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 $0,1,2,3 \ldots 9$.
$\therefore x-5=0$
$\Rightarrow x=5$
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