Statement 1 :
f is odd==> g may be 0, odd, even(except 0)
for g = 0, fg+2 = 2 which is prime
for g = odd, fg will be odd===> fg+2 will be even which is not prime
Hence INSUFF
Statement2:
g is even. possible values of g = 0, 2 ,4, 6
possible values of f = 0, even number (except 0), odd
for f = 0, fg = 0, fg+2 = 2 Prime number
for f = odd, fg will be even, fg+2 will also be even so not prime
for f = even, fg will be even , fg+2 be even so not prime
hence INSUFF
Taken them together
f is odd, g is even
g may be 0 as 0 is an even integer
for g =0, fg+2 will be 2 Prime number
for g != 0, fg+2 will be even not a prime number
Hence INSUFF
Answer is 'E'
Amardeep, what is 'OA'