GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2018, 17:47

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     November 18, 2018

     November 18, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

If n = 8^11 8, what is the units digit of n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 10 Oct 2008
Posts: 14
If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post Updated on: 19 May 2015, 04:22
1
5
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:10) correct 33% (01:09) wrong based on 368 sessions

HideShow timer Statistics

If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8

Originally posted by chenhong1224 on 17 Oct 2008, 09:02.
Last edited by Bunuel on 19 May 2015, 04:22, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1726
GMAT ToolKit User Premium Member
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post Updated on: 17 Oct 2008, 13:12
2
chenhong1224 wrote:
If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8


8(8^10 - 1)
8^1 = 8
8^2 = 16
8^3 = 32
8^4 = 64
8^5 = 128

thus 8^10 ends in 4, 4-1 = 3 , 3*8 = 24 units didgit is 4...c

Originally posted by yezz on 17 Oct 2008, 09:52.
Last edited by yezz on 17 Oct 2008, 13:12, edited 1 time in total.
VP
VP
avatar
Joined: 17 Jun 2008
Posts: 1436
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 17 Oct 2008, 12:51
1
C.

8^11-8 = 8(8^10 - 1).

Now, 8^1 ends with 8
8^2 ends with 4
8^3 ends with 2
8^4 ends with 6..after this last digit will repeat.

Hence, 8^8 will end with 6 and 8^10 will end with 4.
4 - 1 = 3 and 3*8 ends with 4.
VP
VP
avatar
Joined: 17 Jun 2008
Posts: 1225
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 17 Oct 2008, 12:54
chenhong1224 wrote:
If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8

n = 8^11 – 8= 8((2^10)^3 -1)=8((1024^3 -1))=> ####3*8 => 4 is the digit !!!

IMO C
_________________

cheers
Its Now Or Never

Senior Manager
Senior Manager
User avatar
Joined: 21 Apr 2008
Posts: 261
Location: Motortown
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 11 Dec 2008, 17:15
E :8

n = 8^10(8-1) = 7 * 8^10 = 2^30 *7

2^1 - units digit is 2
2^2 - units digit is 4
2^3 - units digit is 8
2^4 - units digit is 16
2^5 - units digit is 2
.......

Basically, units digit cycle repeats every 4 times
So, 2^30 - units digit 4
units digit of 4 * 7 = 8
Senior Manager
Senior Manager
avatar
Joined: 30 Nov 2008
Posts: 470
Schools: Fuqua
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 12 Dec 2008, 14:26
Well more or less similar explanation of what LiveStronger, but getting a different ans.

8 ^ 11 - 8 = 8 (8 ^ 10 - 1)

==> 8 (2 ^ 30 - 1)

Last digit of 2 ^ 30 is 4 based on what explanation LiveStronger is saying. 2 ^ 30 - 1 yields 4 - 1 = 3 as the unit digit. Now on multiply this with 8, we get unit digit as 4.

My Ans will be C.

I see some confusion in this line of explanation.

LiveStronger wrote:
n = 8^10(8-1) = 7 * 8^10 = 2^30 *7
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2378
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 12 Dec 2008, 14:57
haichao wrote:
If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8



n = 8^11 – 8

8^1 has unit digit 8
8^2 has unit digit 4
8^3 has unit digit 2
8^4 has unit digit 6

8^5 has unit digit 8
this is the pattern.

so 8^8 has 6 in unit digit
so 8^12 als has 6 in unit digit
so 8^11 als has 2 in unit digit

so if we deduct 8 from xxxxxxx2, the unit digit will be 4.
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1682
Location: New York
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 13 Dec 2008, 19:41
haichao wrote:
If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8


8^1 = unit digit 8
8^2 = unit digti 4
8^3= unit digit 2
8^4 = unit digt 6
8^5 = unit digit 8
..
repeats for every 4 times.

