Explanation: To determine if a number is divisible by 3 or 9, we use the divisibility rules for these numbers. The rule for divisibility by 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. Similarly, a number is divisible by 9 if the sum of its digits is divisible by 9.
Let's apply these rules to each of the given options:
1. **Option A: 810**
- Sum of digits: \(8 + 1 + 0 = 9\)
- Since 9 is divisible by both 3 and 9, 810 is divisible by both 3 and 9. Therefore, 810 does not meet the criteria of being divisible by 3 but not by 9.
2. **Option B: 270**
- Sum of digits: \(2 + 7 + 0 = 9\)
- Since 9 is divisible by both 3 and 9, 270 is divisible by both 3 and 9. Therefore, 270 does not meet the criteria of being divisible by 3 but not by 9.
3. **Option C: 330**
- Sum of digits: \(3 + 3 + 0 = 6\)
- Since 6 is divisible by 3 but not by 9, 330 is divisible by 3 but not by 9. Therefore, 330 meets the criteria of being divisible by 3 but not by 9.
4. **Option D: 450**
- Sum of digits: \(4 + 5 + 0 = 9\)
- Since 9 is divisible by both 3 and 9, 450 is divisible by both 3 and 9. Therefore, 450 does not meet the criteria of being divisible by 3 but not by 9.
In conclusion, the correct answer is 330 because it is divisible by 3 (since the sum of its digits is 6, which is divisible by 3) but not by 9 (since 6 is not divisible by 9). This example demonstrates the importance of understanding and applying the divisibility rules correctly to solve such problems.