Question: If the number 7x86038 is exactly divisible by 11, then the smallest…

Divisibility rule for 11: the difference between the sum of digits in alternate positions must be a multiple of 11 (including 0).

• Label the digits of the number 7x86038 from left to right: 7, x, 8, 6, 0, 3, 8.

• Sum of digits in odd positions = 7 + 8 + 0 + 8 = 23. Sum of digits in even positions = x + 6 + 3 = x + 9.

• Their difference is 23 - (x + 9) = 14 - x. For the number to be divisible by 11, 14 - x must be a multiple of 11.

• Solve 14 - x = 0, ±11, ... Within the digit range 0–9, the only valid solution is 14 - x = 11, which gives x = 3.

• Therefore the smallest whole number that can replace x to make 7x86038 divisible by 11 is 3.