ReasoningAbility.com

Open vs Closed Shapes

Open vs Closed Shapes problems present five figures where four are closed shapes (continuous boundary enclosing area) and one is an open shape (boundary has a gap). You must identify which figure is open. These problems test understanding of boundary continuity and shape completeness.

10Worksheets
200+Practice Questions
MediumDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Open vs Closed Shapes

Open vs Closed Shapes problems present five figures where four are closed shapes (continuous boundary enclosing area) and one is an open shape (boundary has a gap). You must identify which figure is open. These problems test understanding of boundary continuity and shape completeness.

Prerequisites

Understanding of closed shapes (continuous boundary) Understanding of open shapes (gap in boundary) Visual tracing skills Boundary analysis
Why This Matters: Open vs Closed Shapes appears in 1-2 questions in SSC CGL and Banking PO exams. It tests boundary analysis and shape completeness.

How to Solve Open vs Closed Shapes Problems

1

Step 1: Trace the boundary of each figure mentally

2

Step 2: Determine if you can return to the starting point without lifting your finger

3

Step 3: Figures where boundary is continuous are closed

4

Step 4: Figures with a gap in the boundary are open

5

Step 5: The open figure is the odd one out (or closed figure if majority are open)

Pro Strategy: Trace the boundary with your finger mentally. If you can go around and return to start without lifting, it's closed. If there's a break or gap, it's open.

Example Problem

Example: Four complete circles, one incomplete arc. Which is odd? Solution: Step 1: Circles have continuous boundaries (closed) Step 2: Arc has a gap (open) Step 3: Most common = closed Step 4: Open arc is different Answer: The open arc is the odd one out

Pro Tips & Tricks

  • Closed shapes: circles, squares, triangles, polygons
  • Open shapes: arcs, line segments, incomplete curves
  • A shape with a gap cannot enclose area
  • The open shape often appears as a curve or arc

Shortcut Methods to Solve Faster

If the shape encloses area, it's closed
If you can see through a gap in the boundary, it's open
Most figures in competitive exams are closed; the open one is the outlier

Common Mistakes to Avoid

Not tracing the entire boundary
Confusing a thick line with a closed shape
Missing small gaps in the boundary

Exam Importance

Open vs Closed Shapes is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
0-1 questions
GMAT
0-1 questions
INSURANCE
1-2 questions

Ready to Master Open vs Closed Shapes?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now