If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

AAPL wrote: ↑

Wed Apr 22, 2020 4:29 am

GMAT Paper Tests

If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

A. 0
B. 1
C. 2
D. 3
E. 5

OA B

A nice fast approach is to TEST a possible value of n.
Since n must be a prime number that's greater than 3, let's TEST n = 5

If n = 5, then n² = 5² = 25, and when we divide 25 by 12, we get 2 with REMAINDER 1

Answer: B

Cheers,
Brent

AAPL wrote: ↑

Wed Apr 22, 2020 4:29 am

GMAT Paper Tests

If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

A. 0
B. 1
C. 2
D. 3
E. 5

OA B

We can let n = 5. Thus n^2 = 25 and 25/12 = 2 R 1.

(Note: The answer choices don’t have a choice such as “Can’t be determined.” The question is not asking “what could be the remainder” either. We can safely say the correct answer must be 1, though we only used one value for n. If we want to further ensure that the answer must be 1, we can use another value for n, such as n = 7. We see that n^2 = 49 and 49/12 = 4 R 1. The remainder once again is 1.)

Answer: B