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What is the remainder when 25! + 5! Is divided by 100?

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What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 10 Aug 2018, 20:24
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What is the remainder when 25!+5! is divided by 100?
(1) 0
(B) 5
(C) 25-5
(D) 25
(E) 25+5


New question!!!..

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Re: What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 10 Aug 2018, 20:44
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My logic to solve the question.

25! Will always be divisible by 100.

So we have 5! Remaining.. 5!=120.

120÷100=20

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Re: What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 10 Aug 2018, 21:16
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chetan2u wrote:
What is the remainder when 25!+5! is divided by 100?
(1) 0
(B) 5
(C) 25-5
(D) 25
(E) 25+5


New question!!!..


25! is divisible by 100 (since it consists of 25x4).
5!=120, which leaves a remainder of 20, when divided by 100.
So remainder 20.
Answer (C).
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Re: What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 11 Aug 2018, 00:59
25! will be divisible by 100 hence the remainder will be determined by 5!. 5! = 120 hence when divided by 100, remainder will be 20. IMO C.
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Re: What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 11 Aug 2018, 01:54
When 25! Is divided by 100, remainder would be 0. So all depends on 5! Which is 120. When 120 is divided by 100, remainder is 20. THUS C.

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Re: What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 11 Aug 2018, 02:18
How do you guys determine that 25! is always divisible by a hundred without doing the drawn out calculation?

Someone enlighten me please :)
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Re: What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 11 Aug 2018, 02:22
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Arro44 wrote:
How do you guys determine that 25! is always divisible by a hundred without doing the drawn out calculation?

Someone enlighten me please :)


Arro44

25! = 25*24....................*4*3*2*1
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What is the remainder when 25! + 5! Is divided by 100?  [#permalink]

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New post 12 Aug 2018, 13:28
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25!+5! / 100 = remainder?
Forget 25! as whenever a number crosses 10!, at least two zeros are added to its tail which makes it divisible by 100 (10! = 10*...*5*...2*1 = 100*...).
So, the actual question is, what will be the remainder if 5! = 120 is divided by 100.
Our answer is 20 i.e. 25-5 (C)
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What is the remainder when 25! + 5! Is divided by 100?   [#permalink] 12 Aug 2018, 13:28
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