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

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Manager
Joined: 25 Aug 2004
Posts: 171
Location: MONTREAL
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If p is the product of the integers from 1 to 30, inclusive, [#permalink]  01 Oct 2005, 05:16
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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

Last edited by mbassmbass04 on 01 Oct 2005, 06:55, edited 1 time in total.
Current Student
Joined: 29 Jan 2005
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There must be a simple formula for calculating 1*2*3*4.....30 but I don`t know it. Any hints???
Current Student
Joined: 29 Jan 2005
Posts: 5244
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Kudos [?]: 179 [0], given: 0

1*2*3*4....18*....30/3(18)

Both the 3 and the 18 cancel out.

E.
Manager
Joined: 25 Aug 2004
Posts: 171
Location: MONTREAL
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Kudos [?]: 11 [0], given: 0

ETS loves similar question, they call it Logic questions

Let's count the factors of 3 that exists between 1 and 30

3

3 x 2 = 6

3 x 3 = 9

3 x 4 = 12

3 x 5 = 15

3 x 3 x 2 = 18

3 x 7= 21

3 x 8= 24

3 x 3 x 3 = 27

3 x 10 = 30

There are 14 factors of 3, Answer is 14
SVP
Joined: 05 Apr 2005
Posts: 1733
Followers: 5

Kudos [?]: 38 [0], given: 0

mbassmbass04 wrote:
ETS loves similar question, they call it Logic questions. Let's count the factors of 3 that exists between 1 and 30

3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 3 x 2 = 18
3 x 7= 21
3 x 8= 24
3 x 3 x 3 = 27
3 x 10 = 30
There are 14 factors of 3, Answer is 14

then 3k should be updated as 3^k. as it is 18 is the answer however it is not the correct one......
Manager
Joined: 25 Aug 2004
Posts: 171
Location: MONTREAL
Followers: 1

Kudos [?]: 11 [0], given: 0

Yes, you are totally right, I will update it.
Manager
Joined: 06 Aug 2005
Posts: 197
Followers: 3

Kudos [?]: 5 [0], given: 0

Simple formula

= [30/3] + [30/(3^2)] + [30/(3^3)]
= 10 + 3 + 1
= 14
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