isi-entrance 2022 Q20

isi-entrance · India · UGA Number Theory Combinatorial Number Theory and Counting
A $3 \times 3$ magic square is a $3 \times 3$ rectangular array of positive integers such that the sum of the three numbers in any row, any column or any of the two major diagonals, is the same. For the following incomplete magic square
2736
31

the column sum is
(A) 90
(B) 96
(C) 94
(D) 99
A $3 \times 3$ magic square is a $3 \times 3$ rectangular array of positive integers such that the sum of the three numbers in any row, any column or any of the two major diagonals, is the same. For the following incomplete magic square
\begin{center}
\begin{tabular}{ | l | l | l | }
\hline
27 & 36 &  \\
\hline
 &  &  \\
\hline
31 &  &  \\
\hline
\end{tabular}
\end{center}
the column sum is\\
(A) 90\\
(B) 96\\
(C) 94\\
(D) 99