2) x-y =2

Along with x + y =16 (given) a unique value of y = 7 can be obtained.

Thus S**ufficient****.**

** **

Hence **option (b)**