It is currently 19 Oct 2017, 07:51

STARTING SOON:

Live Chat with Cornell Adcoms in Main Chat Room  |  R1 Interview Invites: MIT Sloan Chat  |  UCLA Anderson Chat  |  Duke Fuqua Chat (EA Decisions)


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is a positive integer, what is the remainder when 3^n is divided

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128853 [0], given: 12183

If n is a positive integer, what is the remainder when 3^n is divided [#permalink]

Show Tags

New post 21 Aug 2017, 06:15
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:02) correct 22% (00:46) wrong based on 46 sessions

HideShow timer Statistics

Kudos [?]: 128853 [0], given: 12183

BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1454

Kudos [?]: 594 [0], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
If n is a positive integer, what is the remainder when 3^n is divided [#permalink]

Show Tags

New post 21 Aug 2017, 07:42
3^1(3) divided by 10 gives us a remainder of 3
3^2(9) divided by 10 gives us a remainder of 9
3^3(27) divided by 10 gives us a remainder of 7
3^4(81) divided by 10 gives us a remainder of 1
3^5(243) divided by 10 gives us a remainder of 3
3^6(729) divided by 10 gives us a remainder of 9
If you look there is a pattern of remainders for the different numbers 3,9,7,1,3,9.....

1. n is a multiple of 8
n can be 8,16,24.... and so on
The remainder will be the same when 3^n is divided by 10 if the values of n are evenly spaced.
Hence, this statement alone is sufficient

2. n is a multiple of 12
n can be 12,24,36.... and so on
The remainder will be the same when 3^n is divided by 10 if the values of n are evenly spaced.
Hence, this statement alone is sufficient(Option D)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 594 [0], given: 16

Senior Manager
Senior Manager
avatar
G
Joined: 25 Feb 2013
Posts: 401

Kudos [?]: 170 [0], given: 31

Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
If n is a positive integer, what is the remainder when 3^n is divided [#permalink]

Show Tags

New post 21 Aug 2017, 08:16
Bunuel wrote:
If n is a positive integer, what is the remainder when 3^n is divided by 10?

(1) n is a multiple of 8
(2) n is a multiple of 12


The question asks what is the value, so we need to know whether a definite value is possible here.

The remainder when any number is divided by 10 will be its Units Digit. So we need to find the unit's digit of integer \(3^n\)

Statement 1: Let \(n = 8k\). so \(3^n = 3^{8k} = (3^4)^{2k}\)
\(3^4 = 81\), so units digit will \(1\) and \(1\) raised to any power will be \(1\). So the unit's digit of \(3^n\) will \(1\), hence the remainder when divided by \(10\) will be \(1\). Sufficient

Statement : Let \(n = 12q\). so \(3^n = 3^{12q} = (3^4)^{3q}\)
\(3^4 = 81\), so units digit will \(1\) and \(1\) raised to any power will be \(1\). So the unit's digit of \(3^n\) will \(1\), hence the remainder when divided by \(10\) will be \(1\). Sufficient

Option \(D\)

Kudos [?]: 170 [0], given: 31

If n is a positive integer, what is the remainder when 3^n is divided   [#permalink] 21 Aug 2017, 08:16
Display posts from previous: Sort by

If n is a positive integer, what is the remainder when 3^n is divided

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.