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# 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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