Question

If the number $\overline{27215x2}$ is completely divisible by 11, then the smallest whole number in place of x will be

• A. $3$
• B. $2$
• C. $1$
• D. $5$

Answer 1

The correct option is A $3$

Using "divisibility by $11$ rule"

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.
Hence, $27215x2$ is divisible by $11$, then $(2+2+5+2)-$ $(7+1+x)$ is divisible by $11$
$(8+x)$ is divisible by $11$
$11$ is divisible by 11
The smallest whole number which can be substituted in the place of $x$ to satisfy the
above equation is $3$ such that $11$ is divisible by $11$.
Hence the answer is $3$.