Question

Identify the digit $d$ such that the number $741d$ is divisible by $6.$

• A. 0
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (A), (C)

6

For the number to be divisible by $6,$ it must be divisible by both $2$ and $3.$

Hence, $d$ must be an even number.

Also, the sum of the digits, $7+4+1+d=12+d$ must be divisible by $3.$

$12$ is divisible by $3.$
$\therefore d$ can be $0$ or any even number that is also a multiple of $3,$ i.e., $6.$
$3\times 1=3$
$3\times 2=6$
$3\times 3=9$

$\therefore d$ can be $0$ or $6.$

Such numbers are $7410$ and $7416.$