What least digit must be assigned to k so that the 7-digit number 86325k6 is divisible by 11?

Given:

The 7-digit number is 86325k6.

Formula Used:

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 a multiple of 11, including 0.

Calculation:

Odd positions: 8, 3, 5, 6

Even positions: 6, 2, k

Sum of digits in odd positions = 8 + 3 + 5 + 6 = 22

Sum of digits in even positions = 6 + 2 + k = 8 + k

For 86325k6 to be divisible by 11:

Difference = (Sum of digits in odd positions) - (Sum of digits in even positions)

⇒ 22 - (8 + k)

⇒ 14 - k

This difference should be a multiple of 11 or 0.

To find the least digit for k: 14 - k = 0 ⇒ k = 14

Since k must be a single digit, we need to check the values for k from 0 to 9:

For k = 3:

Difference = 14 - 3

⇒ Difference = 11

11 is a multiple of 11.

Thus, the least value of k which makes 86325k6 divisible by 11 is 3.

The correct answer is option 2.