What is the missing digit which makes the number 9724* exactly divisible by 6?

Answer : A

Explanation:

Divisibility by 6 requires that the number be divisible by 2 as well as 3 , i.e, the following 2 conditions must be met

i) Unit digit be Zero or even

ii) Sum of digits be divisible by 3

The given number is 9724*

Sum of the digits =9 +7 +2 +4 +* =22+*

The digit which on being added to 22 will give the sum divisible by 3 are

22+2 =24 and 22 +5=7.

2 and 7 satisfy the condition ii.

The blank space is at unit's place. So the missing digit must satisfy the condition (i) also

Out of 2 and 5, only 2 is even.