For what value of digit x is :

28x6 a multiple of 3 ?

According to the divisibility of 3, if the sum of the digits of the number is divisible by 3 then the number is divisible by 3.

28x6 = 2 + 8 + x + 6 = 16 + x. And (16 + x) is should be a multiple of 3.

Hence, 16 + x = 0 ,3, 6, 9, 12, 15, 18, 21, 24, 27, 30……

x = -16, -13, -10, -7, -4, -1, 2, 5, 8, 11…..

Since, x is a digit. ∴ x = 2, 5 or 8