Solve the following
Question:

If $\overline{3 x 2}$ is a multiple of 11, where $x$ is a digit, what is the value of $x ?$

Solution:

Sum of the digits at odd places $=3+2=5$

Sum of the digit at even place $=x$

$\therefore$ Sum of the digit at even place $-$ Sum of the digits at odd places $=(x-5)$

$\because(\mathrm{x}-5)$ must be multiple by 11 .

$\therefore$ Possible values of $(x-5)$ are $0,11,22,33 \ldots$

But $\mathrm{x}$ is a digit; therefore $x$ must be $0,1,2,3 \ldots 9$.

$\therefore x-5=0$

$\Rightarrow x=5$