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

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

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New post 12 Jan 2017, 17:16
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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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Re: What is the remainder when 2^k is divided by 10?  [#permalink]

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New post 12 Jan 2017, 18:11
Hint lies in the cyclicity of 2

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Re: What is the remainder when 2^k is divided by 10?  [#permalink]

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New post 12 Jan 2017, 19:10
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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


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
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Re: What is the remainder when 2^k is divided by 10?  [#permalink]

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New post 15 Jan 2017, 17:36
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==> 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
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Re: What is the remainder when 2^k is divided by 10?  [#permalink]

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New post 01 Nov 2018, 16:36
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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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