What least value must be given to * so that the number 97215 * 6 is divisible by 11 ?

Options

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

Answer

To determine the least value that must be given to * so that the number 97215*6 is divisible by 11, we will 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 97215*6.
- The digits in odd positions are: 9 (1st), 2 (3rd), 5 (5th), and 6 (7th).
- The digits in even positions are: 7 (2nd), 1 (4th), and * (6th).

2. **Sum the digits in odd positions**:
- Sum = 9 + 2 + 5 + 6 = 22.

3. **Sum the digits in even positions**:
- Sum = 7 + 1 + * = 8 + *.

4. **Calculate the difference**:
- Difference = (Sum of odd positions) - (Sum of even positions) = 22 - (8 + *) = 22 - 8 - * = 14 - *.

5. **Set the condition for divisibility by 11**:
- For the number to be divisible by 11, the difference (14 - *) must be either 0 or a multiple of 11.

6. **Check for the first condition (difference = 0)**:
- Set 14 - * = 0.
- This gives us * = 14, which is not a valid single digit (0-9).

7. **Check for the next condition (difference = 11)**:
- Set 14 - * = 11.
- This gives us * = 14 - 11 = 3, which is a valid single digit.

8. **Conclusion**:
- The least value that must be given to * so that 97215*6 is divisible by 11 is 3.

### Final Answer:
The least value for * is **3**.