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which is an integer

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by shibal » Thu Jul 02, 2009 4:06 pm
n and y are positive integers and 450y = n^3, which is an integer?
y / 3 * 2^2 * 5
y / 3^2 * 2 * 5
y / 3 * 2 * 5^2


oa [spoiler]y / 3 * 2^2 * 5[/spoiler]
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by mehravikas » Thu Jul 02, 2009 4:49 pm
break 450 into prime factors - 5^2 * 3^2 * 2

therefore y = n^3 / 5^2 * 3^2 * 2

At a minimum n^3 has to be 5^3 * 3^3 * 2^3 so that y can be an integer

Now plug n^3 / 5^2 * 3^2 * 2 into the answer choices

n^3 / 5^2 * 3^2 * 2 * (3 * 2^2 * 5) => n^3 / 5^3 * 3^3 * 2^3

5^3 * 3^3 * 2^3 / 5^3 * 3^3 * 2^3 = 1 (which is an integer)
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Re: which is an integer

by tohellandback » Fri Jul 03, 2009 12:29 am
shibal wrote:n and y are positive integers and 450y = n^3, which is an integer?
y / 3 * 2^2 * 5
y / 3^2 * 2 * 5
y / 3 * 2 * 5^2


oa [spoiler]y / 3 * 2^2 * 5[/spoiler]
450=5^2 * 3^2 * 2
450y is the cube of a number. so there must be one more 5, one more 3 and 2 more 2's. where are they? they must be in y
now its clear.
A must be an integers.
B- nopes,y has only one 3
C-nopes y has only one 5
The powers of two are bloody impolite!!
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Re: which is an integer

by real2008 » Sun Jul 05, 2009 10:56 am
shibal wrote:n and y are positive integers and 450y = n^3, which is an integer?
y / 3 * 2^2 * 5
y / 3^2 * 2 * 5
y / 3 * 2 * 5^2


oa [spoiler]y / 3 * 2^2 * 5[/spoiler]
hi!

does y/3*2^2*5 mean (y/3)*(2^2)*5
and y / 3^2 * 2 * 5 mean {y/(3^2)}*2*5
and y / 3 * 2 * 5^2 mean (y/3)*2*(5^2)

please clarify....
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