Is the sum of four different positive prime integers an odd integer?

[BTGModeratorVI]

Is the sum of four different positive prime integers an odd integer?

(1) One of the integers is 11.
(2) One of the integers is 2.

Answer: B
Source: GMAT prep

[Brent@GMATPrepNow]

Is the sum of four different positive prime integers an odd integer?

(1) One of the integers is 11.
(2) One of the integers is 2.

Answer: B
Source: GMAT prep

Target question: Is the sum of four different positive prime integers an odd integer?
This is a good candidate for rephrasing the target question.

The key concept involved here is that 2 is the only EVEN prime number, and all other prime numbers are ODD

So, if 2 is among the four primes, then the sum = EVEN + ODD + ODD + ODD = ODD
If 2 is NOT among the four primes, then the sum = ODD + ODD + ODD + ODD = EVEN

So, in order for the sum to be ODD, 2 must be among the four primes.
This means we can rephrase the target question as follows:
REPHRASED target question: Is 2 among the four primes?

Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: One of the integers is 11.
Since we have no information about the other three primes, 2 may or may not be among them.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: One of the integers is 2.
Perfect!
The answer to the REPHRASED target question is YES, 2 is among the four primes
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent