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IF n >0 what is the remainder when 9^{12n+3} is divided by 10

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IF n >0 what is the remainder when 9^{12n+3} is divided by 10  [#permalink]

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New post Updated on: 26 May 2016, 06:56
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IF n >0 what is the remainder when \(9^{12n+3}\) is divided by 10
A 0
B 1
C 2
D 7
E 9

Originally posted by satishchaudharygmat on 26 May 2016, 06:28.
Last edited by chetan2u on 26 May 2016, 06:56, edited 2 times in total.
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Re: IF n >0 what is the remainder when 9^{12n+3} is divided by 10  [#permalink]

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New post 26 May 2016, 06:55
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satishchaudharygmat wrote:
IF n >0 what is the remainder when \(9^{12n+3}\) is divided by 10
A 0
B 1
C 2
D 7
E 9



Hi,
remainder of an integer when divided by 10 is same as the UNIT's digit of the integer

\(9^{12n+3}\) ....\(9^{12n+3}\)will leave the same remainder as \(9^{odd}\) as the pattern in units digit repeats after every two numbers..
9^1 will leave 9 as remainder and 9^2 will leave 1 as remainder..
so \(9^{12n+3}\) will leave 9 as remainder, as 12n+3 will be an odd number
E
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Re: IF n >0 what is the remainder when 9^{12n+3} is divided by 10  [#permalink]

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New post 26 May 2016, 07:27
satishchaudharygmat wrote:
IF n >0 what is the remainder when \(9^{12n+3}\) is divided by 10
A 0
B 1
C 2
D 7
E 9


For every even power, units digit of 9 will be 1 and for every every odd power units digit of 9 will be 9.

Since expression 12n+3 is odd, the units digit will be 9, which will also be the reminder when the expression is divided by 10.

E is the answer
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Re: IF n >0 what is the remainder when 9^{12n+3} is divided by 10  [#permalink]

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New post 26 May 2016, 07:45
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Re: IF n >0 what is the remainder when 9^{12n+3} is divided by 10   [#permalink] 26 May 2016, 07:45
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IF n >0 what is the remainder when 9^{12n+3} is divided by 10

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