If x and y are positive integers, what is the value of y?


(1) y − x = 3

(2) x and y are prime numbers
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Target question: What is the value of y?

Statement 1: y − x = 3
Clearly NOT SUFFICIENT

Statement 2: x and y are prime numbers
Clearly NOT SUFFICIENT

Statements 1 and 2 combined
The GMAT loves to test us on the fact that, although there are infinitely many prime numbers, ONLY ONE of those primes is EVEN
That is, 2 is the only EVEN prime number. All other primes are ODD.

Statement 2 tells us that x and y are prime.
And statement 1 tells us that y − x = 3
Hmmm, y - x = 3, which is odd.
This means that one value is EVEN, and the other value is ODD (since this is the only way to get an odd difference)

If one number is EVEN, then that number must be 2.
So, if y - x = 3, it must be the case that y = 5 and x = 2
So, the answer to the target question is y = 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

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