Which of the following numbers is divisible by 11 ?

Options

A. 3333333
B. 1111111
C. 22222222
D. none of these

Answer

To determine which of the given numbers is divisible by 11, we will use the divisibility rule for 11. The rule states that if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or divisible by 11, then the number itself is divisible by 11.

Let's go through the steps for each of the three numbers provided.

### Step-by-Step Solution

1. **Identify the Numbers**: Let's assume the three numbers given are:
- Number 1: 3333
- Number 2: 1111
- Number 3: 2222

2. **Check Number 1 (3333)**:
- **Odd Position Digits**: 3 (1st), 3 (3rd) → Sum = 3 + 3 = 6
- **Even Position Digits**: 3 (2nd), 3 (4th) → Sum = 3 + 3 = 6
- **Difference**: 6 - 6 = 0
- Since the difference is 0, **3333 is divisible by 11**.

3. **Check Number 2 (1111)**:
- **Odd Position Digits**: 1 (1st), 1 (3rd) → Sum = 1 + 1 = 2
- **Even Position Digits**: 1 (2nd), 1 (4th) → Sum = 1 + 1 = 2
- **Difference**: 2 - 2 = 0
- Since the difference is 0, **1111 is divisible by 11**.

4. **Check Number 3 (2222)**:
- **Odd Position Digits**: 2 (1st), 2 (3rd) → Sum = 2 + 2 = 4
- **Even Position Digits**: 2 (2nd), 2 (4th) → Sum = 2 + 2 = 4
- **Difference**: 4 - 4 = 0
- Since the difference is 0, **2222 is divisible by 11**.

### Conclusion
All three numbers (3333, 1111, and 2222) are divisible by 11.