Even if PG gave you such a task, how would that demonstrate anything relevant? You getting a task and a deadline is the opposite of being entrepreneurial; that's called having a job and a boss and showing that you are an adequate or better employee.

Being entrepreneurial involves you

1) generating ideas,

2) using your intuition to pick a good one,

3) testing it out to see if your intuition is correct (iterate if not), and

4) then execute that idea (and again, iterate as needed)

Or, in short: discovering and exploiting an opportunity

Edit: minor.