GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: If n and y are positive integers and 450y = n^3, which of the followin
[#permalink]
17 Apr 2022, 03:25
"Must be an integer" means the lowest possible value of y.
450y=n3 --> 2∗32∗52∗y=n3. As n and y are integers, y must complete the powers of 2, 3, and 5 to cubes (generally to the multiple of 3).
Thus ymin=22∗3∗5, in this case 2∗32∗52∗y=(2∗3∗5)3=n3.
Notice that for this value of y only the first option is an integer: y3∗22∗5=22∗3∗53∗22∗5=1.
Answer: B.