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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82
When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:20) correct 28% (01:35) wrong based on 96 sessions

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When $$8^{101}-8$$ is divided by 10, what is the remainder?

A. 0
B. 1
C. 2
D. 3
E. 4

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Manager  S
Joined: 30 Mar 2017
Posts: 69
Re: When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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The cyclicity of units digit for 8 raised to positive integers is 4( 8-4-2-6)
Since 8 is raised to 101, the units digit as per the cyclicity will be 8.
And if we subtract 8 from the complete number, the units digit becomes 0, or the number becomes a multiple of 10.
Hence remainder is zero.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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2
==> You get $$8^{101}-8=8(8^{100}-1)$$, and the units digit of ~8 becomes $$~8^1=~8, ~8^2=~4, ~8^3=~2, ~8^4=~6$$.
You get $$8(8^{100}-1)=8{(8^4)^{25}-1}=8{(~6^{25})-1}=8(~6-1)=8(~5)=~0$$, and the answer is A.

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Re: When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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_________________ Re: When 8101-8 is divided by 10, what is the remainder?   [#permalink] 25 Nov 2019, 05:16
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# When 8101-8 is divided by 10, what is the remainder?  