Quote:
Is the positive integer n an odd integer?
(1) n+4 is a prime number.
(2) n+3 is not a prime number
We know that n is positive. Side note: It can't be zero which is neither positive nor negative.
(1) First consider: By definition, a prime number has exactly two divisors, 1 and itself. So the only even prime number is two. Every other even number has at least three divisors 1, 2, and itself. We therefore know that n+4 is odd.
For addition the following rules apply:
odd+odd=even
even+even=even
odd+even=odd
We can conclude that n must be odd. Therefore (1) is sufficient.
Note that we know at this point that the possible answers are a or e. If (2) is n.s. we pick a. If (2) is sufficient we pick e. Even if we can't figure out if (2) is sufficient we have a 50% chance.
(2) First consider. There is an infinite amount of non-prime numbers (both even and odd). So there is an infinite number of possible values for n.
Examples:
If n=1 (which is odd) then n+3=4 (which is not prime)
If n=6 (which is even) then n+3=9 (which is not prime)
So n could be odd or even and therefore (2) is not sufficient.
The answer is a.