Question

In each of the following replace $\ast$ by a digit so that the number formed is divisible by $11:$

A $8\ast 9484$

B $9\ast 53762$

Answer 1

We know that the divisibility rule for $11,$

Consider the part $A$of the question,

$8\ast 9484$

$8+9+8-(\ast +4+4)=0$

$\ast =25-16$

$\ast =9$ (9 is less than 11)

Hence, the value of $\ast =9$

Consider the part $B$

$9\ast 53762$

$9+5+7+2-(\ast +3+6)=0$

$\ast =14$

since 14 is greater than 11,

On performing $\frac{14}{11}$ , we get quotient$=1$ , reminder$=3$

$\ast =3$

Hence, the value of $\ast =3$