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tennis25
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Pearson Vue CAT Quant PS-need help 01 Jan 2006, 04:13
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Hi all, I just took the first GMATPREP cat yesterday and am disappointed as they dont have explanations for your wrong answers. If any of you know how to solve this one it would really help. Thanks and Happy New Year!!!

If y and n are positive intergers and 450y=n^3 which of the following is an interger.
I. y/(3)(2^2)(5)

II. y/(3^2)(2)(5)

III. y/(3)(2)(5^2)

I simply cannot figure out what 450y=n^3 is. Any ideas??? Thank you.



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allabout
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Pearson Vue CAT Quant PS-need help 01 Jan 2006, 05:30
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Before I'll explain it to you. Is II and III the solution?
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BG
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Pearson Vue CAT Quant PS-need help 01 Jan 2006, 06:07
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450=45x10=9x5x10=3^2x5^2x2xY=N^3 then Y should contain 3x5x2^2
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tennis25
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Pearson Vue CAT Quant PS-need help 01 Jan 2006, 06:56
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Thanks BG, I only is the solution but I dont understand how you get to

Y should contain 3x5x2^2 from 3^2x5^2x2xY=N^3

Could you please explain if you have time. Many thanks.
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Pearson Vue CAT Quant PS-need help 01 Jan 2006, 08:35
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since 450y=n^3 and y and n are positive integers, 450y should contain third powers of all factors for n^3 to be an integer. You factor out 450, and see that it is 3^2x5^2x2 so you need Y to contain 2^2x3x5 as factors
hope it helps
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Pearson Vue CAT Quant PS-need help 25 Jan 2006, 07:05
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Hi , I hope to address the problem in the following manner ::-

given :: 450y=n^3

=> n=third_root_of(450y)
=> n=third_root_of(5x3x3x5x2xy)

and also its given that n and y are integers ; so to get n as integer
we have to have , y, such that we can get the third root.

therefore, y should be 5x3x2x2

Once we have the value of y , simply substitute in given options to find out , which one leaves a integer value. And hence the option is (1)

Rgds,
Ak-
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Pearson Vue CAT Quant PS-need help 25 Jan 2006, 17:50
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450 y = n^3 means 5^2 * 3^2 * 2 * y = n^3

So y must be multiple of 5* 3* 2^2

so y = A * 5* 3* 2^2 where A is a +ve integer.

Now put this value of y in I, II and III. Only I comes out be integer.



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