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If N is a positive integer what is the remainder when 2^N

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If N is a positive integer what is the remainder when 2^N  [#permalink]

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New post 17 Oct 2016, 22:41
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If N is a positive interger what is the remainder when \(2^N\) is divided by 10?

1. N is divisible by 2
2. N is divisible by 4
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Re: If N is a positive integer what is the remainder when 2^N  [#permalink]

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New post 18 Oct 2016, 00:46
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gaurav_raos wrote:
If N is a positive interger what is the remainder when \(2^N\) is divided by 10?

1. N is divisible by 2
2. N is divisible by 4


any integer divided by 10 , the remainder is the last digit , so question asks what is the last digit for 2^n. but 2^n has a pattern when it comes to its last digit , a cycle where the last digit repeats

2^1 = 2 , 2^2 = 4 , 2^3 = 8 , 2^4 = 16 , 2^5 =32 , 2^6 = 64, ( if you look at the pattern last digit is (2,4,8,6,2,4,8,6....)

from 1

N is even , thus 2^n could end in either 4 or 6 .... insuff

from 2
N is Divisible by 4 ie 2^n = 2^4m , thus 2^4m will always ends in 6 .... suff and the last digit when 2^4m/10 is 6

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Re: If N is a positive integer what is the remainder when 2^N  [#permalink]

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New post 13 Jun 2017, 03:37
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I have a doubt here in selection of B as an answer.
What if it is 2^4*0 it would be 2^0= 1 and the remainder would not be 6
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Re: If N is a positive integer what is the remainder when 2^N  [#permalink]

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New post 13 Jun 2017, 05:49
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If N is a positive integer what is the remainder when 2^N  [#permalink]

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New post 06 Apr 2018, 08:12
shikha.lakhani wrote:
I have a doubt here in selection of B as an answer.
What if it is 2^4*0 it would be 2^0= 1 and the remainder would not be 6


Missed to note this, if like Bunuel pointed out Positive integer wasnt mentioned i would have gotten this question wrong .. Kudos to you for thinking it..
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Re: If N is a positive integer what is the remainder when 2^N  [#permalink]

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New post 26 May 2018, 08:29
If N is a positive integer what is the remainder when \(2^N\) is divided by 10?
This question reduces to what is unit digit of \(2^N\)

1. N is divisible by 2
if N = 2, unit digit of \(2^N\)= 4, if n = 4, unit digit of \(2^N\) = 6. So \(NOT SUFFICIENT.\)
2. N is divisible by 4
If N = 4n, unit digit of \(2^N\) = 6. hence \(SUFFICIENT.\)

Answer B

Calculating unit digit:
a^(4n+r) has the same unit digit as \(a^r\), if exponent is multiple of 4, find unit digit of \(a^4\)
Principle to calculate unit digit.
1) divide the exponent by 4, and find remainder.
2) unit digit of expression will be the unit digit of base raised to power of remainder.
If remainder is 0. Raise to power of 4.

THIS METHOD IS APPLICABLE FOR ALL DIGITS, no need to remember cyclicity for different digits.
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Re: If N is a positive integer what is the remainder when 2^N &nbs [#permalink] 26 May 2018, 08:29
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