Question
If 7845K854 is divisible by 11, then what is the value
of K?Solution
To check divisibility by 11, subtract the sum of digits in odd positions from the sum of digits in even positions. The result must be divisible by 11. Number: 7 8 4 5 K 8 5 4 Positions: 1 2 3 4 5 6 7 8 Sum of odd positions (1,3,5,7): (7 + 4 + K + 5 = 16 + K) Sum of even positions (2,4,6,8): (8 + 5 + 8 + 4 = 25) Divisibility condition: [(16 + K) - 25 = {Multiple of 11}] K - 9 = 0 {Smallest multiple}) K = 9
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