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

 It is currently 18 Jun 2019, 18:09 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

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

Author Message
TAGS:

Hide Tags

Intern  Joined: 10 Oct 2008
Posts: 12
If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

1
5 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:09) correct 32% (01:08) wrong based on 381 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, 10:02.
Last edited by Bunuel on 19 May 2015, 05:22, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1664
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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, 10:52.
Last edited by yezz on 17 Oct 2008, 14:12, edited 1 time in total.
VP  Joined: 17 Jun 2008
Posts: 1330
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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  Joined: 17 Jun 2008
Posts: 1146
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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  Joined: 21 Apr 2008
Posts: 252
Location: Motortown
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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  Joined: 30 Nov 2008
Posts: 446
Schools: Fuqua
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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  Joined: 29 Aug 2007
Posts: 2262
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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.
_________________
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT
SVP  Joined: 07 Nov 2007
Posts: 1569
Location: New York
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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
_________________
Smiling wins more friends than frowning
Intern  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

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  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

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 V
Joined: 02 Sep 2009
Posts: 55670
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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.

_________________
Manager  Joined: 28 Dec 2012
Posts: 99
Location: India
Concentration: Strategy, Finance
WE: Engineering (Energy and Utilities)
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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  Status: GMAT...Not Again.....
Joined: 19 Oct 2015
Posts: 27
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

pheww.. a close shave got 3 by mistake n then upon seeing no 3 in options, recalculate... n then got 4 _________________
correct if wrong, and a +1 wont hurt for like Keep Faith in God Coz Every Question cannot be answered by Google
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6567
Location: United States (CA)
Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  B
Joined: 20 Jun 2017
Posts: 92
GMAT 1: 570 Q49 V19 Re: If n = 8^11 8, what is the units digit of n?  [#permalink]

Show Tags

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  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

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 Re: If n = 8^11 8, what is the units digit of n?   [#permalink] 15 Sep 2018, 02:01
Display posts from previous: Sort by

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