Question

\[\begin{array}{|c|c|c|} \hline 15 & 225 & 30 \\ \hline 7 & 70 & 20 \\ \hline 3 & ? & 8 \\ \hline \end{array} \]

• A. 70
• B. 12
• C. 16
• D. 24

Hint:

When a center number seems tied to the two ends, try operations like product and then divide by a constant—verify across rows before applying to the missing entry.

Answer 1

The Correct Option is B

Row-wise rule: The middle entry of each row equals \(\dfrac{\text{left} \times \text{right}}{2}\). \[ \begin{aligned} &\text{Row 1: } \frac{15 \times 30}{2} = 225 \quad \checkmark &\text{Row 2: } \frac{7 \times 20}{2} = 70 \quad \checkmark &\text{Row 3: } \frac{3 \times 8}{2} = 12. \end{aligned} \] \[ \boxed{12} \]

Answer 2

Instead of computing the middle value directly, check each option by testing whether it satisfies \(\text{left}\times\text{right}=2\times\text{middle}\), using left \(=3\) and right \(=8\), so \(\text{left}\times\text{right}=24\).

1. Option (a) 70: \(2\times70=140\), not \(24\) — rejected.
2. Option (b) 12: \(2\times12=24\), matching \(3\times8=24\) exactly — confirmed.
3. Option (c) 16: \(2\times16=32\), not \(24\) — rejected.
4. Option (d) 24: \(2\times24=48\), not \(24\) — rejected.

Only option (b) satisfies \(2\times\text{middle}=\text{left}\times\text{right}\).

the correct answer is 12.