Study Notes – Reasoning Ability
Topic: Figure Series
Exam – Village Development Officer (VDO)
Section – Reasoning Ability
Time to Solve – 5–10 minutes
1. Simple Explanation
A Figure Series (also called “Diagram Sequence”) presents a set of geometric figures (shapes, blocks, numbers, etc.) arranged in a linear order.
Each figure in the series is obtained by applying a consistent rule or a combination of rules (addition, subtraction, rotation, reflection, scaling, color change, etc.) to its predecessor.
Your task is to identify the rule and pick the figure that completes the series.
2. Key Points to Remember
| # | Concept | What to Look For | Tips |
|---|---|---|---|
| 1 | Count of elements | Number of shapes, dots, lines, etc. | Increase/decrease by a fixed amount or alternate. |
| 2 | Shape type | Circle → Square → Triangle… | Often the shape itself changes in a cyclic pattern. |
| 3 | Orientation | Rotation, flipping, mirroring | Check if the figure is turned 90°, 180°, etc. |
| 4 | Color | Red → Blue → Green… | Color may follow a sequence or correspond to shape changes. |
| 5 | Size | Scaling up/down | Linear, exponential, or alternating. |
| 6 | Position | Left‑to‑right, top‑to‑bottom, diagonal | Move in a grid or rotate around a pivot. |
| 7 | Number of figures in a group | 1, 2, 3… | The group size may grow or shrink. |
| 8 | Combination of rules | Two or more of the above simultaneously | Identify the simplest rule first; then add more if needed. |
| 9 | Symmetry | Mirror symmetry, rotational symmetry | Look for symmetrical patterns across axes or around a centre. |
| 10 | Edge or interior changes | Filling or emptying of shapes | “Fill” or “hollow” may alternate. |
3. Step‑by‑Step Method
| Step | Action | Example |
|---|---|---|
| 1. Observe | Look at the first two figures. | If Fig 1 is a single red circle, Fig 2 is a single blue square. |
| 2. Identify changes | Note what changed: shape, colour, number, orientation, etc. | Shape changed from circle to square; colour from red to blue. |
| 3. Test a rule | Apply the change to Fig 2 to get Fig 3. | If the rule is “next shape in the order Circle→Square→Triangle”, then Fig 3 should be a triangle. |
| 4. Verify | Check if the rule holds for the next pair(s). | If Fig 3 is a triangle and Fig 4 is a square, the rule may be “alternating shapes.” |
| 5. Combine rules | If one change doesn’t explain the whole series, add others (e.g., colour alternates too). | Shape alternates, colour alternates, making a 4‑figure repeating block. |
| 6. Choose the answer | Apply the final rule to the last given figure to find the missing one. | If Fig 8 is a blue square, the next will be a red triangle. |
4. Worked Example
Series:
Figure 1: 1 red circle
Figure 2: 1 blue square
Figure 3: 2 red triangles
Figure 4: 2 blue squares
Figure 5: 3 red circles
Figure 6: 3 blue triangles
Question: What is Figure 7?
Step 1 – Observe
- Shape sequence: Circle → Square → Triangle → Square → Circle → Triangle
- Colour sequence: Red → Blue → Red → Blue → Red → Blue
- Count sequence: 1 → 1 → 2 → 2 → 3 → 3
Step 2 – Identify Rules
- Number of shapes increases by 1 every two figures (1,1,2,2,3,3,…).
- Colour alternates Red ↔ Blue.
- Shape follows a 3‑term cycle: Circle → Square → Triangle → (back to) Square → Circle → Triangle …
(Notice the cycle length is 4 after the first figure: Square repeats.)
Step 3 – Predict Figure 7
- Count: Next in the pair pattern → 4 shapes.
- Colour: After Blue → Red.
- Shape: Continuing the cycle → Square (since after Triangle comes Square).
Thus Figure 7 should contain 4 red squares.
Answer
Figure 7: 4 red squares
5. Quick Revision Summary
| Topic | What to Remember |
|---|---|
| Definition | Figure series → sequence of geometric figures governed by a rule. |
| Common Changes | Count, shape, colour, orientation, size, position, symmetry. |
| Method | 1. Observe 2. Identify change(s) 3. Test rule 4. Verify 5. Combine 6. Choose. |
| Typical Patterns | Alternating, cyclic, incremental, mirroring, scaling. |
| Practice Tip | Sketch each figure; highlight differences; write a short rule sentence. |
| Answer Check | Ensure the rule is consistent across all given figures. |
Final Thought
In a timed exam, look for the simplest rule first. If the simplest rule does not fit, layer on another change. Most figure‑series questions rely on one or two basic transformations. Good luck!