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# Find the remainder when 51^203 is divided by 7

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Current Student
Joined: 27 May 2014
Posts: 524
GMAT 1: 730 Q49 V41
Find the remainder when 51^203 is divided by 7  [#permalink]

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26 Jan 2017, 18:23
1
5
00:00

Difficulty:

75% (hard)

Question Stats:

48% (01:45) correct 52% (01:31) wrong based on 101 sessions

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Find the remainder when 51^203 is divided by 7?
(A) 4
(B) 2
(C) 1
(D) 6
(E) 5

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Find the remainder when 51^203 is divided by 7  [#permalink]

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26 Jan 2017, 18:31
3
4
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Director
Joined: 14 Nov 2014
Posts: 629
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: Find the remainder when 51^203 is divided by 7  [#permalink]

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27 Jan 2017, 02:40
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
Intern
Joined: 16 Mar 2014
Posts: 27
Concentration: Entrepreneurship, Finance
GMAT 1: 550 Q47 V20
GPA: 3.2
Re: Find the remainder when 51^203 is divided by 7  [#permalink]

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27 Jan 2017, 02:53
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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10 Mar 2018, 23:33
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Re: Find the remainder when 51^203 is divided by 7   [#permalink] 10 Mar 2018, 23:33
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# Find the remainder when 51^203 is divided by 7

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