Question : If the 7-digit number $x$468$y$05 is divisible by 11, then what is the value of ($x$ + $y$)?
Option 1: 12
Option 2: 14
Option 3: 8
Option 4: 10
Correct Answer: 12
Solution :
Given:
If the 7-digit number $x468y05$ is divisible by 11.
Then, Sum of the digits at odd places – Sum of the digits at even places = 0 or, 11
Now, Sum of the digits at odd places – Sum of the digits at even places = 11
$\Rightarrow (x\ +\ 6\ +\ y\ +\ 5)\ -\ (0\ +\ 4\ +\ 8)\ =\ 11$
$\Rightarrow x\ +\ y\ +\ 11\ - 12\ =\ 11$
$\therefore x\ +\ y\ =\ 12$
So, the maximum value of $x\ +\ y$ is 12.
Hence, the correct answer is 12.
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