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

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chenhong1224
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If n = 8^11 8, what is the units digit of n? [#permalink] New post   Updated on: 19 May 2015, 05:22
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If n = 8^11 – 8, what is the units digit of n?

A. 0
B. 1
C. 4
D. 6
E. 8
ShowHide Answer
Official Answer
C

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.
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   17 Oct 2008, 13:51
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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.
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   19 May 2015, 13:53
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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

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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   Updated on: 17 Oct 2008, 14:12
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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.
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   17 Oct 2008, 13:54
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
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   11 Dec 2008, 18:15
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
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   12 Dec 2008, 15:26
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
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   12 Dec 2008, 15:57
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.
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   13 Dec 2008, 20:41
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
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[Integers, Digits] If n = 8^11-8, what is the unit digit of n? A. 0 B. [#permalink] New post   19 May 2015, 01:16
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!
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Re: [Integers, Digits] If n = 8^11-8, what is the unit digit of n? A. 0 B. [#permalink] New post   19 May 2015, 01:46
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
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   19 May 2015, 05:23
Expert Reply
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!
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   24 Oct 2015, 08:58
pheww.. a close shave got 3 by mistake n then upon seeing no 3 in options, recalculate... n then got 4 :lol:
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   19 May 2017, 06:22
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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
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   15 Sep 2018, 01:41
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
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   15 Sep 2018, 02:01
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.

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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   22 Sep 2020, 07:16
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chenhong1224 wrote:
If n = 8^11 – 8, what is the units digit of n?

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



The unit digit cyclicity for 2,3, 7, and 8 is 4
So, we have to divide the 11 by 4 the remainder is 3
now get result 8^3 which is 512
now 512-8= 504
The unit digit is 4
Ans. C
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Re: If n = 8^11 8, what is the units digit of n? [#permalink] New post   06 Apr 2022, 11:42
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Re: If n = 8^11 8, what is the units digit of n? [#permalink]
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