To determine if a number is divisible by 99 it needs to be divisible by 9 and 11.

Correct Option: D

To determine if a number is divisible by 99 it needs to be divisible by 9 and 11.

Divisible by 9 test. If sum of digits is divisible by 9 then the number is divisible by 9.
Divisible by 11 test. If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.

Clearly 114345 is divisible by 9 as well as 11. so,it is divisible by 99.

By hit and trial we find that 632 is divisible by 8. So, * must replaced by 3.

Correct Option: C

By hit and trial we find that 632 is divisible by 8. So, * must replaced by 3.

6 + 1 + 3 + 5 + x + 2 = 17 + x must be divisible by 9.
So, x =1.

Correct Option: B

6 + 1 + 3 + 5 + x + 2 = 17 + x must be divisible by 9.
So, x =1.

If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.

Correct Option: C

If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.

Sum of odd positioned digits - sum of even positioned digits = (9 + 2 + 5 + 6) - (7 + 1 + x) =14 - x

It must be divisible by 11. So x = 3.

On dividing 1056 by 23, we get 21 as remainder
∴ Required number to be added = (23 - 21 ) = 2.

Correct Option: D

On dividing 1056 by 23, we get 21 as remainder
∴ Required number to be added = (23 - 21 ) = 2.