If $\overline{3x2}$ is a multiple of 11, where $x$ is a digit, what is the value of $x$?
Given:
$\overline{3x2}$ is a multiple of 11, where $x$ is a digit.
To do:
We have to find the value of $x$.
Solution:
The number $\overline{3x2}$ is a multiple of 11.
This implies,
It is divisible by 11.
Difference of the sum of its alternate digits is zero or multiple of 11.
Therefore,
Difference of $(2 + 3)$ and $x$ is zero or multiple of 11.
If $x - (2 + 3) = 0$, then $x = 5$
The value of $x$ is 5.
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