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# What is the remainder when 5^37 is divided by 63 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 64997
What is the remainder when 5^37 is divided by 63 ?  [#permalink]

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24 Feb 2020, 02:55
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Difficulty:

75% (hard)

Question Stats:

48% (01:55) correct 52% (01:46) wrong based on 67 sessions

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What is the remainder when $$5^{37}$$ is divided by 63 ?

A. 1
B. 2
C. 3
D. 4
E. 5

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Director
Joined: 25 Jul 2018
Posts: 731
Re: What is the remainder when 5^37 is divided by 63 ?  [#permalink]

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24 Feb 2020, 04:13
2
1
What is the remainder when $$5^{37}$$ is divided by 63 ?

$$5^{37}= 5*5^{36}= 5*125^{12}= 5(126-1)^{12}= 5(63*2-1)^{12}= 5*(63m+...+1)$$

--> Dividing by 63, the remainder will be 5.

The answer choice E is correct
Intern
Joined: 22 Feb 2020
Posts: 7
Re: What is the remainder when 5^37 is divided by 63 ?  [#permalink]

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24 Feb 2020, 04:16
3
1
5^37 = 5^36 * 5
5^36 = 125^12
(125^12)/63 has a remainder of -1
-1^12 = 1
1 * 5(from the first line of the equation) = 5
Intern
Joined: 10 Aug 2019
Posts: 2
Re: What is the remainder when 5^37 is divided by 63 ?  [#permalink]

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26 Feb 2020, 20:04
can you please explain why this doesn't work --->

5^37/63 = 125^34/63 = (63+62)^34/63

Using binomial theorem:
(63m+ .. + 62^34 )/63 = 62^34/63

(63-1)^34/63 = (-1)^34/ 63 = 1
i.e. option A
Director
Joined: 25 Jul 2018
Posts: 731
What is the remainder when 5^37 is divided by 63 ?  [#permalink]

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26 Feb 2020, 21:13
1
Green12345554 wrote:
can you please explain why this doesn't work --->

5^37/63 = 125^34/63 = (63+62)^34/63

Using binomial theorem:
(63m+ .. + 62^34 )/63 = 62^34/63

(63-1)^34/63 = (-1)^34/ 63 = 1
i.e. option A

hi,
The highlighted part above is not correct. It should be
—> $$5^{37} = 5^3*5^{34}$$ or

—> $$5^{37} = 5*5^{36}= 5*5^{3*12} = 5*125^{12}$$

Hope it helps

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CEO
Joined: 03 Jun 2019
Posts: 3182
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: What is the remainder when 5^37 is divided by 63 ?  [#permalink]

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29 Mar 2020, 01:55
Bunuel wrote:
What is the remainder when $$5^{37}$$ is divided by 63 ?

A. 1
B. 2
C. 3
D. 4
E. 5

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Are You Up For the Challenge: 700 Level Questions

Asked: What is the remainder when $$5^{37}$$ is divided by 63 ?

5^3 = 125 = 63*2-1

5^37mod63 = 125^12*5mod63 = (-1)^12*5mod63 = 5mod63

IMO E
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: What is the remainder when 5^37 is divided by 63 ?   [#permalink] 29 Mar 2020, 01:55