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If n is an integer > 0 what is
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03 Jun 2018, 07:25
03 Jun 2018, 07:25
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Question Stats:
81% (01:02) correct
18% (01:36) wrong based on 33 sessions
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If n is an integer \(> 0\) what is the remainder when \(9^{(12n+3)}\) is divided by 10?
src: Orbit Test Prep
src: Orbit Test Prep
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Re: If n is an integer > 0 what is
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04 Jun 2018, 07:36
04 Jun 2018, 07:36
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Approach :
Cyclicity of 9
9 ^1= 9
9^2= 81
9^3= 729 and so on.
hence, 9^even gives unit digit 1 while 9^odd gives unit digit 9.
Therefore,
9^(12n+3) shall give 9^odd digit with n as any integer > 0
Hence, Numerator shall have value 9 as unit digit which when divided by 10 shall give remainder 9.
Cyclicity of 9
9 ^1= 9
9^2= 81
9^3= 729 and so on.
hence, 9^even gives unit digit 1 while 9^odd gives unit digit 9.
Therefore,
9^(12n+3) shall give 9^odd digit with n as any integer > 0
Hence, Numerator shall have value 9 as unit digit which when divided by 10 shall give remainder 9.
