Question

A four digit number $abcd$ is divisible by $11$, If $a+c-b-d$ is a multiple of $mk$ where $m$ is constant and $k\in Z$. Find $m$.

Answer 1

A number is divisible by $11$, if

Sum of digits at odd places$-$Sum of digits at even places$=11k$ (Integer Multiple of $11$ )

So, the four digit number $abcd$ is divisible by $11$ if,

$a+c-(b+d)=11k$

$a+c-b-d=11k$

So, $m=11$