8^11 .. unit digit is 2


8^11 – 8 uniit digit is 4

C
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Intern
Intern
avatar
Joined: 31 Mar 2015
Posts: 3
[Integers, Digits] If n = 8^11-8, what is the unit digit of n? A. 0 B.  [#permalink]

Show Tags

New post 19 May 2015, 00:16
If n = 8^11-8, what is the unit digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8



***
First time posting - if anyone know how I can upload the answer without spoiling it please let me know!
Intern
Intern
avatar
Joined: 06 Aug 2014
Posts: 17
Re: [Integers, Digits] If n = 8^11-8, what is the unit digit of n? A. 0 B.  [#permalink]

Show Tags

New post 19 May 2015, 00:46
jchae90 wrote:
If n = 8^11-8, what is the unit digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8



***
First time posting - if anyone know how I can upload the answer without spoiling it please let me know!

unit digit of 8^11 -8 is
8 ( 8^10 -1 ) so basically we have to find unit digit of 8^10

Now unit digit of 8^1 = 8
8^2 = 4
8^3 = 2
8^4 = 6
8^5 = 8 so cyclicity is 4 => 8^10 will have unit digit same as 8^2 which is 4

So unit digit of 8 ( 8^10 -1 ) = 8 ( 4-1) = 4 so C
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 19 May 2015, 04:23
jchae90 wrote:
If n = 8^11-8, what is the unit digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8



***
First time posting - if anyone know how I can upload the answer without spoiling it please let me know!


Merging topics.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you!
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Joined: 28 Dec 2012
Posts: 102
Location: India
Concentration: Strategy, Finance
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 19 May 2015, 12:53
chenhong1224 wrote:
If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8



Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 8^3 - 8. Now 8^3 has last digit 2. Since 8^11 (or for that matter 8^3) is greater than 8, we subtract 8 from 12 ( the 10+2 --> 10 has come from carry over from the tenth place). thus 12 - 8 = 4 is the answer. Option C

Kudos if you like :)
_________________

Impossibility is a relative concept!!

Intern
Intern
avatar
Status: GMAT...Not Again.....
Joined: 19 Oct 2015
Posts: 30
Location: India
Concentration: Strategy, Entrepreneurship
GMAT 1: 610 Q48 V27
WE: Engineering (Energy and Utilities)
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 24 Oct 2015, 07:58
pheww.. a close shave got 3 by mistake n then upon seeing no 3 in options, recalculate... n then got 4 :lol:
_________________

correct if wrong, and a +1 wont hurt for like :wink:

Keep Faith in God Coz Every Question cannot be answered by Google

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 19 May 2017, 05:22
chenhong1224 wrote:
If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8


Observe that n = 8^11 - 8 = 8(8^10 - 1). Let’s first find the pattern of units digits of powers of 8:

8^1 = 8

8^2 = 4

8^3 = 2

8^4 = 6

8^5 = 8

We see that the pattern of units digits of powers of 8 is 8-4-2-6. Furthermore, the units digit of powers of 8 that are multiples of 4 is 6 and the units digit of powers of 8 that are 2 more than multiples of 4 is 4. That is, the units digit of 8^10 is 4. Replace 8^10 with 4 and we have 8(4 - 1) = 8(3) = 24. Since 24 has a units digit of 4, n also has units digit of 4.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
User avatar
B
Joined: 20 Jun 2017
Posts: 84
GMAT 1: 570 Q49 V19
CAT Tests
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 15 Sep 2018, 00:41
Unit's digit of \(8^{n}\) where 'n' is positive integer repeats after every 4 powers i.e.
\(8^{1}\) = 8
\(8^{2}\) = 64
\(8^{3}\) = 512
\(8^{4}\) = 4096
\(8^{5}\) = 32768
likewise 8^{11} = unit's digit is 2
hence the units digit of \(8^{11}\)-11 = 4
Intern
Intern
User avatar
B
Joined: 13 Mar 2018
Posts: 24
GPA: 3.12
WE: Project Management (Other)
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

New post 15 Sep 2018, 01:01
Unit digit of 8^11 can be found as below:
Unit digit of 8^(4n+3) will be 2. Hence 8^11 will be 2 in it's unit digit.
Hence 8^11-8 will have 4 in it's unit digit. Hence option C will be correct.

Posted from my mobile device
GMAT Club Bot
Re: If n = 8^11 8, what is the units digit of n? &nbs [#permalink] 15 Sep 2018, 01:01
Display posts from previous: Sort by

If n = 8^11 8, what is the units digit of n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.