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GMAT Prep: 'n' & 'y' are positive integers
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kmittal82
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450 = 2 x 3 x 3 x 5 x 5
450y = 2 x 3 x 3 x 5 x 5 x y = n^3
We need to find what should y be so that 450y becomes a number which can be expressed as n^3
if y = 2 x 2 x 3 x 5 , then 450 y = 2^3 * 3^3 * 5*3 = 30^3
thus, if we divide y by 2 x 2 x 3 x 5, we should get an integer.
450y = 2 x 3 x 3 x 5 x 5 x y = n^3
We need to find what should y be so that 450y becomes a number which can be expressed as n^3
if y = 2 x 2 x 3 x 5 , then 450 y = 2^3 * 3^3 * 5*3 = 30^3
thus, if we divide y by 2 x 2 x 3 x 5, we should get an integer.
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kmittal82
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Ok, lets try another way
450y = n^3
y = n * n * n / ( 2 x 3 x 3 x 5 x 5 )
Lets consider option 2
y / (3 x 3 x 2 x 5) = n * n * n / ( 2 x 3 x 3 x 5 x 5 x 3 x 3 x 2 x 5)
= n * n * n / ( 2^2 * 3^4 * 5^3)
This can never be an integer, since the numberator is a perfect cube.
ditto for option 3.
450y = n^3
y = n * n * n / ( 2 x 3 x 3 x 5 x 5 )
Lets consider option 2
y / (3 x 3 x 2 x 5) = n * n * n / ( 2 x 3 x 3 x 5 x 5 x 3 x 3 x 2 x 5)
= n * n * n / ( 2^2 * 3^4 * 5^3)
This can never be an integer, since the numberator is a perfect cube.
ditto for option 3.
