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

Question

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

VyshakhR1995 · Answer

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

rohit8865 · Answer

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

BrentGMATPrepNow · Answer

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  D

Cheers,
Brent

Fdambro294 · Answer

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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MartyMurray · Answer

If p and q are different prime numbers, and n = pq – 2q, then which of the following cannot be true?

We can manipulate the expression in the prompt to get the following:

n = (p - 2)q

A) n is odd

Since p and q are prime, p - 2 and q can both be odd.

odd × odd = odd

This can be true.

Eliminate.

B) n + 3 is a prime number

If p = 2, then n = (p - 2)q = 0

In that case, n + 3 = 3, a prime number.

This can be true.

Eliminate.

C) n is a prime number

If p = 3, then p - 2 = 1.

In that case, n = (p - 2)q is 1 time a prime number, which is prime.

This can be true.

Eliminate.

D) nq is a prime number

Since q is prime, for nq to be prime, n must be 1 or a fraction.

n cannot be 1 or a fraction because no integer p - 2 times a prime q can be 1 or a fraction.

This cannot be true.

Keep.

E) n(p – 2) is a prime number

If p = 3, then p - 2 = 1.

In that case, n = (p - 2)q is 1 times a prime number, which is a prime number

In that case, n(p - 2) is a prime times 1, which is prime.

This can be true.

Eliminate.

Correct answer:   D

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards