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Integers

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by moneyman » Tue Nov 06, 2007 4:23 am
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. 1
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by raulverde » Tue Nov 06, 2007 4:53 am
I come up with 16.

OA please
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by moneyman » Tue Nov 06, 2007 5:10 am
No thats not the answer.Can u pls give an explanation of your answer?Will be very helpful!!
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by camitava » Tue Nov 06, 2007 5:27 am
Hey Moneyman,
IMO 16 too. Because 3*16 is a factor of 30!. Though 3 * (all the other options) are also factor of 30! but 16 is the largest one. And thats why 16.
Correct me If I am wrong


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by moneyman » Tue Nov 06, 2007 6:03 am
Well I got this question from GMAT sets and in that it says the answer is 14.Maybe its wrong!!
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by moneyman » Tue Nov 06, 2007 8:01 am
Hey everyone I would seriously want to apologize for my mistake..Its not 3k its 3^k.Sorry Amitava :oops:
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by Suyog » Tue Nov 06, 2007 11:22 am
Can anyone explain the ans 14?
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by gmatguy16 » Tue Nov 06, 2007 3:54 pm
30 ! = 1*2*3 .........*30
we are not interested in all the numbers in the multiplication,we are only interested in the numbers which are factors of 3

30 ! =3 *6*9*12*.....*27*30
=constant * 3^ 14
hence answer is 14..
hope this helps.
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hi

by lawalx » Wed Nov 07, 2007 12:14 am
please could u explain the constant - where did 14 come from
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by camitava » Wed Nov 07, 2007 4:21 am
lawalx n Suyog, refer the explanation below -
30/3 = 10 so there are 10 multiples of 3 from 1 to 30. Again there are 3 multiples of 9. 9, 18 and 27. 9 = 3 * 3, 18 = 3 * 3 * 2 and 27 = 3 * 3 * 3. So this time, 3 is coming for 4 times. [Leave one 3 as u have already calculated for finding out the multiples of 3.] So total no is = (10 + 4) = 14. Am I clear?
Correct me If I am wrong


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Amitava
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by lawalx » Sat Nov 24, 2007 4:10 pm
gt it

tnx amitava
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