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

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

Rule: if D is a factor of X ——- and D is a factor of Y

Then it must necessarily be true that:

X - Y = Factor of D

P and Q are different prime numbers, which means neither can be 1 ——-> which further means any Multiple of P or Q can never be equal to 1

N = PQ - 2Q

N = (Multiple of Q) - (Multiple of Q)

Thus, N itself must be = (Multiple of Q)

Looking at D:

(N) (Q) = Prime. ————> means that the term (N)(Q) must only be divisible by 1 and itself, (N)(Q)———- and the only way this would be possible is if either one of the individual factors, N or Q, is equal to = 1

However Q = prime number —— so can not be 1

And

N = (Multiple of that prime number) —— so can not be 1 either

Thus the result of (N)(Q) must be divisible by another factor other than 1 and itself, and can NOT be Prime.

(D)

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