Question

If $x$ denotes the digit at hundreds place of the number $67x19$ such that, the number is divisible by $11$. Find possible value of $x$.

Answer 1

$\Rightarrow$ $67x19$ is divisible by 11.

$\Rightarrow$ A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.

$\Rightarrow$ Sum of digits at odd places – sum of digits at even places = 11

$\Rightarrow$ $(6+x+9)-(7+1)=11$

$\Rightarrow$ $15+x-8=11$

$\Rightarrow$ $x+7=11$

$\Rightarrow$ $x=11-7$

$\therefore$ $x=4$