## Integers & Fractions

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### Integers & Fractions

by relaxin99 » Thu Feb 26, 2009 5:14 pm
If n and y are positive integers and 450y = n^3, which of the following must be an integer?

I. y/3 * 2^2 * 5

II. y/ 3^2 * 2 * 5

III. y/3* 2 * 5^2

None
I ONLY
II ONLY
III ONLY
I, II, and III

can someone also please explain their reasoning

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### Re: Integers & Fractions

by x2suresh » Thu Feb 26, 2009 8:17 pm
relaxin99 wrote:If n and y are positive integers and 450y = n^3, which of the following must be an integer?

I. y/3 * 2^2 * 5

II. y/ 3^2 * 2 * 5

III. y/3* 2 * 5^2

None
I ONLY
II ONLY
III ONLY
I, II, and III

can someone also please explain their reasoning
450y = n^3
y*5^2*3^2*2 = n^3

clearly Y= k* 5*3*2^2 --> (to make LHS cube of (number) )
here k is cube of the integer

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by krisraam » Thu Feb 26, 2009 8:27 pm
450y = n^3

==> 5^2 * 3^2 *2 * y = n^3

We know that y and n are integers.

y has to be in a form that makes n an integer

5^2 *3^2 *2 *y = (5*3*2) ^3n where n starts with 1.

Only I satisfies this.

Thanks
raama

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by mjjking » Fri Feb 27, 2009 12:56 am