BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

OG2016 - If n is a prime number greater than 3

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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 » Sun May 01, 2016 9:48 am
boomgoesthegmat 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

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 410
Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members
Location: Worldwide
Thanked: 120 times
GMAT Score:770

by OptimusPrep » Mon May 02, 2016 7:32 pm
boomgoesthegmat 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

OA: B
We can solve this problem by testing values easily.
Assume n = 7, n^2 = 49
Remainder of (49/12) = 1

Another approach: Always remember that any prime number apart from 2 is of the form (6k +- 1)

Assume n = 6k + 1, n^2 = 36k^2 + 12k + 1
Remainder of (n^2/12) = 1

Assume n = 6k - 1, n^2 = 36k^2 - 12k + 1
Remainder of (n^2/12) = 1

Correct option: B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sat Feb 24, 2018 1:19 pm
Hi All,

We're told that N is a PRIME number GREATER than 3. We're asked for the remainder when N^2 is divided by 12. Many questions in the GMAT Quant section can be solved by TESTing VALUES - and this question can be too. In general, you want to choose the 'easiest' value(s) that fit the given situation. You might notice that two of the explanations to this question us N=5 and N=7 - and they both lead to the SAME correct answer. These patterns hold true even when you use a value that isn't the 'easiest' one available. For example...

IF... N=11, then N^2 = (11)^2 = 121
121/12 = 10 r 1

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8137
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Tue Mar 27, 2018 10:42 am
boomgoesthegmat 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
We can let n = 5. Thus n^2 = 25 and 25/12 = 2 R 1.

(Note: Since the answer choices don't have a choice such as "Can't be determined." We can safely say the correct answer must be 1, though we only used one value for n. If we want to make sure further 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1