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# The remainder when 15^23 + 23^23 - Remainders -PS

Author Message
Director
Joined: 08 Jun 2013
Posts: 515
Location: India
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Engineering (Other)
The remainder when 15^23 + 23^23 - Remainders -PS  [#permalink]

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15 Aug 2018, 04:14
1
00:00

Difficulty:

45% (medium)

Question Stats:

55% (00:13) correct 45% (02:41) wrong based on 11 sessions

### HideShow timer Statistics

The remainder when 15^23 + 23^23 is divided by 19 is

A) 4
B) 15
C) 0
D) 18
E) 5

_________________

It seems Kudos button not working correctly with all my posts...

Please check if it is working with this post......

is it?....

Anyways...Thanks for trying

Senior Manager
Joined: 18 Jul 2018
Posts: 493
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: The remainder when 15^23 + 23^23 - Remainders -PS  [#permalink]

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15 Aug 2018, 05:17
Remainder Property $$a^n$$ + $$b^n$$ is divisible by a+b if n is odd.
Here n=23 (odd). Now, a+b = 15+23 =38. Which is completely divisible by 19. Hence remainder is zero.
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Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4272
Location: India
GPA: 3.5
Re: The remainder when 15^23 + 23^23 - Remainders -PS  [#permalink]

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15 Aug 2018, 06:46
Afc0892 wrote:
Remainder Property $$a^n$$ + $$b^n$$ is divisible by a+b if n is odd.
Here n=23 (odd). Now, a+b = 15+23 =38. Which is completely divisible by 19. Hence remainder is zero.

With (C) for the same reasons, well-explained Kudos added....
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VP
Joined: 07 Dec 2014
Posts: 1128
Re: The remainder when 15^23 + 23^23 - Remainders -PS  [#permalink]

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15 Aug 2018, 11:42
Harshgmat wrote:
The remainder when 15^23 + 23^23 is divided by 19 is

A) 4
B) 15
C) 0
D) 18
E) 5

5^3+3^3=152
152/19=8
remainder is 0
C
Re: The remainder when 15^23 + 23^23 - Remainders -PS &nbs [#permalink] 15 Aug 2018, 11:42
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