Friends Alice, Betty, and Cathy are playing a game. Betty and Cathy are each given a square number, such that Betty knows Cathy's number and Cathy knows Betty's, but neither of them know their own. Alice then says: "The sum of the numbers is less than 100."
Betty says: "If Cathy knew the number of possibilities for my number, she would know her own."
Cathy then says: "Now I know my number."What is Cathy's number?<spanclass=′latex−bold′>(A)</span>16<spanclass=′latex−bold′>(B)</span>25<spanclass=′latex−bold′>(C)</span>36<spanclass=′latex−bold′>(D)</span>49<spanclass=′latex−bold′>(E)</span>64