Carcass wrote:
If the sum of two prime numbers x and y is odd, then the product of x and y must be divisible by
(A) 2
(B) 3
(C) 4
(D) 5
(E) 8
Some important rules:
1. ODD + ODD = EVEN
2. ODD + EVEN = ODD
3. EVEN + EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVENIf x + y = ODD, then one of the values must be ODD and the other value must be EVEN
Since 2 is the ONLY EVEN prime number, then we can be certain that either x or y equals 2.
So, xy = (2)(some ODD prime number)
In other words, xy = (EVEN )(ODD) = EVEN (from
rule 5)
So, xy is EVEN, which means xy is divisible by 2
Answer: A
Cheers,
Brent