Explanation:

- We must find numbers divisible by 5 or 7, but not 35, under 1000.

- First, calculate numbers divisible by 5: \( \left\lfloor \frac{999}{5} \right\rfloor = 199 \).

- Calculate numbers divisible by 7: \( \left\lfloor \frac{999}{7} \right\rfloor = 142 \).

- Use the inclusion-exclusion principle for both: \( 199 + 142 - \left\lfloor \frac{999}{35} \right\rfloor \).

- Numbers divisible by 35: \( \left\lfloor \frac{999}{35} \right\rfloor = 28 \).

- Total divisible by 5 or 7: \( 199 + 142 - 28 = 313 \).

- Numbers divisible by 35 (to exclude): 28.

- Result: \( 313 - 28 = 285 \)

Option 1: 285