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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7230
GMAT 1: 760 Q51 V42
GPA: 3.82
When 8101-8 is divided by 10, what is the remainder?  [#permalink]

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19 Jul 2017, 02:02
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Difficulty:

15% (low)

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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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 30 Mar 2017 Posts: 66 Re: When 8101-8 is divided by 10, what is the remainder? [#permalink] ### Show Tags 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. Sent from my Moto G (5) Plus using GMAT Club Forum mobile app Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7230 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When 8101-8 is divided by 10, what is the remainder? [#permalink] ### Show Tags 21 Jul 2017, 01:06 1 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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