If $x$ is a digit of the number $\overline{66784x}$ such that it is divisible by 9, find the possible values of $x$.
Given:
$x$ is a digit such that the number $\overline{66784x}$ is divisible by 9.
To do:
We have to find the possible values of $x$.
Solution:
The number $\overline{66784x}$ is divisible by 9.
This implies,
The sum of its digits will also be divisible by 9.
Therefore,
$6 + 6 + 7 + 8+ 4 + x$ is divisible by 9.
$31 + x$ is divisible by 9
If $x=5$, $31+5=36$ is divisible by 9.
The possible value of $x$ is $5$.
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