If `x` denotes the digit at hundreds place of the number ` 67"x"19 ` such that the number is divisible by 11. Find all possible values of `x` .

Explanation

`67x19 `is divisible by `11`.
A number is divisible by `11`, if the difference between the sum of its digits at odd places and the sum of its digits at even places is either `0` or a multiple of `11`.
Sum of digits at odd places – sum of digits at even places` = 11`
`⇒ (6+x+9)−(7+1)=11`
`⇒ 15+x−8=11`
`⇒ x+7=11`
`⇒ x=11−7`
`∴ x=4`