Last visit was: 08 Jul 2025, 20:03 It is currently 08 Jul 2025, 20:03
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
739,580
Given Kudos: 97,452
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,580
What is the units digit of 13^35? 03 Feb 2019, 22:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

80% (00:39) correct 20% (00:48) wrong based on 127 sessions

History

Date
Time
Result
Not Attempted Yet
What is the units digit of 13^35?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
ShowHide Answer
Official Answer
D
User avatar
AkshdeepS
User avatar
Joined: 13 Apr 2013
Last visit: 08 Jul 2025
Posts: 1,441
Own Kudos:
1,821
 [1]
Given Kudos: 1,001
Status:It's near - I can see.
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Products:
My Reviews
Posts: 1,441
Kudos: 1,821
 [1]
What is the units digit of 13^35? 03 Feb 2019, 22:33
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of 13^35?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

We need to focus only on units digit of 13 and that is 3.

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

Cyclicity = 3, 9, 7, 1 (4 digits)

Divide 35 by 4 = 35/4 = 8 remainder 3

Means 4 complete cycles of 3, 9, 7, 1

Remainder 3 means unit digit is 7.

(D)
User avatar
4d
User avatar
Current Student
Joined: 11 Dec 2013
Last visit: 25 Oct 2022
Posts: 119
Own Kudos:
403
 [1]
Given Kudos: 44
GMAT 1: 730 Q51 V37
GMAT 1: 730 Q51 V37
Posts: 119
Kudos: 403
 [1]
What is the units digit of 13^35? 03 Feb 2019, 22:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
unit digit of powers of three
\(3^1 = 3 \, \, \: | \, \, \: 3^5 = 3\)
\(3^2 = 9 \, \, \; | \, \, \: 3^6 = 9\)
\(3^3 = 7 \, \, \; | \, \, \: 3^7 = 7\)
\(3^4 = 1 \, \, \; | \, \, \: 3^8 = 1\)

Cyclicity of 3 is 4
\(3^{35}\)
35 when divided by four leaves remainder 3
Hence units digits is 7
IMO D
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 08 Jul 2025
Posts: 6,371
Own Kudos:
15,563
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,371
Kudos: 15,563
 [1]
What is the units digit of 13^35? 04 Feb 2019, 00:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of 13^35?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Cyclicity: The concept when the unit digit repeats after a cycle of some powers
e.g. The cyclicity of unit digits for the number with unit digit 2, 3, 7 and 8 is 4
and The cyclicity of unit digits for the number with unit digit 0, 1, 5 and 6 is 1
and The cyclicity of unit digits for the number with unit digit 4 and 9 is 2

The unit digit of \(13^{35}\) = Unit digit of \(3^{35}\) for calculation of unit digit of a number, only it's unit digit is important and any other digit is useless

i.e. Unit digit of 3^35 = unit digit of 3^3 becasue thewhen 35 is divided by cyclicity number 4 then remainder is 3

unit digit of 3^3 = 7

Answer: Option D
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 08 Jul 2025
Posts: 8,319
Own Kudos:
4,790
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,319
Kudos: 4,790
What is the units digit of 13^35? 04 Feb 2019, 02:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of 13^35?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

using cyclicity rule we can solve as only unit digits value is to be determined
the units digit of 13^35 = 3^ 35 = 7
IMO D
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 07 Jul 2025
Posts: 2,243
Own Kudos:
2,457
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,243
Kudos: 2,457
What is the units digit of 13^35? 13 Dec 2023, 08:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
↧↧↧ Detailed Video Solution to the Problem ↧↧↧



We need to find the units digit of \(13^{35}\)

Units digit of \(13^{35}\) will be same as units digit of \(3^{35}\)

Lets start by finding the cyclicity of units' digit in powers of 3

\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3

That means that units digit of power of 3 has a cycle of 4

=> We need to divide the power (35) by 4 and check what is the remainder
35 divided by 4 gives 3 remainder

=> Units digit of \(13^{35}\) = Units digit of \(3^3\) = 7

So, Answer will be D
Hope it helps!

Watch this video to MASTER how to find Units digit of Power of 3­
Moderators:
Bunuel
Math Expert
102594 posts
Krunaal
PS Forum Moderator
679 posts