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Question
If \[\overline{{98215x2}}\] 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 .
\[ \therefore \overline{98215x2}\text{ will be divisible by 4 if } \overline{ x2 } \text{ is divisible by }4 . \]
\[ \therefore \overline{x2} = 10x + 2\]
\[x\text{ is a digit; therefore possible values of }x\text{ are }0, 1, 2, 3 . . . 9 . \]
\[ \overline{x2} = 2, 12, 22, 32, 42, 52, 62, 72, 82, 92\]
\[\text{ The numbers that are divisible by }4\text{ are }12, 32, 52, 72, 92 . \]
\[\text{ Therefore, the values of }x \text{ are }1, 3, 5, 7, 9 .\]
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