Question

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

$39*43$

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 $39*43$ to be divisible by $11$

difference between the sum of the alternate digits$=$$\left(9+4\right)-\left(3+*+3\right)=13-\left(6+*\right)=7-*$

Observe that when $*$$=$$7$, then the difference between the sum of the alternate digits will become $0$, which is multiple of $11$.

Hence, the $*$ will replace by $7$.