Last visit was: 19 May 2025, 13:26 It is currently 19 May 2025, 13:26
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 May 2025
Posts: 101,531
Own Kudos:
725,508
 [1]
Given Kudos: 93,557
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 101,531
Kudos: 725,508
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
vipulgoel
Joined: 03 May 2013
Last visit: 13 Mar 2024
Posts: 92
Own Kudos:
Given Kudos: 114
Location: India
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
sumitkrocks
Joined: 02 Jul 2017
Last visit: 22 Aug 2023
Posts: 639
Own Kudos:
Given Kudos: 333
Location: India
Concentration: Strategy, Technology
GMAT 1: 730 Q50 V39
GMAT 2: 710 Q50 V36
Products:
GMAT 2: 710 Q50 V36
Posts: 639
Kudos: 859
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 May 2025
Posts: 101,531
Own Kudos:
Given Kudos: 93,557
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 101,531
Kudos: 725,508
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sumitkrocks
Bunuel I think question needs to be rephrased to what is the remainder when 2^23 is divided by 10.

Remainder will be 8 as cyclicity of 2 is 4 and last digit of 2^23 will be 8

Bunuel
What is the value when 2^23 is divided by 10?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8

You are right. Edited the typo. Thank you!
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 14 May 2025
Posts: 2,205
Own Kudos:
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: 2,205
Kudos: 2,418
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the remainder of \(2^{23}\) when divided by 10

Theory: Remainder of a number by 10 is same as the unit's digit of the number

(Watch this Video to Learn How to find Remainders of Numbers by 10)

Using Above theory Remainder of \( 2^{23} \) by 10 = unit's digit of \( 2^{23} \)

Now to find the unit's digit of \( 2^{23} \), we need to find the pattern / cycle of unit's digit of power of 2 and then generalizing it.

Unit's digit of \(2^1\) = 2
Unit's digit of \(2^2\) = 4
Unit's digit of \(2^3\) = 8
Unit's digit of \(2^4\) = 6
Unit's digit of \(2^5\) = 2

So, unit's digit of power of 2 repeats after every \(4^{th}\) number.
=> We need to divided 23 by 4 and check what is the remainder
=> 23 divided by 4 gives 3 remainder

=> \(2^{23}\) will have the same unit's digit as \(2^3\) = 8

So, Answer will be E
Hope it helps!

MASTER How to Find Remainders with 2, 3, 5, 9, 10 and Binomial Theorem

Moderators:
Math Expert
101531 posts
PS Forum Moderator
585 posts