If the number 738*69 is divisible by 11, then the missing digit (*) is

Options

A. 5
B. 9
C. 2
D. 1

Answer

To determine the missing digit (*) in the number 738*69 such that it is divisible by 11, we can use the divisibility rule for 11. According to this rule, 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-by-Step Solution:

1. **Identify the positions of the digits**:
- The number is 738*69.
- The positions of the digits are as follows:
- Odd positions: 7 (1st), 8 (3rd), 6 (5th)
- Even positions: 3 (2nd), * (4th), 9 (6th)

2. **Calculate the sum of the odd positioned digits**:
- Sum of odd positions = 7 + 8 + 6 = 21

3. **Calculate the sum of the even positioned digits**:
- Sum of even positions = 3 + * + 9 = 12 + *

4. **Set up the equation for divisibility by 11**:
- According to the rule, we need the difference to be a multiple of 11:
\[ |(Sum \, of \, odd \, positions) - (Sum \, of \, even \, positions)| = |21 - (12 + *)| = |21 - 12 - *| = |9 - *| \]
- This means we need \( |9 - *| \) to be 0 or a multiple of 11.

5. **Consider the possible values for * (0 to 9)**:
- If \( 9 - * = 0 \) then \( * = 9 \)
- If \( 9 - * = 11 \) then \( * = -2 \) (not possible)
- If \( 9 - * = -11 \) then \( * = 20 \) (not possible)

6. **Conclusion**:
- The only valid solution is \( * = 9 \).

Thus, the missing digit (*) is **9**.