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

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Manager
Joined: 01 Nov 2007
Posts: 147
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Kudos [?]: 246 [1] , given: 0

5^k is a factor of the product of odd integers from 99 -199, [#permalink]  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
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 139 [0], given: 1

Re: PS - Facors -Odd integers [#permalink]  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
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2145 [0], given: 359

Re: PS - Facors -Odd integers [#permalink]  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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SVP
Joined: 28 Dec 2005
Posts: 1583
Followers: 2

Kudos [?]: 88 [0], given: 2

Re: PS - Facors -Odd integers [#permalink]  27 Jan 2008, 13:46
id love to know how to approach this question, if anyone cares to explain
CEO
Joined: 29 Mar 2007
Posts: 2591
Followers: 16

Kudos [?]: 234 [0], given: 0

Re: PS - Facors -Odd integers [#permalink]  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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