If ` 31 z ` is a multiple of 11, where z is a digit, what is the value of `z` ?

Explanation

Here, the number is `31z`
Sum of the digits at even places `= 1`
Sum of the digits at odd places `=3+z`
`1 − (3+z) = 11m`
`=>−2−z=11m`
`z` can take values `0` to `9`
Possible values of `−2 − z` are `0, 11, 22, 33` etc.
Least value possible for `−2 − z` is`0`
`−2−z=0`
Therefore,`z=−2`
But `z` cannot be negative.
So, there is no possible positive value of `z` that will make `31z`, a multiple of `11`.