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by ska7945 » Wed Aug 20, 2008 7:57 pm
k is integer, 5^k is factor of product of odd number between 99 and 199 (inclusive), what can be the max value for k?


sorry, i dont have answer choice but oa is 13.
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by parallel_chase » Wed Aug 20, 2008 8:36 pm
list all the odd number which are multiples of 5
105 = 5
115 = 5
125 = 5*5*5
135 = 5
145 = 5
155 = 5
165 = 5
175 = 5*5
185 = 5
195 = 5

k = 13

I was able to this in less than 2 mins but any shorter way would be helpful.
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by vishubn » Wed Aug 20, 2008 10:35 pm
Hi

I didnt understand the stem of the question :( , could u please expalin wat is that we trtying to find coz it says product of odd number so i felt 105*110*so on ...

thanks in adavcne
Vishu
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by parallel_chase » Wed Aug 20, 2008 10:59 pm
The question stem says:

product of odd numbers from 99 to 199 i.e.

99*101*103*105*107*.......*199 has how many factors of 5

Hope its clear now.
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by sudhir3127 » Thu Aug 21, 2008 2:45 am
parallel_chase wrote:list all the odd number which are multiples of 5
105 = 5
115 = 5
125 = 5*5*5
135 = 5
145 = 5
155 = 5
165 = 5
175 = 5*5
185 = 5
195 = 5

k = 13

I was able to this in less than 2 mins but any shorter way would be helpful.
I have different method..

here it goes..

99- 199. number of odd numbers are 51

thus number of 5's are

51/5 + 51/5^2 = 12 but 125 will have 5^3 so need t take one more 5

thus its 12 + 1 =13.

hope it helps..
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