Question

Which of the following is divisible by $9$?
 $\begin{align}
  & \left( A \right)75636 \\
 & \left( B \right)89321 \\
 & \left( C \right)75637 \\
 & \left( D \right)75632 \\
\end{align}$

Answer 1

Hint: From the question given we have been asked to find which number is divisible by $9$ from the given options. As we know that the divisibility rule of $9$ the sum of the digits of the number is divisible by $9$, then the number itself is divisible by $9$. By checking all the options one by one we will get the required answer.

Complete step by step solution:
From the question given we have been asked to find the which number is divisible by $9$ from the given options.
As we know that the divisibility rule of $9$ the sum of the digits of the number is divisible by $9$, then the number itself is divisible by $9$. By checking all the options one by one we will get the required answer.
First will start with option
$\Rightarrow \left( A \right)75636$
Now we have to find the sum of all the digits in the number of option A, the sum we will get is,
$\Rightarrow 75636=7+5+6+3+6=27$
As we know that the number $27$ is divisible by $9$, so from the divisibility rule of $9$, the whole number will be divisible by $9$.
Therefore, option $\left( A \right)75636$ is divisible by $9$
Now we will check the option B
$\Rightarrow \left( B \right)89321$
Now we have to find the sum of all the digits in the number of option B, the sum we will get is,
$\Rightarrow 89321=8+9+3+2+1=23$
As we know that the number $23$ is not divisible by $9$, so from the divisibility rule of $9$, the whole number will not be divisible by $9$.
Therefore, option $\left( B \right)89321$ is not divisible by $9$.
Now we will check the option C
$\Rightarrow \left( C \right)75637$
Now we have to find the sum of all the digits in the number of option C, the sum we will get is,
$\Rightarrow 75637=7+5+6+3+7=28$
As we know that the number $28$ is not divisible by $9$, so from the divisibility rule of $9$, the whole number will not be divisible by $9$.
Therefore, option $\left( C \right)75637$ is not divisible by $9$.
Now we will check the option D
$\Rightarrow \left( D \right)75632$
Now we have to find the sum of all the digits in the number of option C, the sum we will get is,
$\Rightarrow 75632=7+5+6+3+2=23$
As we know that the number $23$ is not divisible by $9$, so from the divisibility rule of $9$, the whole number will not be divisible by $9$.
Therefore, option $\left( D \right)75632$ is not divisible by $9$.
By checking all the options, the option $\left( A \right)75636$ is divisible by $9$.

Note: Students should know the divisibility rules from two to eleven, students should also know that the divisibility rule of $9$ and $3$ are similar. Students should add the digits of the number carefully.