Last visit was: 24 Apr 2026, 13:16 It is currently 24 Apr 2026, 13:16
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: 24 Apr 2026
Posts: 109,820
Own Kudos:
811,062
 [2]
Given Kudos: 105,873
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: 109,820
Kudos: 811,062
 [2]
What number is obtained by adding the units digits of 734^97 and 347^8 20 Apr 2016, 00:57
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:23) correct 25% (01:54) wrong based on 145 sessions

History

Date
Time
Result
Not Attempted Yet
What number is obtained by adding the units digits of 734^97 and 347^81?

A. 10
B. 11
C. 12
D. 13
E. 14
ShowHide Answer
Official Answer
B
avatar
mathiaskeul
avatar
Joined: 10 Apr 2016
Last visit: 16 May 2016
Posts: 50
Own Kudos:
27
 [1]
Given Kudos: 7
Concentration: Strategy, Entrepreneurship
GMAT 1: 520 Q29 V30
GPA: 3.01
GMAT 1: 520 Q29 V30
Posts: 50
Kudos: 27
 [1]
What number is obtained by adding the units digits of 734^97 and 347^8 20 Apr 2016, 03:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Units digit of unit 4 to the power of antything:
4 odd
6 even

Units digit is 4

Units digit of unit 7 to the power of anything
7
9
3
1
----> cycle formed. So every four numbers, the fifth number the cycle starts again. 80/4 means 20 cycles, 81 a new cycle starts so 7 as unit
7
9
3

4+7=11 Answer is B beyond any doubt.
avatar
CV7585
avatar
Joined: 29 Jul 2015
Last visit: 14 Jun 2020
Posts: 53
Own Kudos:
42
 [1]
Given Kudos: 68
Location: Australia
Schools: McCombs '19 (D) Darden '19 (D) ISB '18 (A) Tepper '19 (WL) Duke '19 (D) HEC Dec"18 (A)
GMAT 1: 680 Q49 V33
GPA: 3.25
WE:Business Development (Energy)
Schools: McCombs '19 (D) Darden '19 (D) ISB '18 (A) Tepper '19 (WL) Duke '19 (D) HEC Dec"18 (A)
GMAT 1: 680 Q49 V33
Posts: 53
Kudos: 42
 [1]
What number is obtained by adding the units digits of 734^97 and 347^8 20 Apr 2016, 15:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What number is obtained by adding the units digits of 734^97 and 347^81?

A. 10
B. 11
C. 12
D. 13
E. 14

Units digit of 734^97 is 4. (4 raised to the power odd integer).
Units digit of 347^81 is 7. (Powers of 7 end in 7,9,3 or 1. Since 81 is in the form 4n+1; the UD is 7).

therefore 7+4 = 11 Answer B.
avatar
ronny123
avatar
Joined: 12 Jun 2015
Last visit: 16 Oct 2017
Posts: 69
Own Kudos:
80
Given Kudos: 104
Products:
My Reviews
Posts: 69
Kudos: 80
What number is obtained by adding the units digits of 734^97 and 347^8 20 Apr 2016, 17:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We are asked for the unit's digit of 734^97 + 347^81

Let's remove the clutter and make it simpler to calculate
Units digit of 4^97 + 7^81 is the same as above

4^97
Even powers of 4 end with a 6 Odd powers of 4 end in 4
4^2 : 16 4^1: 4
4^4 : 256 4^3 : 64
4^6 : 4096 4^5 : 1024

So, 4^97 should end with a 4

7^81
7 has a power cyclicity of 4 which means the units digit repeats itself after every 4th power
7^1:7
7^2:49
7^3:343
7^4:2401
7^5:16807

accordingly, the 81st power should have the same units digit as the 1st i.e. 7

So , the addition should end with 4 + 7 = 11

Correct Option : B
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,001
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,001
What number is obtained by adding the units digits of 734^97 and 347^8 22 Sep 2020, 23:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Unit digit of \(734^{97}\) = \(4^{97}\)

=> \(4^1\) = 4 [odd power will give 4 as unit digit] and \(4^2\) = 16 [even power will give 6 as unit digit]

=> \(734^{97}\) = 4 as unit digit

Unit digit of \(347^81\) = \(7^{81}\)

=> \(7^{4*20}\) * \(7^1\)

=> \(7^4\) * \(7^1\) = \(7^5\) [At \(5^{th}\) power, every number repeats itself at unit digit place].Therefore,

=>\(347^{81}\) = 7 as unit digit

Adding both 4 + 7 = 11.


Answer B
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,975
Own Kudos:
1,117
Posts: 38,975
Kudos: 1,117
What number is obtained by adding the units digits of 734^97 and 347^8 08 Feb 2025, 07:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109820 posts
Krunaal
Tuck School Moderator
853 posts