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# 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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