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If n is a prime number greater than 3, what is the remainder

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by Brent@GMATPrepNow » Wed Apr 17, 2019 5:50 am
Gmat_mission wrote:If n is a prime number greater than 3, what is the remainder when n² is divided by 12?

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

[spoiler]OA=B[/spoiler]

Source: Official Guide
Choose ANY prime number greater than 3, and test it.

If n = 5, then n² = 5² = 25
When 25 is divided by 12, the quotient is 2 and the remainder is 1

Answer: B

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by swerve » Wed Apr 17, 2019 9:10 am
Any prime number greater than \(3\), can be written as \((6k \pm 1)\); for \(k\) (integer) \(>0\).

So as per \(Q\) Stem, \(n\) will be of the form of \((6k \pm 1)\) AND \(n^2=(6k\pm1)^2=36k^2+1^2\pm12k\).

So, when divided by \(12\), \(n^2=36k^2+1^2\pm12k\), leaves \(1\) as remainder.

Therefore, __B__ is the correct option.
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by Scott@TargetTestPrep » Fri Apr 19, 2019 9:11 am
Gmat_mission wrote: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

[spoiler]OA=B[/spoiler]

Source: Official Guide
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

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