Figure Series – Reasoning Ability
(For Chhattisgarh Police Constable – PG Exam)
1. Simple Explanation
Figure series are a type of problem in which a sequence of geometric figures is given and you have to determine which figure comes next.
Each figure is obtained from its predecessor by applying one or more simple rules such as:
| Rule | Example |
|---|---|
| Addition/Subtraction of elements | Add one more square in each step. |
| Rotation | Rotate the whole figure by 90° each time. |
| Reflection | Mirror the figure horizontally or vertically. |
| Scaling | Increase or decrease the size of the figure. |
| Color change | Change the colour of a part of the figure. |
| Orientation change | Flip the figure left‑right or up‑down. |
| Combination | Two or more of the above rules applied together. |
The key is to spot the common transformation that takes one figure to the next.
2. Key Points to Remember
| # | Point | Why it matters |
|---|---|---|
| 1 | Look at the entire figure first | A global change (rotation, reflection) can be easier than focusing on a single element. |
| 2 | Count elements | Number of shapes, lines, dots, or corners often change systematically. |
| 3 | Check symmetry | Many series involve symmetry changes or mirror images. |
| 4 | Observe orientation | If a figure is slanted, note its angle (30°, 45°, 60°, 90°). |
| 5 | Note colour changes | Colour may cycle through a set (Red → Green → Blue → Red …). |
| 6 | Look for modular patterns | Some series repeat every 2, 3, or 4 figures. |
| 7 | Avoid over‑complicating | Usually one simple rule governs the series; don’t add unnecessary steps. |
| 8 | Eliminate options quickly | If an option contradicts a clear rule, discard it immediately. |
3. Step‑by‑Step Approach
- Write down each figure clearly (draw or mentally sketch).
- Identify the difference between Fig‑1 & Fig‑2, Fig‑2 & Fig‑3, …
- List possible rules that explain all observed differences.
- Test the rule on the last figure to predict the next one.
- Match the predicted figure with the options provided.
4. Worked Example
Question
The following sequence of figures is given.
Which figure will come next?
Figure 1: Two small circles side by side (left → right)
Figure 2: Two small circles plus one large circle above them
Figure 3: Two small circles plus two large circles above them
Figure 4: Two small circles plus three large circles above them
Options
A. 4 large circles above the two small circles
B. 1 large circle above the two small circles
C. 5 large circles above the two small circles
D. 3 large circles above the two small circles
Solution
| Step | Observation | Rule deduced |
|---|---|---|
| 1 | Between Fig‑1 & Fig‑2: +1 large circle added. | Add one large circle each step. |
| 2 | Between Fig‑2 & Fig‑3: +1 large circle again. | Consistent with rule 1. |
| 3 | Between Fig‑3 & Fig‑4: +1 large circle again. | Consistent. |
| 4 | Predict Fig‑5: +1 large circle → 4 large circles. |
Answer: A – Four large circles above the two small circles.
5. Another Example with Rotation
Question
Fig‑1: A triangle pointing upwards
Fig‑2: Same triangle rotated 90° clockwise
Fig‑3: Same triangle rotated 180° from Fig‑1 (i.e., pointing downwards)
Fig‑4: Same triangle rotated 270° clockwise from Fig‑1
Which figure comes next?
Options
A. Triangle pointing upwards again
B. Triangle rotated 90° counter‑clockwise from Fig‑1
C. Triangle rotated 180° clockwise from Fig‑1
D. Triangle rotated 270° counter‑clockwise from Fig‑1
Solution
| Step | Observation | Rule deduced |
|---|---|---|
| 1 | Sequence of rotations: 0°, 90°, 180°, 270° | Increment of 90° clockwise each time. |
| 2 | Next rotation: 360° (full circle) → back to 0° | Triangle pointing upwards again. |
Answer: A – Triangle pointing upwards again.
6. Quick Revision Summary
| Category | What to Check | Typical Pattern |
|---|---|---|
| Number of Elements | Count shapes, dots, lines | +1, +2, +3… or alternating +1 / -1 |
| Orientation | Check angles or direction | 90° rotation, 180° flip |
| Symmetry | Mirror left‑right or top‑bottom | Horizontal flip every 2 steps |
| Size | Size of shapes increases or decreases | Scale by 1.5× each step |
| Colour | Colour changes in a cycle | Red→Green→Blue→Red |
| Combination | Two rules together (e.g., add shape + rotate) | Add + rotate together |
- Always start by comparing Fig‑1 to Fig‑2.
- Once a