When solving numerical patterns, test different combinations of operations (e.g., multiplication, addition) to identify consistent relationships across all examples.
Step 1: Analyze the Pattern.
The given diagrams suggest a relationship between the numbers around the central box and the number inside the box. Let's break it down step by step.
Step 2: Examine the First Diagram.
\[
\begin{array}{ccc}
6 & \boxed{111} & 3
5 & &
\end{array}
\]
Top numbers: $6$ and $3$
Bottom number: $5$
Central number: $111$ Step 3: Examine the Second Diagram.
\[
\begin{array}{ccc}
4 & \boxed{105} & 2
7 & &
\end{array}
\]
Top numbers: $4$ and $2$
Bottom number: $7$
Central number: $105$ Step 4: Identify the Relationship.
Let’s hypothesize a formula based on the given numbers. A common pattern in such problems is to use multiplication, addition, or a combination of operations involving the top and bottom numbers.
First Diagram:
\[
\text{Central number} = (6 \times 3) + (5 \times 6) = 18 + 30 = 111
\]
Second Diagram:
\[
\text{Central number} = (4 \times 2) + (7 \times 6) = 8 + 42 = 105
\]
Step 5: Apply the Pattern to the Third Diagram.
\[
\begin{array}{ccc}
4 & \boxed{?} & 3
2 & &
\end{array}
\]
Top numbers: $4$ and $3$
Bottom number: $2$
Central number: $?$
Using the same formula:
\[
\text{Central number} = (4 \times 3) + (2 \times 6) = 12 + 80 = 92
\]
Step 6: Match with the Options.
The missing term is $92$, which corresponds to Option (B)
