how many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

Let's analyze each number to determine if it is divisible by 3 but not by 9.

Step 1: Divisibility rules

• A number is divisible by 3 if the sum of its digits is divisible by 3.
• A number is divisible by 9 if the sum of its digits is divisible by 9.

Step 2: Check each number

1. 2133
   • Sum of digits = 2 + 1 + 3 + 3 = 9
   • 9 is divisible by 3 and 9
   • So, 2133 is divisible by 9 (and also by 3)
   • Exclude (since we want divisible by 3 but not by 9)
2. 2343
   • Sum of digits = 2 + 3 + 4 + 3 = 12
   • 12 is divisible by 3 but not by 9
   • Include
3. 3474
   • Sum of digits = 3 + 4 + 7 + 4 = 18
   • 18 is divisible by 9 (and 3)
   • Exclude
4. 4131
   • Sum of digits = 4 + 1 + 3 + 1 = 9
   • 9 is divisible by 9 (and 3)
   • Exclude
5. 28
   • Sum of digits = 2 + 8 = 10
   • 10 is not divisible by 3
   • Exclude

Step 3: Conclusion

Only 2343 is divisible by 3 but not by 9.

Final answer:

1 number satisfies the condition.