GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Nov 2018, 19:57

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

# For a positive integer n, when 3^n is divided by 5, what is the remain

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Apr 2013
Posts: 34
For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

### Show Tags

03 Jul 2017, 14:20
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:21) correct 21% (00:58) wrong based on 112 sessions

### HideShow timer Statistics

For a positive integer n, when 3^n is divided by 5, what is the remainder?

(1) n is a multiple of 4.
(2) n is a multiple of 2.
VP
Joined: 05 Mar 2015
Posts: 1000
Re: For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

### Show Tags

03 Jul 2017, 18:11
1
roastedchips wrote:
For a positive integer n, when 3^n is divided by 5, what is the remainder?
1) n is a multiple of 4.
2)n is a multiple of 2.

3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^6=729
...
...
(1) for n ,every multiple of 4 have last digit =1 (since last digit of 3^n repeats after every 4 nos.)
remainder will be 3
suff

(2) for n, every multiple of 2 will have last digit =3^2 (i.e =9) or 3^4 (i.e last digit =1)
remainder may be 4 or 1
not suff

Ans A
Intern
Joined: 07 Jun 2018
Posts: 5
If n is a positive integer what is the remainder when 3^n is divided  [#permalink]

### Show Tags

Updated on: 10 Jul 2018, 22:03
If n is a positive integer what is the remainder when 3^n is divided by 5.

(1) n is multiple of 4
(2) n is multiple of 2

Originally posted by sharank on 10 Jul 2018, 21:27.
Last edited by Bunuel on 10 Jul 2018, 22:03, edited 1 time in total.
Renamed the topic and edited the question.
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 997
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
Re: If n is a positive integer what is the remainder when 3^n is divided  [#permalink]

### Show Tags

10 Jul 2018, 21:39
To find the reminder when $$3^n$$ is divided by 5

Statement 1

n is multiple of 4

=> $$3^n$$ can be written as $$3^{4x}$$ where x is an integer $$\geq$$ 0

The cyclicity of 3 is 3, 9, 7, 1, ....

Hence $$3^{4x}$$ always produces an integer where units digit is 1

=> Reminder is 1 when 3^n is divided by 5

Statement 1 sufficient

Statement 2

n is a multiple of 2

=> $$3^n$$ can be written as $$3^{2x}$$ where x is an integer $$\geq$$ 0

The units digit of 3^n can be either 9 or 1

Hence statement 2 is not sufficient

Hence option A
_________________

If you like my post press kudos +1

New project wSTAT(which Schools To Apply To?)

New - RC Butler - 2 RC's everyday

Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

### Show Tags

10 Jul 2018, 22:08
sharank wrote:
If n is a positive integer what is the remainder when 3^n is divided by 5.

(1) n is multiple of 4
(2) n is multiple of 2

Merging topics.

Similar questions to practice:
https://gmatclub.com/forum/give-n-is-a- ... 92528.html
https://gmatclub.com/forum/if-n-is-a-po ... 47625.html
https://gmatclub.com/forum/if-n-is-a-po ... 05067.html
_________________
Director
Joined: 11 Feb 2015
Posts: 566
For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

### Show Tags

09 Aug 2018, 17:22
sharank wrote:
If n is a positive integer what is the remainder when 3^n is divided by 5.

(1) n is multiple of 4
(2) n is multiple of 2

This is a value Q. So we need a definite answer.

3^n follows a pattern of the units digit repeats in an interval of every 4. i.e. units digit will be 3,9,7,1,3,9,7,1,...

Statement 1: So when 3^n is divided by 5 we get a definite answer as remainder = 1.
Statement 2: we could have a remainder of 1 or 4 hence we do not have a definite answer.

Option A is the correct answer.
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

For a positive integer n, when 3^n is divided by 5, what is the remain &nbs [#permalink] 09 Aug 2018, 17:22
Display posts from previous: Sort by