For what value of digit x is :

24x divisible by 6 ?

According to the divisibility of 6, if the number is divisible by 2 and 3 both then the number is divisible by 6.

24x is a multiple of 2 and 3 both.

To make 24x divisible by 2 ⇒ x should be 0 or an even number.

So, x = 0, 2, 4, 6 or 8 ………….(1)

To make 24x divisible by 3 ⇒ 2 + 4 + x is a multiple of 3.

⇒ 6 + x is a multiple of 3.

⇒ 6 + x = 0 , 3, 6, 9, 12, 15, 18, ……………

⇒ x = -6, -3, 0, 3, 6, 9, 12, ……………

Since x is a digit. So, x = 0, 3, 6, 9 …………(2)

From (1) and (2), x = 0 or 6.