Figure Series – Study Notes for CUET PG (Reasoning Ability)
What you’ll learn
• What a figure series is
• Common transformation patterns
• Systematic approach to solve any figure‑sequence question
• Key points to remember before the exam
• A worked example with full reasoning
• Quick revision checklist
1. Simple Explanation
A figure series (also called pattern sequence or shape series) is a set of two or more geometric figures arranged in a specific order. Each figure is obtained from the previous one by applying one or more transformations (rotation, reflection, scaling, translation, addition/subtraction of elements, colour change, etc.). Your task is to identify the rule that governs the sequence and predict the next figure (or fill a missing one).
2. Key Points
| # | Point | Why it matters |
|---|---|---|
| 1 | Identify the base figure | The first figure is your reference; all transformations are relative to it. |
| 2 | Look for changes in orientation | Rotations (90°, 180°, 270°), flips, or mirroring. |
| 3 | Check size alterations | Scaling up/down, stretching/compressing. |
| 4 | Count elements | Number of shapes, vertices, or segments often changes systematically. |
| 5 | Colour & fill | Colour changes may follow a cycle (e.g., red → blue → green). |
| 6 | Position shifts | Translation along X/Y axes; diagonal shifts. |
| 7 | Combination of rules | A series may involve more than one transformation simultaneously. |
| 8 | Rule consistency | Verify that the proposed rule holds for all consecutive pairs. |
| 9 | Avoid over‑fitting | Don’t invent a rule that only works for one pair; always test the whole series. |
| 10 | Time‑management | Spend ≈30–45 s on the first 2–3 figures; the pattern usually emerges quickly. |
3. Systematic Approach
- List all figures (A, B, C, …) in order.
- Compare adjacent pairs (A→B, B→C, …).
- Note each change:
- Rotation angle
- Reflection axis
- Size ratio
- Added/removed elements
- Colour shift
- Position shift
- Formulate a rule that explains all observed changes.
- Apply the rule to the last figure to predict the next one.
- Cross‑check: ensure the rule works backward (C→B, B→A) if necessary.
- Answer: choose the figure from the options that matches the predicted one.
4. Worked Example
Question (illustrated)
Figure 1: A solid square (4 sides, all equal).
Figure 2: A solid square rotated 90° and split into 4 equal triangles.
Figure 3: A solid square rotated 180° and split into 4 equal triangles.
Figure 4: A solid square rotated 270° and split into 4 equal triangles.
Options
A. Solid square rotated 0° and split into 4 equal triangles
B. Solid square rotated 90° and split into 4 equal triangles
C. Solid square rotated 180° and split into 4 equal triangles
D. Solid square rotated 270° and split into 4 equal triangles
Step‑by‑Step Reasoning
| Figure | Orientation change | Extra elements? | Observation |
|---|---|---|---|
| 1 → 2 | 0° → 90° (clockwise) | None added | Rotation by +90° |
| 2 → 3 | 90° → 180° | None added | Rotation by +90° |
| 3 → 4 | 180° → 270° | None added | Rotation by +90° |
- Rule: Each step rotates the square 90° clockwise.
- Size and internal division stay constant (4 triangles).
- Therefore, the next figure will be the square rotated 360° (i.e., back to 0°).
Answer: Option A – solid square rotated 0° and split into 4 equal triangles.
Common Pitfalls
| Pitfall | Fix |
|---|---|
| Mistaking rotation for reflection | Check if orientation changes consistently in the same direction. |
| Ignoring internal divisions | Count sub‑shapes; they often form part of the rule. |
| Over‑fitting on a single figure | Verify that the rule applies to all consecutive pairs. |
5. Quick Revision Summary
- Start with the base figure – all transformations reference this shape.
- Look for systematic changes: rotation, reflection, scaling, element count, colour, position.
- Rule should work for every adjacent pair in the series.
- Common transformation list
- Rotation: 0°, 90°, 180°, 270° (clockwise or counter‑clockwise)
- Reflection: horizontal, vertical, diagonal
- Scaling: increase/decrease by a factor (e.g., double the side length)
- Translation: shift right/left/up/down by a fixed distance
- Element addition/removal: number of shapes, lines, or points changes by a constant amount
- Colour cycle: e.g., red → blue → green → red …
- Solve in 2–3 seconds after you spot the first change; the pattern will usually repeat.
- Practice: Use past CUET PG papers and mock tests; focus on quick pattern recognition.
6. Quick Practice Questions (for your own use)
- Series A
1) Triangle (solid,