GMATPrepNow wrote:

If p and q are different prime numbers, and n = pq – 2q, then which of the following cannot be true?

A) n is odd

B) n + 3 is a prime number

C) n is a prime number

D) nq is a prime number

E) n(p – 2) is a prime number

Another approach:

... then which of the following cannot be true? So, if an answer choice CAN be true, we'll ELIMINATE it.

A) n is odd

If p = 3 and q = 5, then n = 5, which is odd.

ELIMINATE A

B) n + 3 is a prime number

If p = 3 and q = 2, then n = 2, which means n + 3 = 5, and 5 IS prime.

ELIMINATE B

C) n is a prime number

If p = 3 and q = 5, then n = 5, which is prime.

ELIMINATE C

D) nq is a prime number

I can't find a counter-example, so I'll leave D and move onto E...

E) n(p – 2) is a prime number

If p = 3 and q = 5, then n = 5, which means n(p – 2) = 5, and 5 IS prime

ELIMINATE E

By the process of elimination, the correct answer is

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com

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