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archiebanker
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 Posted: Sun Jun 29, 2008 8:46 am Post subject: Largest value of x question |
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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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Ian Stewart
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| Posted: Sun Jun 29, 2008 9:04 am Post subject: Re: Largest value of x question |
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| archiebanker wrote: |
What is the largest value of x that makes 30!/3x an integer?
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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
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| Posted: Sun Jun 29, 2008 5:37 pm Post subject: |
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| 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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Stuart Kovinsky
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| Posted: Mon Jun 30, 2008 1:19 am Post subject: Re: Largest value of x question |
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| 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 
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