Question:
If $\overline{98215 x 2}$ is a number with $x$ as its tens digit such that is is divisible by 4 . Find all possible values of $x$.
Solution:
A natural number is divisible by 4 if the number formed by its digits in units and tens places is divisible by $4 .$
$\therefore \overline{98215 x 2}$ will be divisible by 4 if $\overline{x 2}$ is divisible by 4 .
$\therefore \overline{x 2}=10 x+2$
$x$ is a digit; therefore possible values of $x$ are $0,1,2,3 \ldots 9$.
$\overline{x 2}=2,12,22,32,42,52,62,72,82,92$
The numbers that are divisible by 4 are $12,32,52,72,92$.
Therefore, the values of $x$ are $1,3,5,7,9$.
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