Figure Series

Figure series questions are a common and important part of the General Intelligence and Reasoning section in competitive exams like SSC CGL. These questions test your ability to identify patterns, logical progression, and relationships between a sequence of figures. The core idea is to understand the rule or transformation that governs the series and then apply it to predict the next figure in the sequence or find the missing figure.

In a typical figure series question, you will be presented with a set of figures arranged in a specific order. You need to carefully observe these figures and deduce the underlying logic. This logic can involve various types of transformations, such as rotation, reflection, addition or deletion of elements, changes in size or position, combination of shapes, or a combination of these.

Types of Transformations to Look For

To excel in figure series, you must be adept at spotting different types of transformations. Let's break down the common ones:

1. Rotation

Figures might rotate clockwise or counter-clockwise. The rotation can be by a fixed angle (e.g., 45°, 90°, 180°) or by a variable angle. Sometimes, the entire figure rotates, or only a specific component within the figure rotates.

• Clockwise Rotation: The figure turns in the direction of the clock hands.
• Counter-Clockwise Rotation: The figure turns in the opposite direction of the clock hands.
• Angle of Rotation: Pay attention to the degree of rotation. Is it consistent? Does it increase or decrease?

2. Reflection

Reflection involves mirroring an image. This can be across a vertical axis (like a mirror placed to the side), a horizontal axis (like a mirror placed above or below), or even a diagonal axis.

• Horizontal Reflection: The left side becomes the right side, and vice versa.
• Vertical Reflection: The top becomes the bottom, and vice versa.

3. Movement (Translation)

Elements within the figure or the entire figure may shift their position. This movement can be:

• Direction: Up, down, left, right, or diagonal.
• Distance: Does the element move a fixed number of steps or spaces? Does the distance increase or decrease?

4. Addition or Deletion of Elements

New elements might be added to the figure in each step, or existing elements might be removed.

• Number of Elements: Does the count of a particular shape or symbol increase or decrease?
• Location of Addition/Deletion: Where are the elements added or removed? Often, there's a pattern to this, like adding to the next corner or deleting from the top.

5. Change in Size or Shape

The size of elements (increasing or decreasing) or their shape (e.g., a circle becoming a square, a line becoming a curve) can change according to a rule.

6. Combination of Elements

Sometimes, two or more figures combine to form the next figure in the series. This could involve overlapping shapes, merging elements, or applying logical operations (like AND, OR, XOR on shapes).

7. Change in Shading or Filling

The shading or filling pattern of a figure might change systematically. For instance, a sector of a circle might get filled, or a shaded region might move to an adjacent section.

8. Internal Elements and Borders

Pay attention to both the outer boundary of the figure and any internal lines or shapes. Both can be subject to transformations independently or dependently.

How to Approach Figure Series Questions

Solving figure series questions requires a systematic approach. Follow these steps:

1. Analyze the First Few Figures: Look at the first two or three figures and try to identify the most obvious changes. Is there a rotation? A new element appearing?
2. Identify the Pattern: Once you have a potential rule, check if it holds true for the subsequent figures in the given series. If the pattern breaks, re-evaluate your initial assumptions.
3. Look for Multiple Patterns: Sometimes, there might be more than one logical pattern. Choose the simplest and most consistent one. Often, exam questions are designed with a primary, clear pattern.
4. Consider Components Separately: If a figure has multiple parts (e.g., a square with a diagonal line and a circle inside), analyze the movement or changes of each component individually.
5. Check for Clockwise vs. Counter-Clockwise: Be precise about the direction of rotation or movement.
6. Count Elements: Keep a tally of specific shapes or symbols if they appear to be added or removed.
7. Focus on Position: Track the positions of elements. Are they moving along the perimeter? Moving towards the center?
8. Test Potential Answers: If you are given options, you can sometimes work backward from the options to see which one logically follows the established pattern.

Example Scenarios and Explanations

Let's illustrate with some common patterns.

