4. How many 2-digit positive integers have an even number of positive divisors?
Solution:
84
An integer has an odd number of divisors precisely if it is a square. So we take the 90 2-digit numbers $(10,11, \ldots, 99)$ and remove the 6 squares $\left(4^{2}, 5^{2}, \ldots, 9^{2}\right)$, for a total of 84.