Problem Solving

VJesus12 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) = 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

VJesus12 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

Alternatively, we can use the process of elimination to solve the question.

The question asks "the product of x and y must be divisible by..."
So, if we can show that the product xy is NOT divisible by a certain answer choice, then we can ELIMINATE that answer choice.

GIVEN: the sum of two prime numbers x and y is odd
So, for example, x = 2 and y = 7 satisfies the given information.
xy = (2)(7) = 14, so it's possible that xy = 14

Now check the answer choices....

(A) 2. 14 IS divisible by 2. So, KEEP A for now.
(B) 3. 14 is NOT divisible by 3. ELIMINATE B
(C) 4. 14 is NOT divisible by 4. ELIMINATE C
(D) 5. 14 is NOT divisible by 5. ELIMINATE D
(E) 8. 14 is NOT divisible by 8. ELIMINATE E

By the process of elimination, the correct answer is A

Cheers,
Brent

Hi VJesus12,

This question is all about Number Property rules, so you can either TEST VALUES or use your knowledge of those NP rules to answer the question. As an aside, the fact that X and Y are PRIME is actually irrelevant to this question. If the two variables are positive integers, and their sum is ODD, then one of the variables MUST be EVEN and the other MUST be ODD. The product of an even and an odd is ALWAYS EVEN. By extension, even numbers are ALWAYS divisible by 2.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

VJesus12 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

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