badger - To repeatedly and annoyingly ask someone to do something.
Every time that Arnold asked Samantha to go out on a date, she would tell him firmly ‘No’. But each time he saw her, he would badger her again and again about wanting to go out, and again she said 'No!'
astute - Ability to understand things quickly and clearly, and to use the knowledge well
From a very early age, Gail instinctively knew everything about business, and and after college she proved to be an astute business woman, and became a millionaire before the age of 30.