Question

$1x35$ is divisible by $9$ if $x$ $=$ _______.

Answer 1

Finding the missing number:

$1x35$ is four digit number and $x$ is a single-digit number.

A number is divisible by $9$ if the sum of its digits is also divisible by $9$. and A number is divisible by $9$ means it is a multiple of $9$.

So consider,

The sum of the digits is

$1+x+3+5$$=$ A number multiple of $9$ .

$x+9$ $=$ A number multiple of $9$ .

According to the question, $x$ is a single-digit number.

Here, there are two possible cases for $x$ i.e. $x$ $=$ $0$ or $x$ $=$ $9$ .

Case i :

If $x$ $=$ $0$ then

$x+9$ $=$$0$ $+$ $9$

$=$$9$ . ( So, $9$ is divisible by $9$ ).

Case ii :

If $x$ $=$ $9$ then

$x+9$ $=$$9$ $+$ $9$

$=$$18$ . ( So, $18$ is divisible by $9$ ).

Therefore, it is observed that there are two possible single digit values for $x$ to get a four digit number divisible by $9$ from above two cases.

Hence, the value of $x$ is $0$ or $9$ .