Goa PSC – Reasoning Ability
Topic: Figure Series
Figure series tests your ability to spot patterns in a sequence of shapes.
Typical questions appear in the Pattern & Sequence section of the Reasoning Ability paper.
1. Simple Explanation
A figure series is a set of geometric images arranged in a clear order (usually 4–6 figures).
Your job is to predict the missing figure or the next figure in the sequence.
Think of it as a visual arithmetic problem:
What operation is applied to the shape to get the next one?
2. Key Points & Strategies
| # | Concept | How to Spot It | Quick Tips |
|---|---|---|---|
| 1 | Shape Type | Does the figure change (square → triangle → circle, etc.)? | Note each shape’s name; lists often repeat in a cycle. |
| 2 | Size Change | Are the figures getting larger or smaller? | Look for proportional scaling (2 ×, ½ ×, etc.). |
| 3 | Orientation | Rotation, flipping, mirroring? | Count 90°/180° turns or left‑right flips. |
| 4 | Number of Elements | Do items appear/disappear? | Count dots, lines, or sub‑shapes. |
| 5 | Color | Colors change? | Track the sequence of colors (red → green → blue). |
| 6 | Position | Are shapes moving left/right/up/down? | Check coordinates or relative placement. |
| 7 | Combination of Operations | Two or more rules applied together? | Solve in the order given (e.g., rotate → enlarge). |
| 8 | Symmetry & Reflection | Mirror images? | Look for vertical/horizontal symmetry. |
| 9 | Complex Transformations | Fractal, tessellation, or pattern inside pattern | Break into smaller components. |
| 10 | Logical Consistency | Does one rule make sense for all figures? | If a rule fails on any figure, discard it. |
Common Patterns
• Rotation by 90° each step
• Adding one side each step (triangle → square → pentagon)
• Alternating colors
• Scaling by a factor (double, halve, 1.5×)
• Mirror image on every other figure
3. Worked Example
Question (Sample):
Figure 1 Figure 2 Figure 3 Figure 4
▲ (red, 3 sides) ■ (red, 4 sides) ◯ (red, 0 sides) ?
(▲ = triangle, ■ = square, ◯ = circle)
Step‑by‑Step Analysis
| Property | Fig 1 | Fig 2 | Fig 3 | Observation |
|---|---|---|---|---|
| Shape | Triangle | Square | Circle | Shape changes every step |
| Sides | 3 | 4 | 0 | Number of sides increases by 1, then drops to 0 (circle) |
| Color | Red | Red | Red | Color stays red |
Hypothesis 1 – Shape Cycle
The shape sequence: Triangle → Square → Circle → ???
Common cycles:
- Triangle → Square → Pentagon
- Triangle → Square → Circle → Triangle (cycle of 3)
Hypothesis 2 – Size/Side Count
- 3 → 4 → 0 (circle)
- Next could be 3 again (triangle) or 5 (pentagon).
Check with Options
Suppose options are:
A. Triangle (red, 3 sides)
B. Pentagon (red, 5 sides)
C. Hexagon (red, 6 sides)
D. Star (red, 5 points)
The only shape that keeps the cycle consistent (Triangle → Square → Circle → Triangle) is A. Triangle.
Answer: A. Triangle (red, 3 sides)
Quick Rationale
- The shape repeats every 3 figures.
- Color never changes.
- Sides follow the pattern 3 → 4 → 0 → 3.
4. Quick Revision Summary (Cheat Sheet)
| Rule | What to Look For | Typical Answer |
|---|---|---|
| Rotation | 90°, 180°, 270° turns | Next figure rotated accordingly |
| Reflection | Mirror across vertical/horizontal axis | Mirror image |
| Size Change | Larger/smaller by factor 2, ½, 1.5 | Scale up/down |
| Shape Cycle | Sequence of shapes (tri → sqr → circ) | Repeat cycle |
| Color Cycle | Red → Blue → Yellow | Next color in list |
| Element Count | Dots/lines added each step | Add one more element |
| Position Shift | Move right/down by one unit | Shift accordingly |
| Combined | Two rules together | Apply both in order |
Practice Tips
- Label each figure (shape, size, color, orientation).
- Tabulate the changes column‑wise.
- Look for the rule that works for all figures; discard any that fail.
- Check if more than one rule applies; solve in the order given.
- Eliminate options that break the identified rule.
Remember: The sequence always follows a single consistent rule (or a fixed combination). If a rule seems to work for all but one figure, it’s usually a red flag.
Final Thought
Mastering figure series is all about pattern recognition and systematic analysis. Use the table of key points as a quick reference during the exam, and practice with a variety of patterns to build speed and confidence. Happy studying!