How to determine the mass of a galaxy?
I think she should have clarified the question by putting velocity and radius in the same choice.

By looking at her answer, it seems reasonable to think that velocity is more important. However  without knowing the radius we cannot determine the mass of the stellar system. She argued this idea by saying that the size is approximately known for stellar systems. But I don't think that is a solid argument. 

Theoritically we should know both R and V to calculate M. 

Note: I did not understand why you wrote kinetic energy= gravitational force ? Thats not possible. 

In stellar bounded system you should use virial theorem. By stating that $-2&lt;E&gt;=&lt;U&gt;$  and from there you get 

$$M=v^2R/G$$