Study Notes – Figure Series
Bihar Patwari / Lekhpal – Reasoning Ability
1. Simple Explanation
A Figure Series question presents a sequence of shapes (or a single shape that changes) and asks you to choose the next shape from four alternatives.
The goal is to detect the hidden rule – it can be numerical, geometric, colour‑based, or a combination.
Key idea:
Identify common properties (size, number of sides, angles, orientation, colour, symmetry, etc.) that change from one figure to the next.
Once the rule is found, apply it to predict the next figure.
2. Key Points / Checklist
| Step | What to Look For | Why It Helps |
|---|---|---|
| 1. Count | # of figures, # of shapes inside each figure | Many series are based on increasing or decreasing counts. |
| 2. Shape type | Triangle, square, rectangle, circle, etc. | Some series change shape type sequentially. |
| 3. Size/Dimensions | Height, width, side length, radius | Size often grows or shrinks by a fixed ratio or increment. |
| 4. Orientation / Rotation | 0°, 90°, 180°, 270° rotations or flips | Rotational patterns are common. |
| 5. Symmetry | Mirror, rotational symmetry order | Symmetry can increase or decrease. |
| 6. Colour | Colour changes, addition or removal of colour | Colour is a simple coding mechanism. |
| 7. Arrangement / Pattern | Grid, diagonal, concentric, radial | The spatial arrangement may follow a rule (e.g., “add one dot on each side”). |
| 8. Combination | Two or more properties changing together | Some questions combine rotation with size change, etc. |
Tip:
- Start with the simplest rule (count, shape type).
- If none fits, move to more complex properties (size, orientation, colour).
- Always check the alternatives – they sometimes give away the rule.
3. Worked Example
Question (illustrated):
Figure 1: 3 circles arranged in a row (all same size, same colour)
Figure 2: 4 circles arranged in a row (same size, same colour)
Figure 3: 5 circles arranged in a row (same size, same colour)
Figure 4: ?
Options:
A. 6 circles in a row
B. 5 circles in a row, but twice the size
C. 6 circles arranged in a triangle
D. 4 circles in a row
Step‑by‑Step Solution
| Step | Observation | Reasoning |
|---|---|---|
| 1. Count figures | 3 → 4 → 5 | Increment by +1 |
| 2. Shape type | Circles | Constant |
| 3. Arrangement | Row | Constant |
| 4. Size & colour | Same | Constant |
| 5. Apply rule | Next count = 5 + 1 = 6 | |
| 6. Choose option | Option A matches |
Answer: A. 6 circles in a row
A More Challenging Example
Sequence:
Figure A: 1 triangle pointing up
Figure B: 2 triangles, one pointing up, one pointing down
Figure C: 3 triangles, two pointing up, one pointing down
Figure D: ?
Options:
- 4 triangles – 2 up, 2 down
- 4 triangles – 3 up, 1 down
- 4 triangles – 1 up, 3 down
- 4 triangles – 4 up
Solution
| Step | Observation | Rule |
|---|---|---|
| 1. Count triangles | 1 → 2 → 3 | +1 each step |
| 2. Orientation pattern | +1 down‑oriented each step (0,1,1,…) | |
| 3. Predict next orientation | 3 triangles → 2 up, 2 down (because we add one down‑oriented) | |
| 4. Check options | Option 1 matches |
Answer: Option 1 – 4 triangles, 2 up, 2 down
4. Quick Revision Summary
| Topic | What to Remember |
|---|---|
| Common Rules | Count, shape type, size, orientation, colour, symmetry, arrangement |
| Procedure | 1) List all observable changes 2) Test simplest rule 3) If none, try combinations 4) Verify with alternatives |
| Common Traps |
- Colour change may be a red herring.
- Size can be ratio (×2, ÷2) or additive (+1).
- Orientation may alternate (up/down) or rotate (90° each step). | | Speed Tips |
- Scan all four options first; one will often match the rule.
- Practice with 5‑figure series – the 5th figure is usually the answer. | | Practice | Solve at least 10 figure‑series questions per day. |
Good luck with your preparation!
Keep practicing the pattern‑recognition process, and you’ll tackle any figure‑series question confidently.