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# If p and q are different prime numbers, and n = pq – 2q, then which of

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GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4558
GMAT 1: 770 Q49 V46
If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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24 Apr 2017, 06:19
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Difficulty:

55% (hard)

Question Stats:

64% (02:10) correct 36% (02:14) wrong based on 165 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

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Senior Manager
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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24 Apr 2017, 06:32
1
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
Joined: 05 Mar 2015
Posts: 949
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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24 Apr 2017, 10:47
1
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
Joined: 11 Sep 2015
Posts: 4558
GMAT 1: 770 Q49 V46
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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25 Apr 2017, 05:37
1
Top Contributor
1
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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Joined: 09 Sep 2013
Posts: 14445
Re: If p and q are different prime numbers, and n = pq – 2q, then which of  [#permalink]

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23 Aug 2018, 22:49
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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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