What is the value of x so that the seven digit number 91876x2 is divisible by 72?

As per the question,

Number 91876x2 is divisible by 72,

It means that it is individually divisible by 9 and 8 because $$72=8\times 9$$

Divisible by 8-

Any number is divisible by 8, if the last 3 digit of that particular number is divisible by 8.

So here, 6x2 will be divisible by 8 if, x=3 and 7.

Divisible by 9-

Any number is divisible by 9, if the sum of the digit of the number is divisible by 9.

So, here $$\Rightarrow 9+1+8+6+x+2=33+x$$

By taking x=3, the number will be divisible by 9.

Hence, x=3 will be the correct answer.