Question

Given that the number is divisible by 9, where y is a digit, what are the possible values of y?

Answer 1

$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\overline{67\mathrm{y}19}\mathrm{is}\mathrm{a}\mathrm{multiple}\mathrm{of}9. \\ \therefore (6+7+\mathrm{y}+1+9)\mathrm{is}\mathrm{a}\mathrm{multiple}\mathrm{of}9. \\ \therefore (23+\mathrm{y})\mathrm{is}\mathrm{a}\mathrm{multiple}\mathrm{of}9. \\ 23+\mathrm{y}=0,9,18,27,36... \\ \mathrm{But}\mathrm{x}\mathrm{is}\mathrm{a}\mathrm{digit}.\mathrm{So},\mathrm{x}\mathrm{can}\mathrm{take}\mathrm{values}0,1,2,3,4...9. \\ 23+\mathrm{y}=27 \\ \Rightarrow \mathrm{y}=4 \end{gathered}$$