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VP
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How many zeros does 1000! end with? 100 148 250 248 200 [#permalink]
 19 Mar 2008, 04:16
How many zeros does 1000! end with?
100
148
250
248
200
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CEO
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Re: factorial and exp [#permalink]
19 Mar 2008, 04:31
1. each of zeros are defined as 2*5. 2. It is obviously that 1000! contains fewer the number of 5 than the number of 2. Therefore, the number of 5 determined the number of zeros. (1000-5)/5+1=200 (1000-25)/25+1=40 (1000-125)/125+1=8 (625-625)/625+1=1 N=200+40+8+1=249 
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Re: factorial and exp [#permalink]
19 Mar 2008, 04:33
walker wrote: 1. each of zeros are defined as 2*5. 2. It is obviously that 1000! contains greater the number of 5 than the number of 2. Therefore, the number of 5 determined the number of zeros. (1000-5)/5+1=200 (1000-25)/25+1=40 (1000-125)/125+1=8 (625-625)/625+1=1 N=200+40+8+1=249 how did you know that it contains more 5 than 2?
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CEO
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Re: factorial and exp [#permalink]
19 Mar 2008, 04:37
kazakhb wrote: how did you know that it contains more 5 than 2? Sorry, it have to be "It is obviously that 1000! contains fewer the number of 5 than the number of 2"
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Re: factorial and exp [#permalink]
19 Mar 2008, 04:41
walker wrote: 1. each of zeros are defined as 2*5. 2. It is obviously that 1000! contains fewer the number of 5 than the number of 2. Therefore, the number of 5 determined the number of zeros.
(1000-5)/5+1=200
(1000-25)/25+1=40
(1000-125)/125+1=8
(625-625)/625+1=1N=200+40+8+1=249 sorry for dumb question, could you explain logics behind the calculation you have made
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CEO
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Re: factorial and exp [#permalink]
19 Mar 2008, 04:52
kazakhb wrote: sorry for dumb question, could you explain logics behind the calculation you have made Nb----X----X----X----X----X----X----X----Ne Nb - is the first number in sequence Ne - is the last number in sequence d - is the step The total number = (Ne-Nb)/d+1 I use this formula to avoid silly mistakes. BTW, my answer is not correct 
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Director
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Re: factorial and exp [#permalink]
19 Mar 2008, 05:18
I say 148 ...but its just a strategic guess.. I thought 100 is way to low and 250 to high.
I basically rephrased to say..how many factors of 10 are in 1000!?
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CEO
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Re: factorial and exp [#permalink]
19 Mar 2008, 07:57
walker wrote: 1. each of zeros are defined as 2*5. 2. It is obviously that 1000! contains fewer the number of 5 than the number of 2. Therefore, the number of 5 determined the number of zeros. (1000-5)/5+1=200 (1000-25)/25+1=40 (1000-125)/125+1=8 (625-625)/625+1=1 N=200+40+8+1=249 Another method I use here is to just divide 1000! by the powers of 5. 1000!/5 = 200 1000!/25 = 40 1000!/125 =8 1000!/625 ~1 All adds up to 249...??? Perhaps I we round up on the last one?
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Re: factorial and exp [#permalink]
19 Mar 2008, 09:41
i am getting 249 as well..
ans choices are off..
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CEO
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Re: factorial and exp [#permalink]
19 Mar 2008, 11:00
walker wrote: 1. each of zeros are defined as 2*5. 2. It is obviously that 1000! contains fewer the number of 5 than the number of 2. Therefore, the number of 5 determined the number of zeros. (1000-5)/5+1=200 (1000-25)/25+1=40 (1000-125)/125+1=8 (625-625)/625+1=1 N=200+40+8+1=249 why did you do [(1000 - 25)/5 + 1 ] i do: 1000/5 = 200 1000/25 = 40 1000/125 = 8 1000/625 = 1 so total = 249
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CEO
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Re: factorial and exp [#permalink]
19 Mar 2008, 11:32
GMAT TIGER wrote: why did you do [(1000 - 5)/5 + 1 ]
i do:
1000/5 = 200
1000/25 = 40
1000/125 = 8
1000/625 = 1
so total = 249 to avoid some GMAT traps For example, n is the product of 4*5*...999 and m is the product of 5*6*...1000 In both cases we have range = 995=(999-4)=(1000-5). n contains 248 zeros but m contains 249 zeros the formula "The total number = (Ne-Nb)/d+1" helps to avoid this trap.
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Re: factorial and exp [#permalink]
10 Jan 2012, 14:57
walker wrote: 1. each of zeros are defined as 2*5. 2. It is obviously that 1000! contains fewer the number of 5 than the number of 2. Therefore, the number of 5 determined the number of zeros. (1000-5)/5+1=200 (1000-25)/25+1=40 (1000-125)/125+1=8 (625-625)/625+1=1 N=200+40+8+1=249 Hm, I dont see how you got 249 using this formula. (1000-5)/5+1 = 165 ?! Could you please explain how that formula avoids traps? Thanks a lot!
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Re: factorial and exp
[#permalink]
10 Jan 2012, 14:57
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