If *381 is divisible by 11,then the digit at the place of * is:

Options

A. 0
B. 1
C. 4
D. 7

Answer

To determine the digit represented by * in the number *381 such that the entire number is divisible by 11, we can follow these steps:

### Step 1: Understand the divisibility rule for 11
To check if a number is divisible by 11, we use the rule that states:
- Take the sum of the digits in the odd positions and the sum of the digits in the even positions.
- The difference between these two sums should be either 0 or a multiple of 11.

### Step 2: Identify the digits in the number *381
In the number *381:
- The digits are: * (unknown), 3 (2nd position), 8 (3rd position), and 1 (4th position).

### Step 3: Assign positions to the digits
- Odd positions: * (1st position) and 8 (3rd position)
- Even positions: 3 (2nd position) and 1 (4th position)

### Step 4: Calculate the sums of the odd and even positioned digits
- Sum of the odd positioned digits: * + 8
- Sum of the even positioned digits: 3 + 1 = 4

### Step 5: Set up the equation based on the divisibility rule
According to the divisibility rule:
\[ (* + 8) - 4 = 0 \quad \text{or} \quad (* + 8) - 4 = 11 \]

### Step 6: Solve the first equation
1. **For the first case:**
\[ * + 8 - 4 = 0 \implies * + 4 = 0 \implies * = -4 \]
This is not possible since a digit cannot be negative.

### Step 7: Solve the second equation
2. **For the second case:**
\[ * + 8 - 4 = 11 \implies * + 4 = 11 \implies * = 11 - 4 \implies * = 7 \]

### Step 8: Conclusion
The digit at the place of * is 7. Therefore, the complete number is 7381, which is divisible by 11.

### Final Answer
The digit at the place of * is **7**.

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