-  (6 + 5 + 3 + 8) - (x + 2 + 6) = (14 - x). Now, (14 - x) is divisible by 11, when x = 3

To solve this question, we will use the divisibility rule for 11. According to this rule, if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11, then the number is divisible by 11.

For the given number 86325*6, the sum of digits at odd places is 8 + 6 + 3 + 2 + 5 = 24 and the sum of digits at even places is 0* + 3 + 5 = 8.

Therefore, the difference between the two sums is 24 – 8 = 16.

Since 16 is not divisible by 11, the number 86325*6 is not divisible by 11.

Now, to make the number divisible by 11, we need to find the least value of * so that the difference between the two sums is divisible by 11.

Let us assume that * = x.

Therefore, the number becomes 86325x6.

The sum of digits at odd places is 8 + 6 + 3 + 2 + 5 + x = 25 + x and the sum of digits at even places is 0x + 3 + 5 = 8.

Therefore, the difference between the two sums is 25 + x – 8 = 17 + x.

This difference should be divisible by 11, i.e., 17 + x = 11n, where n is an integer.

We get, x = 11n – 17.

Since x should be a positive integer, the least value of x is 3.

Therefore, the least value of * for which the number 86325*6 is divisible by 11 is 3.

Hence, option C is the correct answer.

Detailed Explanation:
• Divisibility rule for 11: If the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11, then the number is divisible by 11.
• For the number 86325*6, the sum of digits at odd places is 8 + 6 + 3 + 2 + 5 = 24 and the sum of digits at even places is 0* + 3 + 5 = 8.
• Therefore, the difference between the two sums is 24 – 8 = 16.
• Since 16 is not divisible by 11, the number 86325*6 is not divisible by 11.
• To make the number divisible by 11, we need to find the least value of * so that the difference between the two sums is divisible by 11.
• Let us assume that * = x.
• Therefore, the number becomes 86325x6.
• The sum of digits at odd places is 8 + 6 + 3 + 2 + 5 + x = 25 + x and the sum of digits at even places is 0x + 3 + 5 = 8.
• Therefore, the difference between the two sums is 25 + x – 8 = 17 + x.
• This difference should be divisible by 11, i.e., 17 + x = 11n, where n is an integer.
• We get, x = 11n – 17.
• Since x should be a positive integer, the least value of x is 3.
• Therefore, the least value of * for which the number 86325*6 is divisible by 11 is 3.
• Hence, option C is the correct answer.

If you think the solution is wrong then please provide your own solution below in the comments section .