Explanation:

- To find two-digit numbers divisible by 3, start from 12 and go up to 99. The sequence includes numbers like 12, 15, 18,..., 99.

- The count of such numbers is calculated using the formula for the arithmetic sequence: `(99 - 12) / 3 + 1 = 30`.

- For numbers divisible by 5, start from 10 and go up to 95. The sequence includes numbers like 10, 15, 20,..., 95.

- The count is: `(95 - 10) / 5 + 1 = 18`.

- Using the principle of inclusion-exclusion, subtract those counted twice, i.e., divisible by both 3 and 5 (15, 30,..., 90). Count is: `(90 - 15) / 15 + 1 = 6`.

- Total = 30 + 18 - 6 = 42