How many of the following numbers are divisible by 3 but not by 10 ?
2133,2343,3474,4131,5286,5340,6330,7347,8110, 9276

Options

A. 5
B. 6
C. 7
D. 0

Answer

To determine how many of the given numbers are divisible by 3 but not by 10, we will follow these steps:

### Step 1: Check divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3. We will calculate the sum of the digits for each number and check if it is divisible by 3.

1. **2133**:
- Sum of digits = 2 + 1 + 3 + 3 = 9 (divisible by 3)

2. **2343**:
- Sum of digits = 2 + 3 + 4 + 3 = 12 (divisible by 3)

3. **3474**:
- Sum of digits = 3 + 4 + 7 + 4 = 18 (divisible by 3)

4. **4131**:
- Sum of digits = 4 + 1 + 3 + 1 = 9 (divisible by 3)

5. **5286**:
- Sum of digits = 5 + 2 + 8 + 6 = 21 (divisible by 3)

6. **5340**:
- Sum of digits = 5 + 3 + 4 + 0 = 12 (divisible by 3)

7. **6330**:
- Sum of digits = 6 + 3 + 3 + 0 = 12 (divisible by 3)

8. **7347**:
- Sum of digits = 7 + 3 + 4 + 7 = 21 (divisible by 3)

9. **8110**:
- Sum of digits = 8 + 1 + 1 + 0 = 10 (not divisible by 3)

10. **9276**:
- Sum of digits = 9 + 2 + 7 + 6 = 24 (divisible by 3)

### Step 2: Check divisibility by 10
A number is divisible by 10 if its last digit is 0. We will check the last digit of each number that is divisible by 3.

- **2133**: Last digit is 3 (not divisible by 10)
- **2343**: Last digit is 3 (not divisible by 10)
- **3474**: Last digit is 4 (not divisible by 10)
- **4131**: Last digit is 1 (not divisible by 10)
- **5286**: Last digit is 6 (not divisible by 10)
- **5340**: Last digit is 0 (divisible by 10)
- **6330**: Last digit is 0 (divisible by 10)
- **7347**: Last digit is 7 (not divisible by 10)
- **8110**: Last digit is 0 (divisible by 10)
- **9276**: Last digit is 6 (not divisible by 10)

### Step 3: Count the numbers divisible by 3 but not by 10
From the above checks, the numbers that are divisible by 3 but not by 10 are:
- 2133
- 2343
- 3474
- 4131
- 5286
- 7347
- 9276

### Final Count
There are **7 numbers** that are divisible by 3 but not by 10.

### Summary
The total count of numbers divisible by 3 but not by 10 is **7**.

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