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If p and q are different prime numbers, and n = pq

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GRE Instructor
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If p and q are different prime numbers, and n = pq [#permalink] New post 12 May 2017, 06:53
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Question Stats:

40% (01:31) correct 60% (01:27) wrong based on 10 sessions
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

*kudos for all correct solutions
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com
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GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1238
Followers: 46

Kudos [?]: 1126 [0], given: 7

Re: If p and q are different prime numbers, and n = pq [#permalink] New post 13 May 2017, 04:38
Expert's post
GreenlightTestPrep 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



One 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
[Reveal] Spoiler:
D


Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: If p and q are different prime numbers, and n = pq   [#permalink] 13 May 2017, 04:38
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If p and q are different prime numbers, and n = pq

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