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

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Manager
Joined: 17 Aug 2018
Posts: 109
Location: India
Schools: IIMA
GMAT 1: 640 Q46 V32
If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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30 Nov 2019, 11:47
1
00:00

Difficulty:

85% (hard)

Question Stats:

36% (02:09) correct 64% (02:07) wrong based on 45 sessions

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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
Senior Manager
Joined: 16 Feb 2015
Posts: 355
Location: United States
If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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30 Nov 2019, 23:20
4
1
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 give kudos, if you find my explanation Good Enough
##### General Discussion
VP
Joined: 19 Oct 2018
Posts: 1304
Location: India
Re: If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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30 Nov 2019, 19:09
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
Manager
Joined: 17 Aug 2018
Posts: 109
Location: India
Schools: IIMA
GMAT 1: 640 Q46 V32
If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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01 Dec 2019, 01:32

going through video by accessing the link may help.
Manager
Joined: 17 Aug 2018
Posts: 109
Location: India
Schools: IIMA
GMAT 1: 640 Q46 V32
Re: If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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15 Dec 2019, 00:57
(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.
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1060
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: If you divide 5^2500 by 7, which remainder do you get?  [#permalink]

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15 Dec 2019, 01:21
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.

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Re: If you divide 5^2500 by 7, which remainder do you get?   [#permalink] 15 Dec 2019, 01:21
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