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5^k is a factor of the product of odd integers from 99 -199,

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Manager
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5^k is a factor of the product of odd integers from 99 -199, [#permalink] New post 24 Jan 2008, 10:50
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5^k is a factor of the product of odd integers from
99 -199, what is the greatest possible value of k?

1. 12
b. 17
c. 22
d. 25
e. 48
Director
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Re: PS - Facors -Odd integers [#permalink] New post 24 Jan 2008, 11:03
actually it's 13, so I have to go with A.

105 + 10s, s = 0 ... 9 -> 10
125 + 50l, l = 0,1 -> 2
125 -> 1

10+2+1= 13
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Re: PS - Facors -Odd integers [#permalink] New post 24 Jan 2008, 11:04
Expert's post
It's strange. I got 13....

105 - 1
115 - 1
125 - 3
135 - 1
145 - 1
155 - 1
165 - 1
175 - 2
185 - 1
195 - 1
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Re: PS - Facors -Odd integers [#permalink] New post 27 Jan 2008, 13:46
id love to know how to approach this question, if anyone cares to explain :)
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Re: PS - Facors -Odd integers [#permalink] New post 27 Jan 2008, 22:14
walker wrote:
It's strange. I got 13....

105 - 1
115 - 1
125 - 3
135 - 1
145 - 1
155 - 1
165 - 1
175 - 2
185 - 1
195 - 1


Same approach. Took me about 3 min to reach this though. I also get 13. So I guess A it is then.

This problem looks harder than it really is. Essentially what walker and I did here is realize that all we need to care about is the number of 5's from 99-199. we don't include the evens so just start counting out the odds with factors of 5:

105, 115, 125, etc...

105 -> 5*21 115-> 5*23 125-> 5*25 etc...

We see that there should be a 5^13 as a factor of the product of the odd integers from 99 to 199.


Not sure why its 12 though.
Re: PS - Facors -Odd integers   [#permalink] 27 Jan 2008, 22:14
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5^k is a factor of the product of odd integers from 99 -199,

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