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If n is an integer > 0 what is

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Active Member
Joined: 07 Jan 2018
Posts: 694
Followers: 11

Kudos [?]: 770 [1] , given: 88

If n is an integer > 0 what is [#permalink]  03 Jun 2018, 07:25
1
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Question Stats:

71% (00:54) correct 28% (02:53) wrong based on 7 sessions
If n is an integer > 0 what is the remainder when $$9^1^2^n^ +^3$$ is divided by 10?

src: Orbit Test Prep

[Reveal] Spoiler:
9
Intern
Joined: 03 Jun 2018
Posts: 6
Followers: 0

Kudos [?]: 6 [2] , given: 0

Re: If n is an integer > 0 what is [#permalink]  04 Jun 2018, 07:36
2
KUDOS
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.
Intern
Joined: 26 May 2018
Posts: 37
Followers: 0

Kudos [?]: 7 [0], given: 2

Re: If n is an integer > 0 what is [#permalink]  05 Jun 2018, 00:43
Good one!
Re: If n is an integer > 0 what is   [#permalink] 05 Jun 2018, 00:43
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