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

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Manager
Joined: 04 Jan 2008
Posts: 116
If p is the product of the integers from 1 to 30, inclusive, [#permalink]

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06 Sep 2008, 00:24
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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 3^k is a factor of p?

(A) 10
(B) 12
(C) 14
(D) 16
(E) 18

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Director
Joined: 23 Sep 2007
Posts: 761

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06 Sep 2008, 00:36
dancinggeometry 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

C

the product of the integers from 1 to 30, inclusive, contains 3^14 as a factor.
Manager
Joined: 11 Apr 2008
Posts: 198

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06 Sep 2008, 17:49
It is the total number of 3 content in 30! which is 14
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Manager
Joined: 04 Jan 2008
Posts: 116

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06 Sep 2008, 23:24
OA is C. Bin 2 problem.
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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08 Sep 2008, 10:28
dancinggeometry 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

30/3 + 30/3^2 (nearest integer < this value )+30/3^3(nearest integer < this value)
= 10+3+1=14
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Joined: 07 Nov 2007
Posts: 1738
Location: New York

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09 Sep 2008, 03:26
scthakur wrote:
x2suresh wrote:
dancinggeometry 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

30/3 + 30/3^2 (nearest integer < this value )+30/3^3(nearest integer < this value)= 10+3+1=14

What is the logic behind this?

30/3 = 10 (there are 10 numbers which are divisible by 3 .. ( 3,6,9,12,15,18,21,24,27,30)
but, in the above we are missing.. additional threes in 9 =3^2,18=2*3^3,27=3*3^2
to count the second threes that are missing.
30/3^3 =3.33~=3
still we are missing third three in 27 (3^3)
similarly
30/3^3 = 1.11~=1 this will givie the third three from 27

If p is the product of the integers from 1 to 90, inclusive, what is the greatest integer k for which 3^k is a factor of p?

90/3=30
90/9=10
90/27=10/3=3.3~3
90/81=10/9=1.1~1

k=30+10+3+1=45

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Zumit PS 001   [#permalink] 09 Sep 2008, 03:26
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