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# Powers

Author Message
Director
Joined: 01 Apr 2008
Posts: 882
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 30

Kudos [?]: 707 [0], given: 18

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07 Nov 2009, 00:18
00:00

Difficulty:

(N/A)

Question Stats:

67% (01:05) correct 33% (00:00) wrong based on 5 sessions

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What is the remainder when 43 raised to the power 86 is divided by 5?

a.0
b.1
c.2
d.3
e.4
Manager
Joined: 19 Aug 2009
Posts: 79
Followers: 1

Kudos [?]: 251 [0], given: 46

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07 Nov 2009, 00:44
Economist wrote:
What is the remainder when 43 raised to the power 86 is divided by 5?

a.0
b.1
c.2
d.3
e.4

By remainder thm,
43^86/5 R----->3^86/5..........(43/5...gives rem 3)

now 86/4 gives is of the form 4n+2
3^4n+2 gives last digit as 9 ( eg n=0, 3^2=9, 3^6= 729)

and ...9/5 will giv remainder 4
ans e
Manager
Joined: 27 Oct 2009
Posts: 146
Location: Montreal
Schools: Harvard, Yale, HEC
Followers: 1

Kudos [?]: 91 [0], given: 18

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07 Nov 2009, 10:19
Remainder of 43^86/5 will be equal to remainder of 3^86/5 as 3 is remainder of 43/5

3^86 = (3^2)^43 = 9^43 = a number having 9 as unit
=> remainder of 9^43/5 = 4
Re: Powers   [#permalink] 07 Nov 2009, 10:19
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