Answer is u(x,0)>u(y,0)>u(x',0), solve this you will get the inequality.
And alpha =1 it is risk neutrality , the preferences will be anywhere along the budget line
When alpha < 1 it is risk averse with convex preferences, optimal bundle will be only at one particular point on budget line.
I was able to solve the question whereas economic intuition I was not able to explain during interview. I expect most of the economic students will be able to get this intuition, as of I saw at least half of them were able to solve this question