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What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b

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Joined: 02 Sep 2009
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Kudos [?]: 132595 [1], given: 12326

What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b [#permalink]

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New post 06 Oct 2017, 04:49
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

46% (01:03) correct 54% (01:50) wrong based on 37 sessions

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Kudos [?]: 132595 [1], given: 12326

Expert Post
1 KUDOS received
Math Expert
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P
Joined: 02 Aug 2009
Posts: 5201

Kudos [?]: 5826 [1], given: 117

Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b [#permalink]

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New post 06 Oct 2017, 06:41
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Bunuel wrote:

CHALLENGE QUESTIONS



What will be the remainder when \(13^7 + 14^7 + 15^7 + 16^7\) is divided by 58?

A. 0
B. 1
C. 28
D. 30
E. 57


hi..

Here we have to remember that \(a^n+b^n\) is always div by a+b when n is ODD

so 58 should tell you that 58=2*29 and the numbers in equation also add up to 29 - 13+16 and 14+15
\(13^7 + 14^7 + 15^7 + 16^7= (13^7+16^7)+(14^7+15^7)\)

two things
1) the entire sum is \(Odd^7+Even^7+Odd^7+Even^7\).. here total will be EVEN
2) now \(13^7+16^7\) will be div by 13+16=29 and similarly \(14^7+15^7.\).

so the the EQUATION is div by 2 and also by 29..

thus remainder will be 0

ans A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5826 [1], given: 117

Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b   [#permalink] 06 Oct 2017, 06:41
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What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b

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