3. How many natural numbers less than 2016 are divisible by 2 or 3, but not by 5?
First method:

We consider the set of natural numbers less than 2016, i.e., the set $\{1,2,3,4, \ldots, 2015\}$.

Among the natural numbers less than 2016, there are 1007 numbers divisible by 2, 671 numbers divisible by 3, and 335 numbers divisible by 6, which means they are divisible by both 2 and 3.

Thus, among the natural numbers less than 2016, there are $1007+671-335=1343$ numbers divisible by 2 or 3 (we subtract 335 because we counted the numbers divisible by both 2 and 3 twice). The numbers divisible by both 2 and 5 are 201, the numbers divisible by both 3 and 5 are 134, and the numbers divisible by 6 (i.e., by both 2 and 3) and 5 are 67.

It follows that the numbers divisible by 2 or 3, and also by 5, are $201+134-67=268$ (we counted the numbers divisible by both 2 and 3 twice, so we subtract 67).

Finally, the numbers less than 2016 that are divisible by 2 or 3, but not by 5, are $1343-268=1075$.