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Posts: 11
Updated on: 19 May 2015, 04:22
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.
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.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
68% (01:08) correct
32%
(01:11)
wrong
based on 486
sessions
History
Date
Time
Result
Not Attempted Yet
chenhong1224
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
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.
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.
chenhong1224
n = 8^11 – 8= 8((2^10)^3 -1)=8((1024^3 -1))=> ####3*8 => 4 is the digit !!!
IMO C
Posts: 113
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
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
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.
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
Posts: 1,012
haichao
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.
haichao
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
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!
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!
Posts: 14
jchae90
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
jchae90
Merging topics.
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chenhong1224
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
pheww.. a close shave got 3 by mistake n then upon seeing no 3 in options, recalculate... n then got 4 
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Expert reply
Posts: 22,742
chenhong1224
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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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
\(8^{1}\) = 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
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
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
chenhong1224
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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