if n is a integer and n²

50 = 2*5^2

n^2 is divisible by 50 implies that it is divisible by 2^2*5^2 (100)

Therefore n is divisible by 10. D.

Ergh. Thats a horrible explanation.

given n²/50=an inetger
=> n²/2*5²=an integer

n² must have 2² and 5² (squares have even powers and given that n is an integer)
=> n must have 2 and 5 ie n must be atleast 10
if n is atleast 10, the greatest divisor can be 10. (the number itself is its greatest divisor)

hence, D

It's like the following:

if n^3 is divisible by 240, then what can be the minimum highest factor of n?

You see that 240 = 2^4x3x5

Hence, n must contain at least all these numbers in equal manner:

n n n
2 2 2
3 - -
2 - -
5 - -

From this we can imply that n includes at least a 3, a 5 and 2 2s, hence 60 is a factor of n.

OA: D