Question

The least value of $x$ so that $97215x6$ is divisible by $11$ is ____ .

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is C $3$

Divisibility Test for $11$ :

$\to$ Take the alternating sum of the digits in the number, read from left to right. If that is divisible by $11$, so is the original number.

So, for instance, $2728$ has alternating sum of digits $2-7+2-8 = -11$.

Since, $-11$ is Divisible by $11$, So is $2728$.

Here,

Given number is $97215X6$

For it to be divisible by $11$,

$9-7+2-1+5-X+6$ should also be divisible by $11$.

$\Rightarrow$ $14-X$ is Divisible by $11$

$\therefore X=3$