Question

Find all possible values of x for which the 4-digit number 320x is divisible by 3. Also, find the numbers.

Answer 1

If a number is divisible by 3, then the sum of the digits is also divisible by 3.

$3+2+0+x=5+x$ must be divisible by 3.
This is possible in the following cases:
$$\begin{gathered} i)x=1 \\ \therefore 5+x=6 \\ \mathrm{Thus},\mathrm{the}\mathrm{number}\mathrm{is}3201. \end{gathered}$$

$$\begin{gathered} ii)x=4 \\ \therefore 5+x=9 \\ \mathrm{Thus},\mathrm{the}\mathrm{number}\mathrm{is}3204. \end{gathered}$$

$$\begin{gathered} iii)x=7 \\ \therefore 5+x=12 \\ \mathrm{Thus},\mathrm{the}\mathrm{number}\mathrm{is}3207. \end{gathered}$$