Which of the following numbers is divisible by 11?

Options

A. 1011011
B. 1111111
C. 22222222
D. 3333333

Answer

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

Let's break down the solution step by step:

### Step 1: Identify the Numbers
Let's assume the four numbers given are:
1. 1011011
2. 22222222
3. 1111111
4. 1234567

### Step 2: Apply the Divisibility Rule for Each Number
We will check each number one by one.

#### Checking Number 1: 1011011
- **Odd positions (from the right):** 1, 1, 0, 1 (1st, 3rd, 5th, 7th)
- Sum of odd positions = 1 + 1 + 0 + 1 = 3
- **Even positions (from the right):** 1, 0, 1 (2nd, 4th, 6th)
- Sum of even positions = 1 + 0 + 1 = 2
- **Difference:** 3 - 2 = 1 (not divisible by 11)

#### Checking Number 2: 22222222
- **Odd positions (from the right):** 2, 2, 2, 2 (1st, 3rd, 5th, 7th)
- Sum of odd positions = 2 + 2 + 2 + 2 = 8
- **Even positions (from the right):** 2, 2, 2, 2 (2nd, 4th, 6th, 8th)
- Sum of even positions = 2 + 2 + 2 + 2 = 8
- **Difference:** 8 - 8 = 0 (divisible by 11)

#### Checking Number 3: 1111111
- **Odd positions (from the right):** 1, 1, 1, 1 (1st, 3rd, 5th, 7th)
- Sum of odd positions = 1 + 1 + 1 + 1 = 4
- **Even positions (from the right):** 1, 1, 1 (2nd, 4th, 6th)
- Sum of even positions = 1 + 1 + 1 = 3
- **Difference:** 4 - 3 = 1 (not divisible by 11)

#### Checking Number 4: 1234567
- **Odd positions (from the right):** 7, 5, 3, 1 (1st, 3rd, 5th, 7th)
- Sum of odd positions = 7 + 5 + 3 + 1 = 16
- **Even positions (from the right):** 6, 4, 2 (2nd, 4th, 6th)
- Sum of even positions = 6 + 4 + 2 = 12
- **Difference:** 16 - 12 = 4 (not divisible by 11)

### Conclusion
From our calculations, only **22222222** is divisible by 11.

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