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# How many zeroes does 100! end with? a) 20 b) 24 c) 25 d) 30

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Senior Manager
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How many zeroes does 100! end with? a) 20 b) 24 c) 25 d) 30 [#permalink]  06 Aug 2006, 20:15
How many zeroes does 100! end with?

a) 20

b) 24

c) 25

d) 30

e) 32
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Re: zeros in 100! [#permalink]  06 Aug 2006, 20:25
Imo..B
Guessing
multiples of 5 within 100 => 20
multiples of 25 within 100 => 4
20+4 = 24..

What is OA?? Never seen this type of question.
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Senior Manager
Joined: 06 Jul 2004
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You are right. It's 24.
could you explain your answer? I am sorry, i didn't get it.
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for every person who doesn't try because he is
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Senior Manager
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shoonya wrote:
You are right. It's 24.
could you explain your answer? I am sorry, i didn't get it.

10=5*2

Let's consider 10!..

1*2*3*4*5*6*7*8*9*10
1*2*3*4*6*7*8*9*(5*2*10)
5*2*10 = 100, => thus, it will end with two zeros.

20! => 5*10*15*20 => 0000 it will end with 4 zeros.
(I guess we only need to count multiples of 5 since there are enough 2s.)

100!
multiples of 5 within 100 => 20
(5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100)
multiples of 25 within 100 => 4 (since 25,50,75,100 => have two 5s..)

20+4 = 24..
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Senior Manager
Joined: 06 Jul 2004
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Location: united states
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Kudos [?]: 13 [0], given: 0

very neat. Thanks for the explanation.
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for every person who doesn't try because he is
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Senior Manager
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Is this a GMAT question? Seems too odd...
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