Question

If $3x2$ is a multiple of $11$, where $x$ is a digit, what is the value of $x$?

Answer 1

The alternating sum of the of digits of a number divisible by $11$ are in multiples of 11

i.e, sum of the even places subtracted from sum of odd places will be in multiples of 11

For $3x2,$ sum of the even places $=x,$

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

So, $5-x=11n,$

At $n=0\Rightarrow 5-x=0,$

$\therefore x=5$