Question

If 24x is a multiple of 11 , what is the value of x?

Answer 1

If a number is divisible by 11, the difference between the sum of digits at even places and the sum of digits at odd places will be a multiple of 11.

Given number is $24x$

Sum of digits at even places $=4$

Sum of digits at odd places $=2+x$

$\Rightarrow 4$ $-$ $(2+x)$ $=$ $11\times m$

$\Rightarrow 2-x=11m$

$\therefore x$ can take values from $0$ to $9$

Possible values of $2$ $-$ $x$ are $0,$ $11,$ $22,$ $33$ etc

Least value possible for $2$ $-$ $x$ is $0$

$\Rightarrow 2-x=0$

Therefore $x=2$