Figure Series – Reasoning Ability (HTET)
Figure series are a common question type in reasoning tests.
You are given a sequence of shapes or drawings, and you must choose the figure that logically completes the series.
The key is to detect the underlying rule that transforms one figure into the next.
1. Simple Explanation
A figure series is a list of geometrical patterns where each successive figure is derived from the previous one by applying a consistent rule (rotation, reflection, scaling, addition of elements, etc.).
Your job is to:
- Observe every figure carefully.
- Spot the consistent change between consecutive figures.
- Predict the next figure (or choose the correct one from options).
The rule may involve one or more of the following transformations:
| Transformation | What to look for |
|---|---|
| Rotation | Direction (clockwise / counter‑clockwise) and angle (90°, 180°, 270°). |
| Reflection | Mirror image across a vertical, horizontal, or diagonal axis. |
| Translation (shifting) | Movement of the figure along X or Y axis. |
| Scaling (size change) | Enlargement or reduction. |
| Color change | Shift in color(s) of parts of the figure. |
| Number of elements | Addition or removal of shapes or marks. |
| Orientation change | The figure’s orientation relative to the page. |
| Combination | Two or more of the above applied together. |
2. Key Points for Solving
| Step | What to Do | Tips |
|---|---|---|
| 1. List all visible attributes | Shape type, size, color, orientation, number of elements, position, symmetry. | Use a checklist or table. |
| 2. Compare consecutive figures | Note changes in each attribute. | Highlight differences in bold or color. |
| 3. Identify the dominant change | The rule usually involves one primary transformation. | If multiple changes, pick the one that repeats in every step. |
| 4. Test the rule | Apply the identified rule to the last figure to get the next one. | Verify against all options. |
| 5. Double‑check | Make sure no other rule fits better or that you didn't miss a subtle change. | Quick mental check: “Does this rule hold for all steps?” |
3. Worked Example
The Series
| Fig. | Description |
|---|---|
| 1 | A right‑angled triangle with the right angle at the bottom‑left corner (hypotenuse vertical). |
| 2 | Same triangle rotated 90° clockwise (right angle now at bottom‑right). |
| 3 | Triangle rotated another 90° clockwise (right angle at top‑right). |
| 4 | Triangle rotated another 90° clockwise (right angle at top‑left). |
| 5 | Triangle rotated another 90° clockwise (back to bottom‑left). |
Question: Which figure completes the series? (Options A–D)
Step‑by‑Step Analysis
-
Identify the transformation
- Each figure is the previous one rotated 90° clockwise.
-
Confirm consistency
- Fig. 1 → Fig. 2: 90° clockwise.
- Fig. 2 → Fig. 3: 90° clockwise.
- Fig. 3 → Fig. 4: 90° clockwise.
- Fig. 4 → Fig. 5: 90° clockwise.
-
Predict the next figure
- Rotating Fig. 5 another 90° clockwise brings us back to the orientation of Fig. 1.
- Result: A right‑angled triangle with the right angle at the bottom‑left corner.
-
Match with options
- Option A (triangle with right angle at bottom‑left) matches the prediction.
- Other options show different orientations or shapes → discard.
Solution
Correct answer: Option A –