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# What is the remainder when 2^k is divided by 10?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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What is the remainder when 2^k is divided by 10?  [#permalink]

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12 Jan 2017, 18:16
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Difficulty:

45% (medium)

Question Stats:

68% (01:24) correct 32% (01:46) wrong based on 96 sessions

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What is the remainder when $$2^k$$ is divided by 10?

1) k is a positive multiple of 10
2) k is a positive multiple of 4

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 04 Jan 2017 Posts: 9 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 12 Jan 2017, 19:11 Hint lies in the cyclicity of 2 Sent from my SM-G610F using GMAT Club Forum mobile app Manager Joined: 17 Apr 2016 Posts: 79 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 12 Jan 2017, 20:10 1 1 What is the remainder when 2^k is divided by 10? 1) k is a positive multiple of 10 2) k is a positive multiple of 4 Solution:- 2^1=2 2^2=4 2^3=8 2^4=16 On continuing we observe that the last digit follows a cyclic pattern:- 2,4,8,6 Statement 1:- If k=10, the remainder will be 4. If k=20, the remainder will be 6. Hence the first statement is not sufficient. Statement 2:- K is multiple of 4. Hence if k=4, remainder is 6. If k=8, remainder is 6. Likewise for each k, the remainder is 6. Hence sufficient. Answer-B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 15 Jan 2017, 18:36 1 ==> Modify the original condition and the question. The remainder dividing $$2^k$$ by $$10 is ~2^1=~2, ~2^2=~4, ~2^3=~8, ~2^4=~6.$$ Thus, when it comes to ones, 2-->4-->8-->6-->2… are repeated, which means they have a cycle of four. Hence, the answer is 2) and B. Answer: B _________________ 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$79 for 1 month Online Course"
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Re: What is the remainder when 2^k is divided by 10?  [#permalink]

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01 Nov 2018, 17:36
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Re: What is the remainder when 2^k is divided by 10?   [#permalink] 01 Nov 2018, 17:36
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