Question

Which option will replace the question mark?

• A. Fig A
• B. Fig B
• C. Fig C
• D. Fig D

Hint:

Break down complex multi-grid patterns by analyzing each quadrant independently as its own separate number sequence. Solving one quadrant (like the Top-Left: 2, 3, 4, 5) often reduces the options to one or two choices.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question belongs to the topic of

Pattern Sequences and Grid-based Progressions.
We are given a sequential series of four \(2 \times 2\) grids containing dots. The second frame of the sequence is missing (replaced by a question mark). We need to deduce the rule governing the dot counts in each quadrant and select the correct missing grid.

Step 2: Key Formula or Approach:
Let the four quadrants of each grid be represented as:
- Top-Left (TL), Top-Right (TR)
- Bottom-Left (BL), Bottom-Right (BR)
We count the dots in each quadrant for the visible frames and search for a consistent mathematical progression (arithmetic, step-wise, or alternating).

Step 3: Detailed Explanation:

• Let us record the dot counts in each quadrant for the available frames:
- Frame 1: TL = 2, TR = 1, BL = 0, BR = 1. (Total = 4)
- Frame 2 (?): Let us assume it is Option C: TL = 3, TR = 2, BL = 1, BR = 1. (Total = 7)
- Frame 3: TL = 4, TR = 2, BL = 1, BR = 2. (Total = 9)
- Frame 4: TL = 5, TR = 2, BL = 2, BR = 2. (Total = 11)

• Let us analyze the progression for each quadrant using Option C:
- Top-Left (TL): 2 \(\to\) 3 \(\to\) 4 \(\to\) 5. This is a perfect arithmetic progression with a constant increase of +1 in every step.
- Top-Right (TR): 1 \(\to\) 2 \(\to\) 2 \(\to\) 2. This represents a step function where the value increases by 1 and then stabilizes.
- Bottom-Left (BL): 0 \(\to\) 1 \(\to\) 1 \(\to\) 2. This is a step-wise progression that increases by +1 every second step (specifically on odd steps).
- Bottom-Right (BR): 1 \(\to\) 1 \(\to\) 2 \(\to\) 2. This is also a step-wise progression that increases by +1 every second step (specifically on even steps).

• This highly consistent, interlocking set of logical rules confirms that Option C fits the progression perfectly, creating a balanced and progressive distribution of dots.


Step 4: Final Answer:
Option (C) correctly replaces the question mark.