Question

If x is a digit such that the number $\overline{18x71}$ is divisible by 3, find possible values of x.

Answer 1

$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\overline{18\mathrm{x}71}\mathrm{is}\mathrm{a}\mathrm{multiple}\mathrm{of}3. \\ \therefore (1+8+\mathrm{x}+7+1)\mathrm{is}\mathrm{a}\mathrm{multiple}\mathrm{of}3. \\ \therefore (17+x)\mathrm{is}\mathrm{a}\mathrm{multiple}\mathrm{of}3. \\ \therefore 17+x=0,3,6,9,12,15,18,21... \\ \mathrm{But}x\mathrm{is}\mathrm{a}\mathrm{digit}.\mathrm{So},\mathrm{x}\mathrm{can}\mathrm{take}\mathrm{values}0,1,2,3,4...9. \\ 17+x=18\Rightarrow \mathrm{x}=1 \\ 17+x=21\Rightarrow \mathrm{x}=4 \\ 17+x=24\Rightarrow \mathrm{x}=7 \\ x=1,4,7 \end{gathered}$$