I find both statements independently as sufficient.
A - 'coz when a number is divisible by 8,it's also divisible by 4.remainder 5 divided by 4 will always leave 1 as remainder.
so from choice A ,1 will be remainder.
B- is sufficient 'coz any even number will be of the form 2x.so if p = sq(2a) + sq(2b)= 4[sq(a) + sq(b)].dividing such a number
by 4 will always give remainder 0.
My answer is D.
How do you get even number? To me, stmt2 simply says that p = a^2 + b^2.
For a=1 and b=2, p = 5 and remainder = 1 when divided by 4.
For a=1 and b=3, p = 10 and remainder = 2 when divided by 4.
Hence, B is insufficient.