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Very familiar GMAT ques, but missing somewhere - Plz help

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Very familiar GMAT ques, but missing somewhere - Plz help [#permalink] New post 01 Dec 2012, 01:35
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

I get k = 13, 10 multiples of 3 + 1(for 9)+ 2(for 27) = 13. But not in any answer options. Can anyone help?
[Reveal] Spoiler:
C
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Re: Very familiar GMAT ques, but missing somewhere - Plz help [#permalink] New post 01 Dec 2012, 05:13
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SreeViji wrote:
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

I get k = 13, 10 multiples of 3 + 1(for 9)+ 2(for 27) = 13. But not in any answer options. Can anyone help?
[Reveal] Spoiler:
C


p = 30!. To find the highest power of 3 there is a formula:

30/3 + 30/9 + 30/27 (We need only the whole number part) = 10 + 3 + 1 = 14. Answer is C. You are leaving out the extra 3 in 18... :)

Illustration :

3 -->1
6 -->1
9 -->2
12-->1
15-->1
18-->2
21-->1
24-->1
27-->3
30-->1

In total... 14
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Re: Very familiar GMAT ques, but missing somewhere - Plz help [#permalink] New post 01 Dec 2012, 19:48
Thank youso much...i saw this formula in gmat club,but forgot. Thanks for your time anyways
Re: Very familiar GMAT ques, but missing somewhere - Plz help   [#permalink] 01 Dec 2012, 19:48
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