Goa TET – Reasoning Ability
Figure Series – Study Notes
Objective – Master the art of spotting hidden patterns in successive figures.
Exam Orientation – Competitive tests (IIT‑JEE, JEE‑Mains, JEE‑Advanced, State TETs) require fast and accurate pattern recognition.
Key Idea – Treat each figure as a vector in a multi‑dimensional attribute space:
- Shape (circle, square, triangle, etc.)
- Color (red, blue, green, …)
- Orientation (rotated, flipped, mirrored)
- Size (area/length)
- Position (row, column, relative to others)
- Number of elements (count)
Each successive figure changes one or more of these attributes according to a deterministic rule.
1. Common Pattern Families
| # | Pattern Type | Typical Change | Example |
|---|---|---|---|
| 1 | Rotation / Reflection | Rotate 90°, 180°, 270° or mirror horizontally/vertically | A line of three squares → same line rotated 90° |
| 2 | Size Scaling | Incrementally increase or decrease size | Single circle → radius increases by 1 mm each step |
| 3 | Number Increment | Add or remove objects | 1 triangle → 2 triangles → 3 triangles |
| 4 | Color Alternation | Alternate colors in a cycle | Red → Green → Blue → Red |
| 5 | Position Shift | Translate horizontally/vertically | A square moves one cell right each step |
| 6 | Shape Transformation | Change shape while keeping other attributes | Square → Triangle → Hexagon |
| 7 | Composite Pattern | Combination of two or more of the above | 1st figure: square → 2nd: square rotated 90°, doubled in size |
Rule – In a single series, only one of the attributes changes predictably at a time.
Exception – Some series intentionally combine two attributes (e.g., count and size), but the change pattern for each attribute is independent.
2. Systematic Analysis Framework
-
Identify the “stable” attributes – those that remain constant across all figures.
Example: All figures have exactly one shape; shape size is constant but color changes. -
List the changing attributes
- Create a table with rows = figures, columns = attributes.
- Fill in values (e.g.,
Circle,Red,Size 1,Position (1,1)).
-
Detect linear or cyclic patterns
- Linear:
1, 2, 3, 4…orRed, Green, Blue, Red… - Cyclic: After a certain period the pattern resets.
- Linear:
-
Check for multiple rules
- If one attribute follows a linear trend and another follows a cycle, both are valid rules.
- Verify the rule holds for all given figures.
-
Predict the next figure
- Apply the derived rule(s).
- If ambiguous, choose the rule that respects all constraints.
3. Derivation of Patterns – A Worked Example
Problem Statement
Figure 1 : 3 squares in a row, all red
Figure 2 : 4 squares in a row, all green
Figure 3 : 5 squares in a row, all blue
Step‑by‑Step Derivation
| Fig | # of squares | Color | Size | Position |
|---|---|---|---|---|
| 1 | 3 | Red | 1x1 | Left‑aligned |
| 2 | 4 | Green | 1x1 | Left‑aligned |
| 3 | 5 | Blue | 1x1 | Left‑aligned |
Observations
- Number of squares: +1 each step → linear rule:
n = 3 + (k-1) - Color: Red → Green → Blue → cycle of 3 → formula:
color[k] = cycle[(k-1) mod 3] - Size & Position: unchanged → constant.
Prediction for Figure 4
n = 3 + (4-1) = 6squarescolor = cycle[(4-1) mod 3] = cycle[0] = Red- All other attributes unchanged.
Answer: 6 red squares in a row.
4. Tricky Points & Common Pitfalls
| # | Pitfall | Why it’s problematic | How to avoid |
|---|---|---|---|
| 1 | Assuming a single attribute change | A series may hide a dual rule (count + color). | Build a full attribute table; check all attributes for consistent patterns. |
| 2 | Misidentifying the starting point |