For what value of digit x is :

3x26 a multiple of 6 ?

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

3x26 should be a multiple of 2 and 3 both.

3x26 is divisible by 2 as it has even number 6 at its unit place.

To make 3x26 divisible by 3 ⇒ 3 + x + 2 + 6 should be a multiple of 3.

⇒ 11 + x should be a multiple of 3.

⇒ 11 + x = 0 , 3, 6, 9, 12, 15, 18……

⇒ x = -11, -8, -5, -2, 1, 4, 7, ……………

Since x is a digit. So, x = 1, 4, or 7.