Question

Mateo was listing out the numbers which are divisible by $12.$
In a particular number $9864$, he mistakenly fed $6$ in the tens place. Find the appropriate smallest digit.

• A. 9
• B. 6
• C. 0
• D. (b) and (c) above.

Answer 1

The correct option is C 0

Divisibility by $12$ indicates that the number must be divisible by $3$ and $4.$

Let the number be represented as $98x4.$

For divisibility by $3,$
$9+8+x+4=21+x$ must be divisible by $3.$
$\therefore x=0,3,6$ or $9$

For divisibility by $4,$ the last two digits $x4$ must be divisible by $4.$
Out of the four value of $x,$ only $0$ and $6$ satisfies the condition.

The smallest digit is $0.$
$\therefore$ The correct number is $9804.$