Which one of the following numbers is divisible by 11?

Options

A. 45678940
B. 54857266
C. 87524398
D. 93455120

Answer

To determine which number is divisible by 11, we will apply the divisibility rule for 11. According to this rule, we need to find the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. If this difference is divisible by 11, then the number itself is divisible by 11.

Let's go through the options step by step.

### Step 1: Check the first option: 45678940
- **Odd positions:** 4 (1st), 6 (3rd), 8 (5th), 4 (7th)
- Sum = 4 + 6 + 8 + 4 = 22
- **Even positions:** 5 (2nd), 7 (4th), 9 (6th), 0 (8th)
- Sum = 5 + 7 + 9 + 0 = 21
- **Difference:** 22 - 21 = 1
- **Divisibility Check:** 1 is not divisible by 11.

### Step 2: Check the second option: 58764256
- **Odd positions:** 5 (1st), 7 (3rd), 6 (5th), 6 (7th)
- Sum = 5 + 7 + 6 + 6 = 24
- **Even positions:** 8 (2nd), 4 (4th), 2 (6th), 5 (8th)
- Sum = 8 + 4 + 2 + 5 = 19
- **Difference:** 24 - 19 = 5
- **Divisibility Check:** 5 is not divisible by 11.

### Step 3: Check the third option: 87524398
- **Odd positions:** 8 (1st), 5 (3rd), 4 (5th), 9 (7th)
- Sum = 8 + 5 + 4 + 9 = 26
- **Even positions:** 7 (2nd), 2 (4th), 3 (6th), 8 (8th)
- Sum = 7 + 2 + 3 + 8 = 20
- **Difference:** 26 - 20 = 6
- **Divisibility Check:** 6 is not divisible by 11.

### Step 4: Check the fourth option: 93455120
- **Odd positions:** 9 (1st), 4 (3rd), 5 (5th), 2 (7th)
- Sum = 9 + 4 + 5 + 2 = 20
- **Even positions:** 3 (2nd), 5 (4th), 1 (6th), 0 (8th)
- Sum = 3 + 5 + 1 + 0 = 9
- **Difference:** 20 - 9 = 11
- **Divisibility Check:** 11 is divisible by 11.

### Conclusion:
The only number that is divisible by 11 is **93455120** (Option 4).