What is the least value of x for which the 7-digit number 6893x54 is divisible…

A number divisible by 22 must be divisible by 2 and 11. • Divisible by 2 → last digit is 4 (already OK). • For divisibility by 11: Sum of odd-position digits − sum of even-position digits must be a multiple of 11. Positions: 6 8 9 3 x 5 4 (Odd places) = 6 + 9 + x + 4 = 19 + x (Even places) = 8 + 3 + 5 = 16 Difference = (19 + x) − 16 = x + 3 For divisibility by 11 → x + 3 must be 0, 11, 22... Smallest x ≥ 0 giving this = 8 (because 8 + 3 = 11)