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For a positive integer n, when 3^n is divided by 5, what is the remain

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For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

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New post 03 Jul 2017, 15:20
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For a positive integer n, when 3^n is divided by 5, what is the remainder?

(1) n is a multiple of 4.
(2) n is a multiple of 2.
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Re: For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

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New post 03 Jul 2017, 19:11
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roastedchips wrote:
For a positive integer n, when 3^n is divided by 5, what is the remainder?
1) n is a multiple of 4.
2)n is a multiple of 2.


3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^6=729
...
...
(1) for n ,every multiple of 4 have last digit =1 (since last digit of 3^n repeats after every 4 nos.)
remainder will be 3
suff

(2) for n, every multiple of 2 will have last digit =3^2 (i.e =9) or 3^4 (i.e last digit =1)
remainder may be 4 or 1
not suff

Ans A
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If n is a positive integer what is the remainder when 3^n is divided  [#permalink]

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New post Updated on: 10 Jul 2018, 23:03
If n is a positive integer what is the remainder when 3^n is divided by 5.

(1) n is multiple of 4
(2) n is multiple of 2

Originally posted by sharank on 10 Jul 2018, 22:27.
Last edited by Bunuel on 10 Jul 2018, 23:03, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If n is a positive integer what is the remainder when 3^n is divided  [#permalink]

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New post 10 Jul 2018, 22:39
To find the reminder when \(3^n\) is divided by 5

Statement 1

n is multiple of 4

=> \(3^n\) can be written as \(3^{4x}\) where x is an integer \(\geq\) 0

The cyclicity of 3 is 3, 9, 7, 1, ....

Hence \(3^{4x}\) always produces an integer where units digit is 1

=> Reminder is 1 when 3^n is divided by 5

Statement 1 sufficient

Statement 2

n is a multiple of 2

=> \(3^n\) can be written as \(3^{2x}\) where x is an integer \(\geq\) 0

The units digit of 3^n can be either 9 or 1

Hence statement 2 is not sufficient

Hence option A
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Re: For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

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New post 10 Jul 2018, 23:08
sharank wrote:
If n is a positive integer what is the remainder when 3^n is divided by 5.

(1) n is multiple of 4
(2) n is multiple of 2


Merging topics.

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For a positive integer n, when 3^n is divided by 5, what is the remain  [#permalink]

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New post 09 Aug 2018, 18:22
sharank wrote:
If n is a positive integer what is the remainder when 3^n is divided by 5.

(1) n is multiple of 4
(2) n is multiple of 2


This is a value Q. So we need a definite answer.

3^n follows a pattern of the units digit repeats in an interval of every 4. i.e. units digit will be 3,9,7,1,3,9,7,1,...

Statement 1: So when 3^n is divided by 5 we get a definite answer as remainder = 1.
Statement 2: we could have a remainder of 1 or 4 hence we do not have a definite answer.

Option A is the correct answer.
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For a positive integer n, when 3^n is divided by 5, what is the remain &nbs [#permalink] 09 Aug 2018, 18:22
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