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

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To check divisibility by 11, the difference between the sum of digits in odd positions and the sum of digits in even positions must be a multiple of 11 (including 0).

Number: 7 8 4 5 K 8 5 4
Positions: 1 2 3 4 5 6 7 8

Sum of digits at odd positions (1, 3, 5, 7): 7 + 4 + K + 5 = 16 + K
Sum of digits at even positions (2, 4, 6, 8): 8 + 5 + 8 + 4 = 25

Difference = (16 + K) - 25 = K - 9

For divisibility by 11, K - 9 must be divisible by 11.

Possible values for K - 9: 0, ±11, ±22, ...

Since K is a single digit (0-9), the only feasible value is K - 9 = 0 → K = 9.

Therefore, the value of K is 9.

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