Question

In each of the following numbers, replace $*$ by a digit to make the number divisible by $11$.

$467*91$

Answer 1

A number is divisible by $11$ if the difference between the sum of the alternate digits is $0$ or a multiple of $11$.

For the number $467*91$ to be divisible by $11$

Difference between the sum of the alternate digits$=$$\left(4+7+9\right)-\left(6+*+1\right)=20-\left(*+7\right)=13-*$

Observe that when $*$$=$$2$, then the difference between the sum of the alternate digits will become $11$, which is multiple of $11$.

Hence, the $*$ will replace by $2$.