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
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.