Problem Solving

If n and y are positive integers and 450y = n^3, which of the following is true.

I) y/3*2^2*5
II) y/3^2*2*5
III) y/3*2*5^2

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

Can someone please explian this problem. I will provide the OA soon.

Thanks in advance.

Hope this helps!

https://www.beatthegmat.com/gmat-ques-t7101.html#28081

I am not able to understand the answer options..can someone please put appropriate brackets so that the options can be interpreted.

The options -

I) y/3*2^2*5
II) y/3^2*2*5
III) y/3*2*5^2

are actually like -

I) y/(3*2^2*5)
II) y/(3^2*2*5)
III) y/(3*2*5^2)

Is it clear to you gmatguy16, now?

450y =n^3

so we need a value of y which will make the expr 450y a perfect cube

450 = 3^2 * 5^2 *2

i.e none of the peime factors have the power of 3

so y must provide this

i.e y should have a 3,5,& two 2's to have powers of 3 of all the prime factors in 450y

in general y should be of the form 3^n*5^n*2^n+1

where n should be a value such that n +2 is a multiple of 3

so we can say here that y will be divisible by 3*5*2^2

hence A I only