Scenario 1: Simple Rotation and Addition

Imagine a series starting with a triangle. Figure 1: A triangle. Figure 2: The triangle rotated 90° clockwise and a square added inside. Figure 3: The figure from step 2, with the triangle rotated another 90° clockwise, and the square inside also rotated 90° clockwise. A circle is added.

Analysis:

• The triangle is rotating 90° clockwise in each step.
• A new shape is added in each step (square, then circle).
• The newly added shape also rotates 90° clockwise in the subsequent step.

The next figure would have the triangle rotated another 90°, the square rotated another 90°, the circle rotated another 90°, and a new shape (e.g., a pentagon) would be added, also rotating 90°.

Scenario 2: Movement of an Element

Consider a square with a dot inside. Figure 1: Square with dot in the top-left corner. Figure 2: Square with dot in the top-right corner. Figure 3: Square with dot in the bottom-right corner.

Analysis:

• The dot moves clockwise along the perimeter of the square.
• It moves one corner at a time.

The next figure would have the dot in the bottom-left corner.

Scenario 3: Change in Number of Sides/Elements

A series of polygons. Figure 1: Triangle (3 sides). Figure 2: Square (4 sides). Figure 3: Pentagon (5 sides).

Analysis:

• Each figure is a regular polygon.
• The number of sides increases by one in each step (3, 4, 5).

The next figure would be a hexagon (6 sides).

Scenario 4: Internal Line Transformations

A rectangle with internal lines. Figure 1: Rectangle with one vertical line dividing it in half. Figure 2: Rectangle with two vertical lines dividing it into thirds. Figure 3: Rectangle with one horizontal line dividing it in half.

Analysis:

• In step 1, a vertical line is added.
• In step 2, another vertical line is added.
• In step 3, the orientation of the lines changes from vertical to horizontal, and the number of lines might reset or follow a new rule. This type can be tricky. Let's assume a pattern: Alternate between adding vertical lines and adding horizontal lines.

If the pattern is "add vertical lines, then add horizontal lines", the next step might involve adding a second horizontal line to divide the rectangle into thirds horizontally. Or, if the pattern is "add one line, then add one line, then change orientation and start again", it could be one horizontal line. Careful observation is key.

Scenario 5: Combination and Interaction

A circle and a square. Figure 1: A circle to the left of a square. Figure 2: The circle is now inside the square. Figure 3: The square is now inside the circle.

Analysis:

• The relative positions of the circle and square change.
• There seems to be an alternating pattern of containment: Circle outside Square, then Circle inside Square, then Square inside Circle.

The next figure might revert to the circle being outside the square, perhaps to the right this time, or the pattern of containment might continue if a third shape was involved.

Common Pitfalls and How to Avoid Them

Students often make mistakes in figure series due to overlooking details or assuming patterns too quickly.

• Overlooking Minor Changes: A slight shift in position, a change in shading, or the addition of a small dot can be crucial. Always examine every part of the figure.
• Focusing on Only One Element: If a figure has multiple components, don't just track one. Ensure the pattern applies to all relevant parts.
• Incorrect Direction/Angle: Mistaking clockwise for counter-clockwise or misjudging the angle of rotation is common. Double-check these.
• Assuming Linearity When It's Not: Not all patterns are simple additions or rotations. Sometimes, elements might disappear and reappear, or the rule might change based on the step number.
• Getting Confused by Complexity: Break down complex figures into simpler components and analyze each one's transformation.

Practice is Key

Figure series questions, like many reasoning problems, improve significantly with practice. The more examples you work through, the quicker you will become at recognizing common patterns and identifying the specific logic in new problems.

When practicing, don't just solve the problem; analyze *why* the answer is correct. Understand the rule. If you get a question wrong, revisit it later and try to figure out the pattern you missed. This deliberate practice will build your analytical skills and speed, which are essential for performing well under exam conditions.