Figure series: Reasoning Ability Notes for Maharashtra PSC

Maharashtra PSC – Reasoning Ability

Figure Series – Complete Study Notes

Why Study Figure Series?
In the Maharashtra PSC (Competitive) exams, the Figure Series section tests your ability to spot patterns, recognise geometric transformations and apply logical reasoning. Mastery of this topic gives you a steady advantage because the same basic principle is reused in different forms across the exam.

1. What is a Figure Series?

A Figure Series is a sequence of two‑ or three‑dimensional shapes in which each figure is derived from its predecessor by a transformation (rotation, reflection, scaling, translation, colour change, etc.). The task is to predict the next figure in the sequence.

Key Idea:

Identify the transformation rule that maps Figure 1 → Figure 2, Figure 2 → Figure 3, and then apply it one more time.

2. Common Transformation Types

Transformation	Visual Cue	Typical Symbolic Notation	Example in PSC
Rotation	Figure turns around a fixed point (center)	`Rθ` (θ = 90°, 180°, 270°)	Figure rotates 90° clockwise each step
Reflection	Figure flips over an axis	`M` (mirror)	Upper left ↔ Upper right
Scaling (Dilation)	Size changes but shape stays same	`k` (scale factor)	Size increases by 2× each step
Translation	Figure shifts position	`T(v)` where `v` = vector	Moves right by one cell
Colour Change	Colour of elements changes	`C`	Red → Green → Blue
Combination	Two or more of the above simultaneously	e.g., `R90 + M`	Rotate 90° then reflect

Tip: PSC problems rarely mix too many transformations; usually one simple rule governs the series.

3. Step‑by‑Step Problem‑Solving Approach

Step	What to Do	Why It Matters
1. Identify the “reference point”	Find the centre of symmetry or the pivot of rotation.	Many series revolve around a fixed point.
2. Check for rotation	Look for identical shapes rotated by 90°, 180°, or 270°.	Rotation is the most common rule.
3. Verify reflection	Mirror the figure horizontally/vertically.	Spot if element positions swap across an axis.
4. Inspect scaling	Compare sizes: are all dimensions doubled, halved, or unchanged?	Scaling often appears in “growing” series.
5. Detect translation	Is the whole figure shifted right/left/up/down?	Translation is rare but easy to spot.
6. Look at colour patterns	Colours cycle or alternate.	Colour changes often accompany shape changes.
7. Combine observations	If two rules fit, test both.	A combined rule may yield the correct next figure.
8. Cross‑check all options	Re‑apply the suspected rule from figure n to figure n+1.	Ensures consistency.

Remember: In PSC, the answer set is usually 5 options. If you are unsure, eliminate the clearly wrong ones first.

4. Deriving the Next Figure – Worked Example

Sample Question (Illustrative)

Figure 1:  ●  ●
           ●  ●

Figure 2:  ●  ●
           ●  ●

Figure 3:  ●  ●   (The upper‑left square is missing)
           ●  ●

Analysis

Identify the reference point – the centre of the 2×2 grid.
Observe rotation – no change in orientation.
Check for reflection – no mirror effect.
Look for scaling – sizes unchanged.
Look for translation – no shift.
Colour change – not applicable.
Missing element – the upper‑left square disappears in Figure 3.

Pattern Deduction

Step	Transformation	Result
1 → 2	No change	identical
2 → 3	Remove one element (upper‑left)	3rd figure
3 → 4	Remove next element (upper‑right)	4th figure

Thus, the next figure will have the lower‑right square missing.

Answer – Option that shows the lower‑right square missing.

Why this works:
The series removes one square per step in a clockwise order (UR → LR → LL → UL).
Tricky point: Many examinees think the pattern is about rotation, but here it is about progressive deletion.

5. Important “Formulae” (Rule Templates)

Rule	Template	Example
Rotation by θ	`F_{n+1} = rotate(F_n, θ)`	90° clockwise each step
Reflection across axis A	`F_{n+1} = reflect(F_n, A)`	Mirror horizontally
Scale by factor k	`F_{n+1} = scale(F_n, k)`	Size doubles
Translation by vector v	`F_{n+1} = translate(F_n, v)`	Shift right by