Question

The digits A, B, C are such that the three digit numbers A88, 6B8, 86C are divisible by 72, then the determinant is divisible by $\left|\begin{array}{ccc}A& 6& 8\\ 8& B& 6\\ 8& 8& C\end{array}\right|$

• A. 76
• B. 144
• C. 216
• D. 276

Answer 1

The correct option is B 144

$100A+80+8=72{\lambda }_{1}600+10B+8=72{\lambda }_{2}800+60+C=72{\lambda }_3{\lambda }_1,{\lambda }_2,{\lambda }_3ϵI.\left|\begin{array}{ccc}A& 6& 8\\ 8& B& 6\\ 8& 8& C\end{array}\right|(R_3\leftarrow R_3+10R_2+100R_1)=\left|\begin{array}{ccc}A& 6& 8\\ 8& B& 6\\ 72{\lambda }_1& 72{\lambda }_2& 72{\lambda }_3\end{array}\right|A88isdiv.by72\Rightarrow A88isdiv.by9\Rightarrow A+8+8isdiv.by9\therefore A=26B8isdiv.by9\Rightarrow B=4.$