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
Integers & Fractions
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450y = n^3relaxin99 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
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
I only is the answer.

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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
==> 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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Can somebody elaborate more please?
thanks!
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