If the number 4 8 3 0 7 * 8 is divisible by divisible by 11, then the missing digit (*) is

Options

A. 5
B. 3
C. 2
D. 1

Answer

To find the missing digit (*) in the number 48307*8 such that the number is divisible by 11, we will follow these steps:

### Step 1: Understand the divisibility rule for 11
A number is divisible by 11 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 a multiple of 11.

### Step 2: Identify the positions of the digits
For the number 48307*8, we can label the positions of the digits as follows:
- Position 1: 4 (odd)
- Position 2: 8 (even)
- Position 3: 3 (odd)
- Position 4: 0 (even)
- Position 5: 7 (odd)
- Position 6: * (even)
- Position 7: 8 (odd)

### Step 3: Calculate the sum of the digits at odd positions
The digits at the odd positions are 4, 3, 7, and 8. Therefore, we calculate:
\[ \text{Sum of odd positions} = 4 + 3 + 7 + 8 = 22 \]

### Step 4: Calculate the sum of the digits at even positions
The digits at the even positions are 8, 0, and *. Therefore, we calculate:
\[ \text{Sum of even positions} = 8 + 0 + * = 8 + * \]

### Step 5: Set up the equation for divisibility by 11
Now, we need to find the difference:
\[ \text{Difference} = \text{Sum of odd positions} - \text{Sum of even positions} \]
\[ \text{Difference} = 22 - (8 + *) = 22 - 8 - * = 14 - * \]

### Step 6: Solve for the missing digit
For the number to be divisible by 11, the difference must be either 0 or a multiple of 11. Thus, we set up the equation:
1. \( 14 - * = 0 \)
2. \( 14 - * = 11 \)

#### Case 1: \( 14 - * = 0 \)
\[ * = 14 \]
This is not possible since * must be a single digit (0-9).

#### Case 2: \( 14 - * = 11 \)
\[ 14 - * = 11 \]
\[ * = 14 - 11 \]
\[ * = 3 \]

### Conclusion
The missing digit * is 3. Therefore, the complete number is 4830738, which is divisible by 11.

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