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 D
Cheers,
Brent