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# If p is the product of the integers from 1 to 30, inclusive,

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VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08
If p is the product of the integers from 1 to 30, inclusive, [#permalink]

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16 Oct 2004, 06:56
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If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?

A.10
B.12
C.14
D.16
E.18
Manager
Joined: 13 Oct 2004
Posts: 50

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16 Oct 2004, 07:37
I am understanding this incorrectly ?

p = 30!

so greatest integer k for which 30! / 3k is integer will be 30!/3

so none of the choices work for me.
Manager
Joined: 18 Sep 2004
Posts: 151
Location: Dallas, TX

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16 Oct 2004, 09:26
From the answer choices, E 18 would be the largest K where 3K is divisible by 30!

If K = 18 (2*3*3) then 3 K = 2*3*3*3 and from 30! we have 27 = 3*3*3 and 2 which is divisible by 30!.

However, 18 is not the largest K where 3K is divisible by 30! There are number larger than 18 where 3K is divisible by 30!, if you think about how many 2 can be reduced from 30! You'll understand...
VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

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16 Oct 2004, 23:03
Thanks...in fact the OA is E but without explanations
Seems Nzgmat got it thanks guys
Manager
Joined: 24 Aug 2004
Posts: 66

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17 Oct 2004, 08:28
None of the choices is correct, because the largest factor of 30! wud be 30! itself, and so if i have to find a number k of which 3K is a factor of 30! that number K would be 30!/3 .

So among the choices the given choices 18 is the larget number, so wud go for E.
Manager
Joined: 18 Sep 2004
Posts: 151
Location: Dallas, TX

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18 Oct 2004, 20:54
Totally agree here as the none of the answer choices are really correct... E is just more correct...
CIO
Joined: 09 Mar 2003
Posts: 463

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19 Oct 2004, 09:44
on the same page with everyone else. E works, but not the highest possible.
19 Oct 2004, 09:44
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