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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Divisibility and Remainder !

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 80
Joined: Wed Aug 12, 2009 8:49 pm
Location: San Francisco, CA
Thanked: 16 times

by grockit_jake » Tue Aug 25, 2009 2:20 pm
For this question, we need to know what n is to find the answer.

With remainders, it helps to look for patterns, though. 3 raised to a positive integer will leave a one's digit in the following pattern:

3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3 ......

Because (4n + 3) will yield an ODD number (assuming n is a positive integer) we know that the one's digit will be either 3 or 7.

When dividing by 5, the remainders will either be 3 or 2 respectively.

Again, this depends on n.
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Jul 27, 2009 9:58 am

Re: Divisibility and Remainder !

by raka3399 » Wed Aug 26, 2009 9:37 am
raka3399 wrote:What is the remainder of 3^4n+3 divided by 5 ???

how best to solve such sums efficiently?
Jake , letz assume that n is positive as in 1,2,3,4....

doesn't it make 3^4n+3 have a 7 as its unit digit giving a remainder of 2 when divided by 5 ALWAYS!!!

correct me if am wrong !!

Thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 80
Joined: Wed Aug 12, 2009 8:49 pm
Location: San Francisco, CA
Thanked: 16 times

by grockit_jake » Wed Aug 26, 2009 10:09 am
There is a difference between 3^(4n+3) and 3^4n + 3.

Assuming it's 3^(4n+3):

n=1, 3^(4n+3) = 3^7 = 2187 (remainder of 2)
n=2, 3^(4n+3) = 3^11 = 117147 (remainder of 2)

So yes, you are right. Because of the coefficient of 4, each increase of 1 in n, makes the exponent jump four spots in the 3,9,7,1 pattern, leaving you back at 7.
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Jul 27, 2009 9:58 am

by raka3399 » Wed Aug 26, 2009 1:07 pm
grockit_jake wrote:There is a difference between 3^(4n+3) and 3^4n + 3.

Assuming it's 3^(4n+3):

n=1, 3^(4n+3) = 3^7 = 2187 (remainder of 2)
n=2, 3^(4n+3) = 3^11 = 117147 (remainder of 2)

So yes, you are right. Because of the coefficient of 4, each increase of 1 in n, makes the exponent jump four spots in the 3,9,7,1 pattern, leaving you back at 7.
Sorry Jake guess it could be termed as a presentation error ... yes its 3^(4n+3) divided by 5 :)

many thanks again!

you rock !!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Thu Aug 27, 2009 8:51 am
We certainly need to know that n is a positive integer here. If that's given, we do not need any further information about n to answer the question, regardless of whether the expression is written as (3^4n) + 3 or as 3^(4n + 3). In the first case, we have

(3^4n) + 3 = (3^4)^n + 3 = 81^n + 3.

Since 81^n will end in 1 regardless of the value of n, 81^n + 3 will end in 4, and the remainder will be 4 when 3^4n + 3 is divided by 5.

In the second case, we have

3^(4n + 3) = [3^(4n)]*[3^3] = [81^n]*[3^3] = [81^n]*[27]

and since we are multiplying one number which ends in 1 with a number which ends in 7, the product must end in 7, so the remainder will be 2 when 3^(4n + 3) is divided by 5.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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