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

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Manager
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If p is the product of the integers from 1 to 30, inclusive, [#permalink]

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01 Oct 2005, 06:16
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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

Last edited by mbassmbass04 on 01 Oct 2005, 07:55, edited 1 time in total.
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01 Oct 2005, 07:03
There must be a simple formula for calculating 1*2*3*4.....30 but I don`t know it. Any hints???
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01 Oct 2005, 07:11
1*2*3*4....18*....30/3(18)

Both the 3 and the 18 cancel out.

E.
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01 Oct 2005, 07:22
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
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01 Oct 2005, 07:29
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
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01 Oct 2005, 07:55
Yes, you are totally right, I will update it.
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01 Oct 2005, 09:21
Simple formula

= [30/3] + [30/(3^2)] + [30/(3^3)]
= 10 + 3 + 1
= 14
01 Oct 2005, 09:21
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