Answer should be (E).

1. f is odd. IN SUFFICIENT, as we don't have any information regarding g.
2. g is even. IN SUFFICIENT, as we don't have any information regarding f.

Lets take both statement together.

fg will be even. As odd X even = even.

Again fg + 2 = even integer (because even + even = even)

However fg + 2 = prime number only when fg = 0 (because 2 is the only even prime number and we have already prove that fg + 2 = even integer).

So any how we don't the value of fg, as it could be anything like -1, 0, 1, 2 etc. So again both (1) and (2) are INSUFFICIENT.

Hence IMO (E)

Hope this helps...

codesnooker wrote:Answer should be (E).

1. f is odd. IN SUFFICIENT, as we don't have any information regarding g.
2. g is even. IN SUFFICIENT, as we don't have any information regarding f.

Lets take both statement together.

fg will be even. As odd X even = even.

Again fg + 2 = even integer (because even + even = even)

However fg + 2 = prime number only when fg = 0 (because 2 is the only even prime number and we have already prove that fg + 2 = even integer).

So any how we don't the value of fg, as it could be anything like -1, 0, 1, 2 etc. So again both (1) and (2) are INSUFFICIENT.

Hence IMO (E)

Hope this helps...

Nice explanation codesnooker! I agree with u. But if u take this approach -Taking both stmts in account, fg will be even and thus fg + 2 even.
Again as stmt-1and 2 are saying that f and g are odd and even integers, none of f anf g can be zero.
So fg + 2 can not be equal to 2 in any sense!
So fg + 2 will be even other than 2. So fg + 2 can not be prime. So taking both the stmts, we can conclude that fg + 2 can never be prime. So I can go for C.
- Can u pls point out where I am wrong?

camitava wrote: Again as stmt-1and 2 are saying that f and g are odd and even integers, none of f anf g can be zero.

Zero is even integer. I think you are confused with this point. So fg could be zero also. Hence Fg +2 = 2 (if fg = 0). Hence its gives us a prime number. However if fg = 2 or any other even number, then fg + 2 will gives us a non-prime number.

Check the link if you still have any doubt:- https://en.wikipedia.org/wiki/Evenness_of_zero

Codesnooker, Thanks a lot! Yop! I was confused about the fact Whether zero is an even number or not. If zeros comes as an even number, obviously the best option to chose is E.

Zero is even.
Ans E


Thanks,
Vikas