Largest value of x question

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archiebanker: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Thu Jun 26, 2008 7:52 am

Largest value of x question

by archiebanker » Sun Jun 29, 2008 7:46 am

Found this one difficult, any insight into how to do the question appreciated:

What is the largest value of x that makes 30!/3x an integer?

Any help appreciated.

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Source: Beat The GMAT — Problem Solving | Sun Jun 29, 2008 7:46 am

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Re: Largest value of x question

by Ian Stewart » Sun Jun 29, 2008 8:04 am

archiebanker wrote: What is the largest value of x that makes 30!/3x an integer?

x is in the denominator. If we want to make x as large as possible, we want to make 30!/3x as small as possible. If x is positive, 1 is the smallest integer value that could be equal to 30!/3x.

30!/3x = 1
30! = 3x
30!/3 = x

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archiebanker: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Thu Jun 26, 2008 7:52 am

by archiebanker » Sun Jun 29, 2008 4:37 pm

Thanks for the quick reply, the issue is that the answer choices were 16, 18, 19 and two others i think. Can't remember was on a CAT for Princeton Review (by the way, how accurate are these? I am getting more and more right and staying in the 580 range).

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Re: Largest value of x question

by Stuart@KaplanGMAT » Mon Jun 30, 2008 12:19 am

archiebanker wrote:Found this one difficult, any insight into how to do the question appreciated:

What is the largest value of x that makes 30!/3x an integer?

Any help appreciated.

Are you sure you posted the question correctly?

The largest value of x that makes 30!/3x an integer is a HUGE number.

30!/3 = 30*29*28*27*26*...*5*4*2*1 (i.e. the only thing missing is the 3). So the largest value of x that makes 30!/3x an integer is:

30*29*28*27*26*...*5*4*2*1

which is a lot bigger than 19