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If n = 8^11 8, what is the units digit of n?
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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
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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?
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Updated on: 17 Oct 2008, 14:12
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, 41 = 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?
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17 Oct 2008, 13:51
C.
8^118 = 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?
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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?
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11 Dec 2008, 18:15
E :8
n = 8^10(81) = 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?
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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(81) = 7 * 8^10 = 2^30 *7



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Re: If n = 8^11 8, what is the units digit of n?
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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?
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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 = 8^118, what is the unit digit of n? A. 0 B.
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19 May 2015, 01:16
If n = 8^118, 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 = 8^118, what is the unit digit of n? A. 0 B.
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19 May 2015, 01:46
jchae90 wrote: If n = 8^118, 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 ( 41) = 4 so C



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Re: If n = 8^11 8, what is the units digit of n?
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19 May 2015, 05:23
jchae90 wrote: If n = 8^118, 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: rulesforpostingpleasereadthisbeforeposting133935.html Thank you!
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Re: If n = 8^11 8, what is the units digit of n?
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19 May 2015, 13:53
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
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Re: If n = 8^11 8, what is the units digit of n?
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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
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Re: If n = 8^11 8, what is the units digit of n?
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19 May 2017, 06:22
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 8426. 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?
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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?
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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 8^118 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?
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