If n and y are positive integers and 450Y = n^3, which of the following must be an integer?

I. y/(3 x 2^2 x 5)

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

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

a. None
b. I only
c. II only
d. III only
e. I, II, and III




obtain all prime factors of 450 = 5x5x3x3x2
Therefore 5x5x3x3x2 x y = n^3
in order to make the right hand side a cube, we are missing one 5, one 3, and two 2s in order to make it a perfect cube

thus y/ (3)(5) (2 ^ 2) should be an integer

Answer choice B is the only choice