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When 8101-8 is divided by 10, what is the remainder?

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Math Revolution GMAT Instructor
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When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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New post 19 Jul 2017, 02:02
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A
B
C
D
E

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Question Stats:

77% (01:24) correct 23% (01:24) wrong based on 108 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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Re: When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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New post 19 Jul 2017, 02:18
1
The answer is A
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
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Re: When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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New post 21 Jul 2017, 01:06
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1
==> 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.

Answer: A
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Re: When 8101-8 is divided by 10, what is the remainder?   [#permalink] 21 Jul 2017, 01:06
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When 8101-8 is divided by 10, what is the remainder?

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