Question

In each of the following numbers, replace $M$ by the smallest whole number to make the resulting number divisible by $11$.​
(ii) $3M422$

Answer 1

Step: Find the value of $M$
Given number: $3M422$
A number is divisible by $11$, if the difference of the sum of its digits in odd places from the right side and the sum of digits in even places from the the right side is divisible by $11$.​
​Here,​
Sum of odd digits = $2+4+3$ = $9$​
Sum of even digits = $2+M$ ​
Difference = $9-(2+M)$ = $7–M$
Now, since $M$ is a whole number and we know that $0$ is divisible by $11$.​
Thus, $7-M$ = $0$​
⇒ $M$= $7$.​
Hence, the value of $M$ is $7$.​