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If you divide 5^2500 by 7, which remainder do you get?

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Joined: 17 Aug 2018
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If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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New post 30 Nov 2019, 12:47
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If you divide 5^2500 by 7, which remainder do you get?

A. 0
B. 1
C. 2
D. 3
E. 4
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Joined: 19 Oct 2018
Posts: 1174
Location: India
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Re: If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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New post 30 Nov 2019, 20:09
2500= 3*833+1

\(5^3\)= -1 mod 7

\((5^3)^{833}\)= \((-1)^{833}\) mod 7
\((5^3)^{833}\)= -1 mod 7

\((5^3)^{833}*5\)= -1*5 mod 7
\((5^3)^{833}*5\)= -5 mod 7
\((5^3)^{833}*5\)= (7-5) mod 7
\((5^3)^{833}*5\)= 2 mod 7

C



KaranB1 wrote:
If you divide 5^2500 by 7, which remainder do you get?

A. 0
B. 1
C. 2
D. 3
E. 4
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Joined: 16 Feb 2015
Posts: 176
Location: United States
Concentration: Finance, Operations
Schools: INSEAD, ISB
If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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New post 01 Dec 2019, 00:20
2
KaranB1 wrote:
If you divide 5^2500 by 7, which remainder do you get?

A. 0
B. 1
C. 2
D. 3
E. 4


One More Method is Cyclicity of Remainder.
5^1=5/7 = Remainder 5
5^2=25/7 = Remainder 4
5^3=125/7 = Remainder 6
5^4=625/7 = Remainder 2
5^5=3125/7 = Remainder 3
5^6=15625/7 = Remainder 1
5^7=78125/7 = Remainder 5 (Repeating of Remainder)
So, therefore cyclicity is 6 for remainder.

We divide the Power of 5 with 6. i.e. 2500/6 = Remainder is 4. So 4th order for remainder is 2
IMO-C

:please Please give kudos, if you find my explanation Good Enough :please
Manager
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Joined: 17 Aug 2018
Posts: 95
Location: India
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If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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New post 01 Dec 2019, 02:32
https://www.youtube.com/watch?v=QJQ-hqin2Us

going through video by accessing the link may help.
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If you divide 5^2500 by 7, which remainder do you get?   [#permalink] 01 Dec 2019, 02:32
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If you divide 5^2500 by 7, which remainder do you get?

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