If $\overline{98125x2}$ is a number with $x$ as its tens digits such that it is divisible by 4. Find all the possible values of $x$.

Given:

$\overline{98125x2}$ is a number with $x$ as its tens digits such that it is divisible by 4.

To do:

We have to find all the possible values of $x$.

Solution:

The number $\overline{98125x2}$ is divisible by 4.

This implies,

The number formed by tens digit and units digit will also be divisible by 4.

Therefore,

$\overline{x2}$ is divisible by 4.

If $x=1$, then $x2=12$ is divisible by 4. 

If $x=3$, then $x2=32$ is divisible by 4. 

If $x=5$, then $x2=52$ is divisible by 4. 

If $x=7$, then $x2=72$ is divisible by 4. 

If $x=9$, then $x2=92$ is divisible by 4. 

The possible values of $x$ are $1, 3, 5, 7$ and $9$.