If the sum of two prime numbers x and y is odd, then the product of x

Question

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

Source:   Nova GMAT  
Difficulty Level:   500

BrentGMATPrepNow · Accepted Answer

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) = EVEN

If 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

sashiim20 · Answer

Sum of 2 numbers would be odd only when even number is added to odd number. (Even + Odd = Odd)
Only even prime number is 2. Hence one of the prime numbers must be 2. 
Hence the  product of x and y must be divisible by 2 .  Answer A.

Abhishek009 · Answer

Properties of Prime numbers required for solving this question -

1. All Prime numbers (except 2 ) are ODD
2. Sum of 2 prime numbers (except 2) is always Even

Suggests that either x or y is 2 and the product is even.

Thus, the product must be divisible by 2 , answer will be (A)

sonikavadhera · Answer

All prime numbers except 2 are odd, hence for the sum of two prime numbers to be odd - one has to be even and hence 2, as 2 is the only even prime number
hence IMO 2 (A) is the OA

JeffTargetTestPrep · Answer

All prime numbers are odd, except for 2. Recall that odd + odd = even and that even + odd = odd. If the sum of two prime numbers is odd, then we see that one of the numbers must be 2 and the other number must be odd. Thus, the product xy is a multiple of 2 and must be divisible by 2.

Answer: A

guilherme28 · Answer

Why can not be alternative b, since 2x3=6:3=2?

Bunuel · Answer

The question ask xy MUST be divisible by which one of the following numbers, not COULD be divisible by which one of the following numbers. It COULD be divisible by any prime but it MUST be divisible only by 2. So, it will ALWAYS be divisible by 2, and will be divisible by 3 if and only one of the primes is 3.

guilherme28 · Answer

Oh, that's right! What a dumb question of mine! :lol:

Thanks a lot.

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If the sum of two prime numbers x and y is odd, then the product of x

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