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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If p and q are different prime numbers, and n = pq – 2q, then which of

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GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4337
If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 64% (02:09) correct 36% (02:14) wrong based on 164 sessions

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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

_________________
Senior Manager  G
Joined: 02 Mar 2017
Posts: 252
Location: India
Concentration: Finance, Marketing
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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nq cannot be a prime number
For nq to be a prime number n should be 1---q is already prime----or a fraction
But n = pq-2q
n=q(p-2)---neither a fraction nor one
hence D
All other options can be true
Director  V
Joined: 05 Mar 2015
Posts: 959
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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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

*kudos for all correct solutions

Ans D
for nq to be prime , n must be 1
which is not possible .
since pq are diff primes ,lowest value of n is 0
where p=2 and q=3
but as we choose other prime set for the term pq , pq-2q or n will be greater than 1

Ans D
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4337
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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Top Contributor
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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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Posts: 14123
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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_________________ Re: If p and q are different prime numbers, and n = pq – 2q, then which of   [#permalink] 23 Aug 2018, 22:49
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