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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If p and q are different prime numbers, and n = pq
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12 May 2017, 06:53
12 May 2017, 06:53
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Question Stats:
38% (01:28) correct
61% (01:52) wrong based on 78 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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If p and q are different prime numbers, and n = pq
[#permalink]
13 May 2017, 04:38
13 May 2017, 04:38
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
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 D
Cheers,
Brent
Re: If p and q are different prime numbers, and n = pq
[#permalink]
16 Aug 2021, 19:30
16 Aug 2021, 19:30
1
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
If p and q are different prime numbers, and n = pq – 2q, then which of the following cannot be true?
D) nq is a prime number
I can't find a counter-example, so I'll leave D and move onto E...
By the process of elimination, the correct answer is D
Cheers,
Brent
P=2 q=5
N=0
nq=0 it is not prime number
