Question

If the number 24753x is completely divisible by 72, then which of the following numbers should replace x ?

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The correct option is C 6

$\Rightarrow$ For number to be divisible by $72$ ,it should be divisible by $9$ and $8$.

$\Rightarrow$ Divisibility rule of $8$ : Last 3 digits of number should be divisible by 8.

$\Rightarrow$ Divisibility rule of $9$ : Sum of all digits of number should be multiple of 9 or divisible by 9.

$\Rightarrow$ So, $2+4+7+5+3+x=Multipleof9$

$\therefore$ $21+x=27$

$\therefore$ $x=6$

$\Rightarrow$ The last 3 digit $536$ is divisible by 8.

$\therefore$ $247536$ is completely divisible by $72$.

$\therefore$ The value of $x$ is $6$.