Question

$476\ast \ast 0$ is divisible by both $3$ and $11$. What are the non-zero digits in the hundred's and ten's places respectively?

• A. $8,5$
• B. $6,5$
• C. $6,4$
• D. $2,5$

Answer 1

The correct option is A $8,5$

$\Rightarrow$ Let the given number be $476xy0$.

$\Rightarrow$ Then $(4+7+6+x+y+0)=(17+x+y)$ must be divisible by 3.

$\Rightarrow$ And, $(0+x+7)-(y+6+4)=(x-y-3)$ must be either 0 or 11.

$\Rightarrow$ $x-y-3=0$

$\therefore$ $y=x-3$

$\Rightarrow$ $(17+x+y)=(17+x+x-3)=(2x+14)$

$\Rightarrow$ We get $x=2$ or $x=8$

$\Rightarrow$ $x=2$ can not be possible, so $x=8$

$\Rightarrow$ $y=8-3=5$

$\therefore$ $x=8$ and $y=5$.