UGC‑NET Reasoning Ability – Figure Series
Figure series (also called figure sequence or picture series) are a staple of reasoning sections. You are given a set of pictorial patterns and must predict the next figure or choose the figure that completes the sequence from a set of options.
1. Simple Explanation
- A figure series is a chain of two‑ or three‑dimensional shapes that follow a rule.
- The rule can involve geometry (rotation, reflection, scaling), counting (number of elements, symmetry axes), or logical progression (adding, removing, or rearranging parts).
- Your task:
- Identify the rule that governs the transition from one figure to the next.
- Apply the rule to the last figure to get the next one.
- Select the answer that matches this predicted figure.
2. Key Points to Remember
| # | Concept | What to look for | Typical Questions |
|---|---|---|---|
| 1 | Translation | Same shape shifted horizontally/vertically. | “Find the figure that appears after shifting left by one cell.” |
| 2 | Rotation | Same shape rotated by a fixed angle (90°, 180°, etc.). | “After rotating 90° clockwise, which figure is next?” |
| 3 | Reflection | Mirror image across an axis. | “Which figure shows a reflection across the vertical axis?” |
| 4 | Scaling (Enlargement/Reduction) | Size changes while retaining proportions. | “Which figure is half the size of the previous one?” |
| 5 | Addition / Subtraction of Elements | New shapes or lines appear/disappear. | “Which figure adds a new triangle to the existing set?” |
| 6 | Symmetry & Axes | Number of symmetry axes increases or changes. | “After adding a symmetry axis, which figure is produced?” |
| 7 | Pattern of Colors/Fill | Color shifts, alternating patterns. | “Which figure changes the fill from solid to striped?” |
| 8 | Number of Elements | Count of shapes or lines follows a numeric series (1, 2, 3, …). | “Which figure has the next number of circles?” |
| 9 | Orientation & Position | Relative positions of shapes change (top → bottom, left → right). | “Which figure moves the square from left to right?” |
| 10 | Combination of Rules | Two or more transformations happen simultaneously. | “Which figure shows a rotation followed by a reflection?” |
Tip: Start with the simplest rule (translation, rotation, reflection). If none fits, try counting elements or symmetry.
3. Worked Example
Question:
Consider the following figure series (grid of 3×3 cells). Each figure is a set of black squares on a white background.
Figure 1
X . . . . . . . .Figure 2
. X . . . . . . .Figure 3
. . X . . . . . .Figure 4
. . . X . . . . .Figure 5
. . . . X . . . .Figure 6
. . . . . X . . .Figure 7
. . . . . . X . .Figure 8
. . . . . . . X .Figure 9
. . . . . . . . X
Which figure comes next?
(Options are shown as 3×3 grids, each containing a single black square.)
Step‑by‑Step Solution
-
Observe the Pattern
- In Figures 1–3, the black square moves rightwards one cell.
- In Figures 4–6, it moves downwards one cell.
- In Figures 7–9, it moves rightwards again, completing a cycle.
-
Identify the Rule
- The square traces a clockwise L‑shaped path:
- Move right 3 cells → move down 3 cells → move right 3 cells → move down 3 cells → …
- The path repeats every 6 figures.
- The square traces a clockwise L‑shaped path:
-
Apply the Rule to the Last Figure (Figure 9)
- Figure 9 has the square at the bottom‑right corner.
- Next step: move down one cell, but the grid is only 3×3 → the square would leave the grid.
- Since the square cannot exit, the series resets to the starting position (Figure 1).
- Therefore, Figure 10 will be the same as Figure 1.
-
Select the Correct Option
- Option that matches Figure 1: a black square in the top‑left cell.
Answer: The next figure is the one with the square in the top‑left cell (same as Figure 1).
4. Quick Revision Summary
| Topic | What to Remember | Quick Check |
|---|---|---|
| Identify simple transforms | Translation → shift; Rotation → 90°/180°; Reflection → mirror. | Look for unchanged shape, only position changes. |
| Count elements | Number of shapes/lines changes systematically. | Add 1, double, subtract 1, etc. |
| Symmetry | Number of symmetry axes increases or decreases. | Count axes before and after. |
| Color/Fill | Alternating color patterns, fill changes. | Spot the color change rule. |
| Complex rules | Combination of two or more of the |