Between 1 and 100 there are 25 multiples of 4. Those that are perfect squares are multipliers of 4 which are also perfect squares, since 4 is a perfect square itself. The perfect squares up to 5^2 are 1, 4, 9, 16, 25. So if Mary chooses 4, 16, 36, 64 or 100, that is 5 out of 25 possibilities=1/5.