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Find the remainder when 51^203 is divided by 7

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Joined: 28 May 2014
Posts: 477
GMAT 1: 730 Q49 V41
Find the remainder when 51^203 is divided by 7 [#permalink]

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26 Jan 2017, 19:23
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Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5
[Reveal] Spoiler: OA

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Joined: 02 Aug 2009
Posts: 5715
Find the remainder when 51^203 is divided by 7 [#permalink]

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26 Jan 2017, 19:31
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saswata4s wrote:
Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5

Hi,
$$51^{203}=(49+2)^{203}$$
Here all terms except 2^203 will be div by 7..

Now $$2^{203}=(2^3)^{67}*2^2=8^{67}*4=(7+1)^{67}*4$$
Here $$(7+1)^{67}$$ will leave a remainder of 1, so remainder=1*4=4

A
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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

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Posts: 663
Re: Find the remainder when 51^203 is divided by 7 [#permalink]

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27 Jan 2017, 03:40
saswata4s wrote:
Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5

A is the answer..51 will give 2 as remainder ..(
So 2^203/7
(2^3)^67 * 4/7
(8^67 * 4)/7 (if a equation in form (ax+1)/x then the remainder will be 1(here (7*1+1)/7)
8^67 will give remainder =1
1*4/7=4 is the remainder
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Joined: 16 Mar 2014
Posts: 37
Concentration: Entrepreneurship, Finance
GMAT 1: 550 Q47 V20
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Re: Find the remainder when 51^203 is divided by 7 [#permalink]

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27 Jan 2017, 03:53
Thank you @chatun2u for the explanation. Although I got the answer correct, i wasn't sure about it.
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Re: Find the remainder when 51^203 is divided by 7 [#permalink]

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11 Mar 2018, 00:33
Hello from the GMAT Club BumpBot!

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Re: Find the remainder when 51^203 is divided by 7   [#permalink] 11 Mar 2018, 00:33
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