Question

Find the missing term-

• A. 100
• B. 92
• C. 57
• D. 54

Hint:

For missing term questions in pattern-based figures: Identify Components: Clearly list the numbers in each part of the figure (e.g., outer numbers, inner number).Systematic Trial: Test common mathematical operations (addition, subtraction, multiplication, division, squares, cubes, powers) on the outer numbers to see if they relate to the inner number.

Answer 1

The Correct Option is A

Step 1: Analyze the first two diagrams to find a consistent pattern.
Let's denote the numbers around the circle as:
T = Top, B = Bottom, L = Left, R = Right.
C = Center number.
Diagram 1: Outer numbers: T=2, L=6, R=3, B=5 Center number (C1): 111 Let's try the pattern: $(\text{Sum of Top and Bottom}) \times (\text{Sum of Left and Right}) + \text{X}$.
$(\text{T} + \text{B}) \times (\text{L} + \text{R}) = (2 + 5) \times (6 + 3) = 7 \times 9 = 63$.
To get the center number 111: $63 + \text{X}_1 = 111 \implies \text{X}_1 = 111 - 63 = 48$.
Diagram 2:
Outer numbers: T=1, L=4, R=2, B=7
Center number (C2): 105
Apply the same pattern:
$(\text{T} + \text{B}) \times (\text{L} + \text{R}) = (1 + 7) \times (4 + 2) = 8 \times 6 = 48$.
To get the center number 105: $48 + \text{X}_2 = 105 \implies \text{X}_2 = 105 - 48 = 57$.
Step 2: Identify the pattern in the added values (X).
The added values are $\text{X}_1 = 48$ and $\text{X}_2 = 57$.
The difference between these values is $57 - 48 = 9$.
Let's assume the pattern for the added values (X) continues as a series with a decreasing common difference.
If the difference between consecutive X values is decreasing by 1:
The sequence of differences would be $9, 8, 7, \ldots$.
So, the next added value $\text{X}_3$ for Diagram 3 would be $\text{X}_2 + 8 = 57 + 8 = 65$.
Step 3: Apply the complete pattern to Diagram 3.
Outer numbers: T=3, L=4, R=3, B=2
Center number (C3): ?
First, calculate $(\text{T} + \text{B}) \times (\text{L} + \text{R})$: $(3 + 2) \times (4 + 3) = 5 \times 7 = 35$. Now, add the next value from the X pattern ($\text{X}_3 = 65$): Missing term (C3) = $35 + 65 = 100$.
Step 4: Match the result with the given options.
The calculated missing term is 100, which matches option (1). The final answer is $\boxed{\text{(1)}}$.