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 →

Remainder

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 141
Joined: Fri Jun 24, 2011 4:35 amFollowed by: 1 member
Location: Edison
Thanked: 12 times
by ani781 » Mon Oct 14, 2013 10:40 am
When 51^25 is divided by 13, the remainder obtained is:
A. 12
B. 10
C. 2
D. 1
E. 0

OA after some discussion,but how to approach this kind of a problem ?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 81
Joined: Tue Jun 11, 2013 10:24 pmFollowed by: 1 member
Thanked: 7 times

by sanjoy18 » Mon Oct 14, 2013 10:46 am
Answer A..51 and 13 are co-prime number hence by using Euler theorem

reminder is 12
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Mon Oct 14, 2013 5:15 pm
I think we can see that the units digit is 1, so 1 raised to any number of times will always be 1, so when 1 is divided by 13, we get 12, so has to be A
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members
Location: Bangalore, India
Thanked: 97 times
GMAT Score:750

by ganeshrkamath » Mon Oct 14, 2013 7:47 pm
ani781 wrote:When 51^25 is divided by 13, the remainder obtained is:
A. 12
B. 10
C. 2
D. 1
E. 0

OA after some discussion,but how to approach this kind of a problem ?
13*4 = 52
So 51 mod 13 = -1
51^25 mod 13 = (-1)^25 mod 13 = (-1) mod 13 = 12
Choose A

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

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 » Mon Oct 14, 2013 8:53 pm
vinay1983 wrote:I think we can see that the units digit is 1, so 1 raised to any number of times will always be 1, so when 1 is divided by 13, we get 12, so has to be A
Be careful. The answer is, indeed, A but for a different reason. If we applied the above logic, the remainder when 51^2 is divided by 13 will be 12, but the remainder is actually 1.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 468
Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members
Thanked: 29 times

by vipulgoyal » Tue Oct 15, 2013 3:38 am
When 51^25 is divided by 13, the remainder obtained is:
A. 12
B. 10
C. 2
D. 1
E. 0

OA after some discussion,but how to approach this kind of a problem ?13*4 = 52
So 51 mod 13 = -1
51^25 mod 13 = (-1)^25 mod 13 = (-1) mod 13 = 12
Choose A

----

I think GMAT doesnt suppose students to know mod, ne ways here we go
51^25/13
51/13 = {13(3) +12 }/13 = 12
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Tue Oct 15, 2013 4:07 am
Another approach:

Divide 25 by 4.. the remainder is "1"

So, rephrase the question: (51)^1/13 = 51/13 = 12

Answer [spoiler]{A}[/spoiler]
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1