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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Wed Apr 17, 2019 12:27 am

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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

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Source: Beat The GMAT — Problem Solving | Wed Apr 17, 2019 12:27 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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 nÂ² 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 nÂ² = 5Â² = 25
When 25 is divided by 12, the quotient is 2 and the remainder is 1

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2543; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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