Question

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

$9*8071$

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 $9*8071$ to be divisible by $11$

difference between the sum of the alternate digits$=$$\left(9+8+7\right)-\left(*+0+1\right)=24-\left(*+1\right)=23-*$

Observe that when $*$$=$$1$, then the difference between the sum of the alternate digits will become $22$, which is multiple of $11$.

Hence, the $*$ will replace by $1$.