Question

$20x3$ is a multiple of $3$ if the digit $x$ is ______ or ______ or ______.

Answer 1

It is given that,

$20x3$ is multiple of $3$ if $x$ $=$ ………..or …………..or …………… .

Here,

$20x3$ is Four digit number and $x$ is a single-digit number.

Note : A number is a multiple of $3$ means it is divisible by $3$ So, A number is multiple of $3$ if the sum of its digits is also multiple of $3$.

Consider,

The sum of the digits is

$2+0+x+3$$=$ A number multiple of $3$ .

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

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

Here, There are three possible cases for $x$ to get a number multiple of $3$ i.e $x$ $=$ $1$ or $x$ $=$ $4$ or $x$ $=$ $7$ .

Case i :

If $x$ $=$ $1$ then

$x+5$ $=$$1$ $+$ $5$

$=$$6$ . ( So, $6$ is a multiple of $3$ ).

Case ii :

If $x$ $=$ $4$ then

$x+5$ $=$$4$ $+$ $5$

$=$$9$ . ( So, $9$ is a multiple of $3$ ).

Case iii:

If $x$ $=$ $7$ then

$x+5$ $=$$7$ $+$ $5$

$=$$12$ . ( So, $12$ is a multiple of $3$ ).

Therefore, it is observed that there are three possible single digit values for $x$ to get a four digit number which is multiple of $3$ from above three cases.

Hence, $x$ $=$ $1$ or $4$ or $7$.