NEW HERE? LEARN MORE
close
It is currently 01 Apr 2023, 22:24
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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

What is the last digit of 6^8/2 ?

12 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2458
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
What is the last digit of 6^8/2 ? [#permalink] New post  26 Dec 2009, 18:21
4
Kudos
26
Bookmarks
Expert Reply
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

63% (00:38) correct 38% (00:50) wrong based on 144 sessions

Hide Show timer Statistics

What is the last digit of \(\frac{6^8}{2}\) ?

Try to solve under 10 sec ;)
_________________
HOT! GMAT Club Forum 2020 | GMAT ToolKit 2 (iOS) - The OFFICIAL GMAT CLUB PREP APPs, must-have apps especially if you aim at 700+
Signature Read More
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Expert Reply
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2458
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
Re: Last digit [#permalink] New post  26 Dec 2009, 20:04
22
Kudos
6
Bookmarks
Expert Reply
the last digit of \(6^n\) is always 6 (6*6=36).

But we cannot simply divide the last digit by 2. So, we can rewrite as:

\(6^7 * \frac{6}{2} = 6*3 = 18 --> 8\) :wink:
_________________
HOT! GMAT Club Forum 2020 | GMAT ToolKit 2 (iOS) - The OFFICIAL GMAT CLUB PREP APPs, must-have apps especially if you aim at 700+
Signature Read More
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88685
CAT Tests Forum Quiz Mode Top Member of the Month
Re: Last digit [#permalink] New post  26 Dec 2009, 19:43
8
Kudos
4
Bookmarks
Expert Reply
walker wrote:
What is the last digit of \(\frac{6^8}{2}\) ?

Try to solve under 10 sec ;)


6 in any integer power >0 has the last digit 6. Integer ending with 6 divided by 2 can have 3 or 8 as last digit. But as \(6^8\) will be divisible by 4 for sure, divided by 2 it must give the even number, hence 8 is the correct answer.

Another solution: \(\frac{6^8}{2}=\frac{2^8*3^8}{2}=2^7*3^8\)

Cyclisity of both \(2\) and \(3\) is \(4\), hence \(2^7\) has the same last digit as \(2^3=8\) and \(3^8\) has the same last digit as \(3^4=81\), hence \(8*1=8\).

I used first approach, took me 11 secs :-D , so maybe there is a shortcut?
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88685
CAT Tests Forum Quiz Mode Top Member of the Month
Re: Last digit [#permalink] New post  26 Dec 2009, 20:11
3
Kudos
Expert Reply
walker wrote:
the last digit of \(6^n\) is always 6 (6*6=36).

But we cannot simply divide the last digit by 2. So, we can rewrite as:

\(6^7 * \frac{6}{2} = 6*3 = 18 --> 8\) :wink:


There was a shortcut. +1.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
GMAT TIGER
VP
VP
Joined: 29 Aug 2007
Posts: 1132
Re: Last digit [#permalink] New post  26 Dec 2009, 22:35
2 lions in the same jungle.

Thats interesting .... :wink:
avatar
kp1811
Manager
Manager
Joined: 30 Aug 2009
Posts: 138
Location: India
Concentration: General Management
Re: Last digit [#permalink] New post  26 Dec 2009, 22:41
GMAT TIGER wrote:
2 lions in the same jungle.

Thats interesting .... :wink:


but you are the only tiger :wink:
avatar
pradhan
Intern
Intern
Joined: 22 Sep 2009
Posts: 19
Re: Last digit [#permalink] New post  26 Dec 2009, 23:03
2
Kudos
(6^8)/2 = (6/2) * 6*6*6*6*6*6*6
= 3 * 6*6*6*6*6*6*6
= 18 * 6 *6*6*6*6*6

if 18 is multiplied by any no. of 6 last digit will be 8


hence ans 8

I think this is shortest method
User avatar
jlgdr
VP
VP
Joined: 06 Sep 2013
Posts: 1368
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
GMAT ToolKit User
Re: Last digit [#permalink] New post  17 Oct 2013, 17:15
walker wrote:
the last digit of \(6^n\) is always 6 (6*6=36).

But we cannot simply divide the last digit by 2. So, we can rewrite as:

\(6^7 * \frac{6}{2} = 6*3 = 18 --> 8\) :wink:


Hi @Walker, would you kindly explain why you factorized it that way?
Thanks
Cheers
J :)
User avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1576
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: What is the last digit of 6^8/2 ? [#permalink] New post  18 Feb 2014, 01:47
1
Kudos
6 multiplied by 6 any times would give the last digit 6 itself
However 6 multiplied by 3 would give 8 in the last place.
So has been factorized accordingly
avatar
rrsnathan
Manager
Manager
Joined: 30 May 2013
Posts: 130
Location: India
Concentration: Entrepreneurship, General Management
Schools: Booth '16 Carroll '16 ESADE '16 Foster '16 HEC Jan'16 Haas EWMBA '16 Tuck '16
GPA: 3.82
GMAT ToolKit User
Re: Last digit [#permalink] New post  05 Mar 2014, 12:55
jlgdr wrote:
walker wrote:
the last digit of \(6^n\) is always 6 (6*6=36).

But we cannot simply divide the last digit by 2. So, we can rewrite as:

\(6^7 * \frac{6}{2} = 6*3 = 18 --> 8\) :wink:


Hi @Walker, would you kindly explain why you factorized it that way?
Thanks
Cheers
J :)


To say Cyclicity should not be divided. . so 6 was taken out and then divided by 2 and then multiplied with the cyclicity 6

Tats y its factorized in that way.

Regards,
Rrsnathan.
avatar
dbiersdo
Intern
Intern
Joined: 03 Aug 2012
Posts: 17
Location: United States (OR)
Concentration: Finance, International Business
Schools: Marshall PM '18 (I)
GPA: 3.53
WE:Analyst (Entertainment and Sports)
Reviews Badge
Re: What is the last digit of 6^8/2 ? [#permalink] New post  05 Mar 2014, 23:30
1
Kudos
Is there a reason we don't have any possible options to choose from in the original post?

How my brain processed this:

Step 1 --> 6^(Any Power) will end in a 6 (i.e. 6*6 = 36, 6*6*6 = 216, etc.). To me this makes sense to do first based off order of operations.
Step 2 --> Take any result an divide by 2. Quick and easy would be 36/2 = 18. Any answer will be 8!

Where you can trip yourself up is assuming you take 6/2=3, and to me if you stick to order of operations you can avoid this mistake.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88685
CAT Tests Forum Quiz Mode Top Member of the Month
Re: What is the last digit of 6^8/2 ? [#permalink] New post  06 Mar 2014, 00:25
Expert Reply
dbiersdo wrote:
Is there a reason we don't have any possible options to choose from in the original post?


This is walker's own question, not an official one, so no options.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
GMAT Club Bot
gmatclubot
Re: What is the last digit of 6^8/2 ? [#permalink]
06 Mar 2014, 00:25
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
10506 posts
Bunuel
Math Expert
88685 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3149 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions