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

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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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A
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C
D
E

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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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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
Senior Manager
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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, 00:20
4
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
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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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Re: If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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New post 15 Dec 2019, 01:57
(5^2500)/7 has same remainder as (25^1250)/7 has same remainder as (4^1250)/7 has same remainder as (16^625)/7 has same remainder as (2^625)/7 has same remainder as (32^125)/7 has same remainder as (4^125)/7 has same remainder as (2^250)/7 has same remainder as(32^50)/7 has same remainder as
(4^50)/7 has same remainder as (16^25)/7 has same remainder as (2^25)/7 has same remainder as (32^5)/7 has same remainder as (4^5)/7 has same remainder as (2^10)/7 has same remainder as (32^2)/7 has same remainder as (4^2)/7 has reminder of 2, hence C is the right answer.
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Re: If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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New post 15 Dec 2019, 02:21
5/7 = -2 ( negative remainder )

Now, (-2)^(2500) = 2^(2500).
2^3 = 8
8/7 = 1.

2^3(800)*2^100 = 2^100 = 2^3(33)*2 = 2/7.

Remainder is 2.

C is the answer

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Re: If you divide 5^2500 by 7, which remainder do you get?   [#permalink] 15 Dec 2019, 02:21
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