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# Remainder when 25^10 is divided by 576?

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Intern
Joined: 11 Sep 2012
Posts: 7
Remainder when 25^10 is divided by 576?  [#permalink]

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Updated on: 14 Oct 2018, 05:20
1
00:00

Difficulty:

65% (hard)

Question Stats:

50% (00:54) correct 50% (00:54) wrong based on 12 sessions

### HideShow timer Statistics

Remainder when 25^10 is divided by 576?

1) 241
2) 542
3) 378
4) 405
5) None of these

Posted from my mobile device

Originally posted by asifahmed500 on 14 Oct 2018, 04:48.
Last edited by asifahmed500 on 14 Oct 2018, 05:20, edited 3 times in total.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
Re: Remainder when 25^10 is divided by 576?  [#permalink]

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14 Oct 2018, 07:59
asifahmed500 wrote:
Remainder when 25^10 is divided by 576?

1) 241
2) 542
3) 378
4) 405
5) None of these

Posted from my mobile device

$$Rem(\frac{25^{10}}{576})$$=$$Rem(\frac{(24+1)^{10}}{24^2})$$

Upon expansion of $$(24+1)^{10}$$, the terms will have 24 raised to the power from 0 to 24. Out of which, the terms with $$24^0$$ and $$24^1$$ are not divisible by $$24^2$$. OR the terms with 24 raised to the power greater than or equal to 2 are divisible by $$24^2$$.

So, $$Rem(\frac{(24+1)^{10}}{24^2})$$=$$10C0*24^0+10C1*24^1=1+10*24=241$$

Ans. (A)
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Senior Manager
Joined: 18 Jun 2018
Posts: 262
Re: Remainder when 25^10 is divided by 576?  [#permalink]

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14 Oct 2018, 08:06
asifahmed500 wrote:
Remainder when 25^10 is divided by 576?

1) 241
2) 542
3) 378
4) 405
5) None of these

Posted from my mobile device

OA: A

Remainder $$\frac{25^{10}}{576}$$=Remainder $$\frac{625^{5}}{576}$$=Remainder $$\frac{49^{5}}{576}$$=Remainder $$\frac{97*97*49}{576}$$=Remainder $$\frac{145*97}{576}$$=Remainder $$\frac{241}{576}$$

Remainder$$= 241$$
Re: Remainder when 25^10 is divided by 576?   [#permalink] 14 Oct 2018, 08:06
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