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What is the remainder obtained when 63^25 is divided by 16?

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What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 29 Oct 2018, 06:32
2
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (01:02) correct 38% (00:44) wrong based on 92 sessions

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What is the remainder obtained when \(63^{25}\) is divided by 16?

A. -1
B. 0
C. 5
D. 10
E. 15
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Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 29 Oct 2018, 07:22
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15
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Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 07 Nov 2018, 10:34
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pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.
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Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 07 Nov 2018, 19:38
AnupamKT wrote:
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.

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What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 07 Nov 2018, 20:06
1
AnupamKT wrote:
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.


63^25 can be written as ((64-1)^25)/16

64 is divisible by 16. what is left is -1^25 which turns out to be -1.

Always make numerator in such a manner that it gets divided by denominator.

But remainder can never by negative hence -1+16 (denominator here) gives 15.

Therefore E.
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Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 07 Nov 2018, 20:20
1
AnupamKT wrote:
pandeyashwin wrote:
\(\frac{65^(25)}{16} = -1^(25) = -1\)

Remainder = 16-1 = 15


Please explain why we cannot consider Option A= -1.

As per me, this question should have two answers= -1 & 15. ( NEGATIVE & POSITIVE REMAINDERS )

Please explain the logic behind.


Remainder is ALWAYS positive. If you ever get a negative remainder. Just add the divisor to the negative remainder.

Ex: What's the remainder when 31 is divided by 16.

32 is completely divisible by 16. Hence for 31 we get a negative remainder of -1. Adding the divisor, we get -1+16 = 15.

Hope it's clear

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Re: What is the remainder obtained when 63^25 is divided by 16?  [#permalink]

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New post 07 Nov 2018, 20:59
Unit place cyclicity of 3 -> 3,9,7,1
and Unit place cyclicity of 7 -> 7,9,3,1.

Now,
(63)^25 / 16 = (3 * 3 * 7)^25 /16
=> (3 * 3 * 7)/16 => 63/16
=> remainder as 15.
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Re: What is the remainder obtained when 63^25 is divided by 16?   [#permalink] 07 Nov 2018, 20:59
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