If $x$ is a digit such that the number $\overline{18\times71}$ is divisible by 3, find possible values of $x$.
Given:
$x$ is a digit such that the number $\overline{18\times71}$ is divisible by 3.
To do:
We have to find the possible values of $x$.
Solution:
The number $\overline{18\times71}$ is divisible by 3.
This implies,
The sum of its digits will also be divisible by 3.
Therefore,
$1 + 8 + x + 7+ 1$ is divisible by 3.
$17 + x$ is divisible by 3
If $x=1$, $17+1=18$ is divisible by 3.
If $x=4$, $17+4=21$ is divisible by 3.
If $x=7$, $17+7=24$ is divisible by 3.
The possible values of $x$ are $1, 4$ and $7$.
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