To solve the problem of finding which of the following numbers is divisible by 8 but not by 12, we can follow these steps:
### Step 1: Understand the divisibility rules
- A number is **divisible by 8** if the last three digits of the number form a number that is divisible by 8.
- A number is **divisible by 12** if it is divisible by both 3 and 4.
### Step 2: Analyze the options given
Let's assume the options provided are:
1. 24, 48, 72
2. 8, 16, 24
3. 12, 24, 36
4. 96, 192, 288
### Step 3: Check each option for divisibility by 8 and 12
#### Option 1: 24, 48, 72
- **24**: Divisible by 8 (24 ÷ 8 = 3) and by 12 (24 ÷ 12 = 2).
- **48**: Divisible by 8 (48 ÷ 8 = 6) and by 12 (48 ÷ 12 = 4).
- **72**: Divisible by 8 (72 ÷ 8 = 9) and by 12 (72 ÷ 12 = 6).
- Conclusion: All numbers in this option are divisible by both 8 and 12.
#### Option 2: 8, 16, 24
- **8**: Divisible by 8 (8 ÷ 8 = 1) and not by 12 (8 ÷ 12 is not an integer).
- **16**: Divisible by 8 (16 ÷ 8 = 2) and not by 12 (16 ÷ 12 is not an integer).
- **24**: Divisible by 8 (24 ÷ 8 = 3) and by 12 (24 ÷ 12 = 2).
- Conclusion: 8 and 16 are divisible by 8 but not by 12.
#### Option 3: 12, 24, 36
- **12**: Divisible by 8 (12 ÷ 8 is not an integer) and by 12 (12 ÷ 12 = 1).
- **24**: Divisible by 8 (24 ÷ 8 = 3) and by 12 (24 ÷ 12 = 2).
- **36**: Divisible by 8 (36 ÷ 8 is not an integer) and by 12 (36 ÷ 12 = 3).
- Conclusion: None of the numbers in this option are divisible by 8.
#### Option 4: 96, 192, 288
- **96**: Divisible by 8 (96 ÷ 8 = 12) and by 12 (96 ÷ 12 = 8).
- **192**: Divisible by 8 (192 ÷ 8 = 24) and by 12 (192 ÷ 12 = 16).
- **288**: Divisible by 8 (288 ÷ 8 = 36) and by 12 (288 ÷ 12 = 24).
- Conclusion: All numbers in this option are divisible by both 8 and 12.
### Final Conclusion
The only option where the numbers are divisible by 8 but not by 12 is **Option 2: 8, 16, 24**.
