Question

\[\begin{array}{|c|c|c|} \hline 4 & 7 & 9 \\ \hline 8 & 6 & 8 \\ \hline 3 & 7 & 9 \\ \hline 35 & 49 & ? \\ \hline \end{array} \]

• A. 63
• B. 89
• C. 81
• D. 64

Hint:

When a table has a "result" row, try applying a simple operation column-wise such as \(a\times b + c\).

Answer 1

The Correct Option is C

Rule by columns: Each bottom entry equals \[ (\text{top})\times(\text{middle})+(\text{bottom of the 3rd row}). \] Check first two columns: \[4\times 8 + 3 = 35\] , \(\quad\) \[7\times 6 + 7 = 49\] . So for the third column: \[ 9\times 8 + 9 = 72 + 9 = 81. \] \[ \boxed{81} \]

Answer 2

Use the column rule in reverse — subtract the bottom-of-third-row value from each candidate and check whether the remainder equals the product of the top and middle entries of that column (\(9\times8=72\)).

1. Option (a) 63: \(63-9=54\), not \(72\) — rejected.
2. Option (b) 89: \(89-9=80\), not \(72\) — rejected.
3. Option (c) 81: \(81-9=72\), exactly the required product — confirmed.
4. Option (d) 64: \(64-9=55\), not \(72\) — rejected.

Only option (c) leaves the correct product of \(72\) once the third-row value is removed.

the correct answer is 81.