Last visit was: 25 Apr 2026, 02:56 It is currently 25 Apr 2026, 02:56
Home
Messages
Tests
Schools
Events
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: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,134
Given Kudos: 105,878
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: 109,822
Kudos: 811,134
What is the units digit of 43^19? 07 Apr 2017, 03:44
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:

5% (low)

Question Stats:

86% (00:26) correct 14% (00:39) wrong based on 134 sessions

History

Date
Time
Result
Not Attempted Yet
What is the units digit of \(43^{19}\)?

A. 1
B. 3
C. 5
D. 7
E. 9
ShowHide Answer
Official Answer
D
User avatar
emockus
User avatar
Chat Moderator
Joined: 07 Mar 2016
Last visit: 28 Feb 2024
Posts: 40
Own Kudos:
71
Given Kudos: 74
Posts: 40
Kudos: 71
What is the units digit of 43^19? Updated on: 07 Apr 2017, 09:56
Originally posted by emockus on 07 Apr 2017, 06:04.
Last edited by emockus on 07 Apr 2017, 09:56, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
3^1 = 3
3^2 = 9
3^3 =...7
3^4 =...1

Cycling through 19 times, it ends on 7. Answer "D".
User avatar
IdiomSavant
User avatar
Joined: 14 Sep 2016
Last visit: 03 May 2018
Posts: 45
Own Kudos:
47
Given Kudos: 119
Concentration: Finance, Economics
Schools: Boston U '20 Carroll '20
Schools: Boston U '20 Carroll '20
Posts: 45
Kudos: 47
What is the units digit of 43^19? 07 Apr 2017, 06:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of \(43^{19}\)?

A. 1
B. 3
C. 5
D. 7
E. 9
Show more


3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1 End of pattern. The 4th, 8th, 16th, 20th power. 19th power will be one less. (D), 7.

3^5 = 3
User avatar
eddy8700
User avatar
Joined: 25 Jan 2016
Last visit: 02 Oct 2020
Posts: 86
Own Kudos:
75
Given Kudos: 12
Status:active
Location: India
Concentration: Finance, Entrepreneurship
Schools: Rotman '19 Insead Sept'18 Booth '19
GPA: 4
WE:Web Development (Computer Software)
Schools: Rotman '19 Insead Sept'18 Booth '19
Posts: 86
Kudos: 75
What is the units digit of 43^19? 07 Apr 2017, 08:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the units digit of 43^19?

A. 1
B. 3
C. 5
D. 7
E. 9


3 has a cyclicity of 4
19=4q+3
so basically 3^3=7 unit digit
answer is D
User avatar
broall
User avatar
Retired Moderator
Joined: 10 Oct 2016
Last visit: 07 Apr 2021
Posts: 1,133
Own Kudos:
7,377
Given Kudos: 65
Status:Long way to go!
Location: Viet Nam
Posts: 1,133
Kudos: 7,377
What is the units digit of 43^19? Updated on: 09 Apr 2017, 20:11
Originally posted by broall on 07 Apr 2017, 09:02.
Last edited by broall on 09 Apr 2017, 20:11, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of \(43^{19}\)?

A. 1
B. 3
C. 5
D. 7
E. 9
Show more


\(\begin{align}
43^{19} &=43^{18+1} \\
&=(43^2)^9 \times 43 \\
&= (...9)^{8+1} \times 43 \\
&= (...9)^{2 \times 4} \times [(...9) \times 43] \\
&= [(...9)^2]^4 \times (...7) \\
&=(...1)^4 \times (...7) \\
&= (...1) \times (...7) \\
&= (...7)
\end{align}\)

The answer is D
avatar
ar500
avatar
Joined: 29 Apr 2015
Last visit: 26 Jun 2020
Posts: 14
Own Kudos:
9
Given Kudos: 4
GPA: 3.89
Posts: 14
Kudos: 9
What is the units digit of 43^19? 07 Apr 2017, 09:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Once you identify the pattern (3,9,7,1) you can set up a grid:



3: 1,5, 9,13,17
9: 2,6,10,14,18
7: 3,7,11,15,19
1: 4,8/12,16
User avatar
gracie
User avatar
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,028
Own Kudos:
2,022
Given Kudos: 27
Posts: 1,028
Kudos: 2,022
What is the units digit of 43^19? 07 Apr 2017, 10:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of \(43^{19}\)?

A. 1
B. 3
C. 5
D. 7
E. 9
Show more

units digit cycle from 3^1 to 3^4=3,9,7,1
19/4 gives a remainder of 3
3rd digit in cycle is 7
D
User avatar
mohshu
User avatar
Joined: 21 Mar 2016
Last visit: 26 Dec 2019
Posts: 410
Own Kudos:
143
Given Kudos: 103
Products:
My Reviews
Posts: 410
Kudos: 143
What is the units digit of 43^19? 07 Apr 2017, 10:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
the units digit is same as that of 3^19

3 has a cyclicity of 4..hence units digit of 3^3 = 7

ans 7
avatar
matthewsmith_89
avatar
Joined: 06 Dec 2016
Last visit: 06 Oct 2017
Posts: 177
Own Kudos:
67
Given Kudos: 10
Posts: 177
Kudos: 67
What is the units digit of 43^19? 08 Apr 2017, 12:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
3^0 = 1
3^1 =3
3^2 = 9
3^3=7
3^4 = 1

20 is a multiple of 4. 3^20 = 1
Therefore 3^19 = 7

Which is answer D
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,711
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,711
 [1]
What is the units digit of 43^19? 14 Apr 2017, 05:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the units digit of \(43^{19}\)?

A. 1
B. 3
C. 5
D. 7
E. 9
Show more

Since we need to determine the units digit of 43^19, we really are determining the units digit of 3^19.

The pattern of units digits of 3 when raised to a positive integer exponent is:

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

We see that the pattern is 3-9-7-1. We can generalize this pattern by saying that when the exponent is a multiple of 4, the units digit will be 1. For example, both 3^16 and 3^20 have a units digit of 1.
The units digit of 3^20 is 1, and so 3^19 has a units digit of 7.

Answer: D
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,680
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
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,680
What is the units digit of 43^19? 13 Dec 2023, 08:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
↧↧↧ Detailed Video Solution to the Problem ↧↧↧


We need to find the units digit of \(43^{19}\)

Units digit of \(43^{19}\) will be same as units digit of \(3^{19}\)

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 (19) by 4 and check what is the remainder
19 divided by 4 gives 3 remainder

=> Units digit of \(43^{19}\) = Units digit of \(3^3\) = 7

So, Answer will be D
Hope it helps!­

Link to Theory for Last Two digits of exponents here

Link to Theory for Units' digit of exponents here
Moderators:
Bunuel
Math Expert
109822 posts
Krunaal
Tuck School Moderator
853 posts