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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
Posts: 6529
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the remainder when 2^k is divided by 10?  [#permalink]

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12 Jan 2017, 17:16
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:18) correct 42% (01:26) wrong based on 77 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 $99 for 3 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: 8 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 12 Jan 2017, 18:11 Hint lies in the cyclicity of 2 Sent from my SM-G610F using GMAT Club Forum mobile app Manager Joined: 17 Apr 2016 Posts: 89 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 12 Jan 2017, 19:10 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: 6529 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, 17:36 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$99 for 3 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, 16:36
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the remainder when 2^k is divided by 10? &nbs [#permalink] 01 Nov 2018, 16:36
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