A five digit number 2A78B, is divisible by 55. What is the difference between the maximum and minimum possible value of (A+

Solution.

2A78B

2A78B is divisible by 55 Or 11×5.

So, divisibility rule of 11 and 5

a given number can only be completely divided by 11 if the difference of the sum of digits at odd position and sum of digits at even position in a number is 0 or 11 .

If the last number is either 0 or 5, the entire number is divisible by 5 . 

Maximum possible value of A and B=6 and 5

Maximum possible value of A+B=6+5=11

Minimum value of A and B=1 and 0

Minimum value of (A+B) =1+0=1

Difference between the maximum and minimum possible value of (A+B)=11-1=10.