Problem 105

The largest two-digit number that is a multiple of 7 is $7\times14=98$.

Thus, there are 14 positive multiples of 7 that are less than 100.

However, this includes $7\times1=7$ which is not a two-digit number.

Therefore, there are $14-1=13$ positive two-digit numbers which are divisible by 7.
(Note that these 13 numbers are $14,21,28,35,42,49,56,63,70,77,84,91,$ and 98.)