Delhi TET – Reasoning Ability
Topic: Figure Series
Figure Series questions test your ability to spot a pattern in a sequence of geometric figures (shapes, line‑drawings, arrangements).
You are usually given 4–6 figures and must choose the figure that logically follows.
1. Simple Explanation
A figure series is a visual sequence where each figure is derived from its predecessor by a consistent rule (or set of rules).
The rule can involve:
| Transformation | Example |
|---|---|
| Rotation (90°, 180°, 270°) | A square → rotated square |
| Reflection (mirror image) | A shape → reflected across an axis |
| Scaling (enlarge / shrink) | A triangle → twice the size |
| Translation (shift) | A shape moved right by one unit |
| Color change | Black → white → black |
| Combination | Rotate then scale |
| Creation / deletion | A line added or removed |
Your job is to identify the common rule and predict the next figure.
2. Key Points / Checklist
| Step | What to look for | Tips |
|---|---|---|
| 1. Observe all figures | Shape types, sizes, orientations, colors, number of elements | Write down a quick sketch or list. |
| 2. Identify the operation(s) | Is the shape rotating? Shifting? Size changing? | Look for symmetry: is there a fixed axis? |
| 3. Check consistency | Does the same rule apply to every consecutive pair? | If not, split into sub‑rules (e.g., first two steps one rule, next two another). |
| 4. Look for “missing” operations | Sometimes a figure is “missing” a line or point – the rule may be to add/remove. | Count elements; missing element may be the pattern. |
| 5. Predict the next figure | Apply the rule to the last figure | Verify against multiple answer choices (if MCQ). |
| 6. Double‑check | Does the predicted figure fit all earlier patterns? | If multiple rules fit, choose the simplest. |
Common Pitfalls
- Confusing rotations with reflections – test both if unsure.
- Assuming size changes when only orientation changes – check the actual dimensions.
- Over‑interpreting color changes – color often reflects the “state” (e.g., on/off).
3. Worked Example
Given Series (4 figures) – choose the 5th figure.
Figure 1: Figure 2: Figure 3: Figure 4:
▲ ▲ ▲ ▲
/ \ / \ / \ / \
/___\ /___\ /___\ /___\
- Figure 1 – Equilateral triangle pointing upward.
- Figure 2 – Same triangle rotated 180° → pointing downward.
- Figure 3 – Same triangle rotated 180° again → pointing upward.
- Figure 4 – Same triangle rotated 180° again → pointing downward.
Rule: Every figure is rotated 180° relative to its predecessor.
Prediction: Figure 5 will be a triangle pointing upward (180° rotation from Figure 4).
Answer choice: The upward‑pointing triangle (exactly like Figures 1 & 3).
Another Example (with scaling)
Figure 1: Figure 2: Figure 3:
○ ○○ ○○○
- Figure 1 – One circle.
- Figure 2 – Two circles side‑by‑side.
- Figure 3 – Three circles side‑by‑side.
Rule: Increase the number of identical circles by 1 each step.
Next figure: Four circles side‑by‑side.
4. Quick Revision Summary
- Identify all attributes: shape, size, orientation, color, number of elements.
- Look for simple geometric operations: rotation, reflection, scaling, translation.
- Check consistency: same operation between every consecutive pair.
- Predict by applying the rule to the last figure.
- Verify against all given figures; choose the simplest rule that fits.
- Common patterns:
- Alternating orientation (up/down, left/right).
- Symmetric addition/subtraction (adding a line, deleting a point).
- Progressive scaling (size increases or decreases).
- Color alternation (black/white, red/blue).
Practice tip: Draw a quick sketch for each figure; mark changes with arrows or symbols. The visual aid often reveals the rule instantly.
Good luck with your Delhi TET preparation!