If n and y are positive integers and 450y = n^3, which of the following must be an interger
I. y/ (3 * 2^2 * 5)
II. y/ (3^2 * 2 * 5)
III. y/ 3 * 2 * 5^2
Choose the correct choice from the following options
A) None.  B) I only.  C) II only.  D) III only.  E) I, II, and III
450 y = n^3 -&gt; y = n3/450 -&gt; n3 is divisible by 450 &amp; n is +ve integer. look for values of n^3 such that n is integer and n is divisible by 450. Clearly we have to look in the order of 1000's to find a value such that n3 is divisible by 450 and n is integer.   n3=1000 n =10 not divisible by 450   n3=8000 n =20 not divisible by 450   n3=27000 n =30 divisible by 450 y = 2700/45= 
<gadget id="calculator">2700/45</gadget>
<output>60</output>
60   Look for I, II , III which have denominators 60,90,150.   only I does and hence I only.
<result>B</result>
If n and y are positive integers and 450y = n^3, which of the following must be an interger
I. y/ (3 * 2^2 * 5)
II. y/ (3^2 * 2 * 5)
III. y/ 3 * 2 * 5^2