If the 7-digit number x468y05 is divisible by 11, then the maximum value of (x + y) is :

For a number to be divisible by 11, the difference between the sum of the digits at odd positions and the sum of the digits at even positions must be either 0 or a multiple of 11.
Digits at odd positions (from left): 1st, 3rd, 5th, 7th ⟹x,6,y,5

Sum of odd position digits=x+6+y+5=x+y+11
Digits at even positions (from left): 2nd, 4th, 6th ⟹4,8,0

Sum of even position digits=4+8+0=12
Difference:

Difference=(x+y+11)−12=x+y−1
For divisibility by 11:

x+y−1=0⟹x+y=1
OR

x+y−1=11⟹x+y=12
Since x and y are single digits (0≤x,y≤9), the maximum possible value of (x+y) is 12.