If 7845K854 is divisible by 11, then what is the value of K?

Divisibility Rule for 11
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is either 0 or a multiple of 11.

Step-by-Step Calculation
Identify the positions (from right to left):

Number: 7 8 4 5 K 8 5 4

Positions:

Odd positions (1st, 3rd, 5th, 7th): 4, 8, 5, 8

Even positions (2nd, 4th, 6th, 8th): 5, K, 4, 7

Calculate the sums:

Sum of digits in odd positions = 4 + 8 + 5 + 8 = 25

Sum of digits in even positions = 5 + K + 4 + 7 = 16 + K

Find the difference:

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

Difference = 25 - (16 + K)

Difference = 25 - 16 - K

Difference = 9 - K

Solve for K:
For the number to be divisible by 11, the difference must be 0 or a multiple of 11.

If 9 - K = 0, then K = 9.