Find the missing numbers of a chart

Question

One of my tutees ask me this question, and I have spent almost an hour yet don't see a pattern. Any trick? Thanks.

Answer 1

I think the answer is A.

Because if you rearrange the third row, you can match all the rows together. After rearranging, the element in the 2nd row times that of the 3rd row is that of the 4th row in the same column. Also, you can find that the element in the 2nd row plus that of the 3rd row is that of the 1st row in the same column.

\begin{array}{|r|r|r|r|r|r|r|r|r|r|}\hline 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20\\ =5+6 & =7+5 & =2+11 & =2+12 & =9+6 & =1+15 & =8+9 & =12+6 & = 0+19& =10+10\\ \hline 5 & 7 & 2 & 2 & 9 & 1 & 8 & 12 & 0 & 10\\ \hline 6 & \color{red}{5} & 11 & 12 & 6 & 15 & \color{red}{9} & \color{red}{6} & \color{red}{19} &10 \\ \hline 30 & 35& 22 & 24 & 54 & 15 & 72 & 72 & 0 &100\\ =5\times6 & =7\times5& =2\times11 & =2\times12 & =9\times6 & =1\times15 & =8\times9 & =12\times6 & =0\times19 &=10\times10\\ \hline \end{array}