Question

What least value should be given to * so that the number $653\ast 47$ is divisible by $11?$

• A. $9$
• B. $6$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

$\Rightarrow$ Divisibility by $11$ : A number is divisible by $11$ when the sum of the digits at the odd places and the sum of the digits at the even places are either equal or a multiple of $11$

$\Rightarrow$ Let $\ast$ be $x$

$\therefore$ Sum of even digits = $4+3+6=13$

$\therefore$ Sum of odd digits = $7+x+5=12+x$

$\therefore$ $12+x-13=0$

$\therefore$ $x=1$

$\Rightarrow$ $653147$ id divisible by $11$

$\therefore$ The value of $\ast$ is $1$.