Paper Cutting & Paper Folding – General Aptitude for GATE, PSU, ESE, AE/JE | Priyanka Ma’am

Paper Cutting and Paper Folding are important topics in Spatial Aptitude under General Aptitude and are frequently asked in GATE, PSU, ESE, AE/JE exams. These questions test your visualization and analytical thinking skills.

Basic Concepts

These problems involve folding a paper multiple times and then cutting or punching holes. You need to determine the final pattern when the paper is unfolded.

• Paper Folding: Folding a sheet in different directions
• Paper Cutting: Cutting or punching holes after folding

Important Concepts

1. Symmetry

When paper is folded, cuts are mirrored on all folded sections.

2. Number of Layers

Each fold doubles the number of layers:

• 1 fold → 2 layers
• 2 folds → 4 layers
• 3 folds → 8 layers

3. Direction of Folding

Understand whether folding is horizontal, vertical, or diagonal.

4. Position of Cut

The location of the cut determines final pattern after unfolding.

Types of Questions

• Single fold + single cut
• Multiple folds + multiple cuts
• Hole punching problems
• Symmetry-based pattern questions

Solved Examples

Example 1

A paper is folded once and one hole is punched. How many holes after unfolding?

1 fold → 2 layers → 2 holes

Example 2

Paper folded twice and one cut made. Find number of cuts after unfolding.

2 folds → 4 layers → 4 cuts

Example 3

Paper folded three times and one hole punched. Total holes?

3 folds → 8 layers → 8 holes

Example 4

A square paper is folded twice and a corner is cut. What will be the pattern?

Cut will appear symmetrically on all unfolded layers → 4 identical cuts at symmetric positions

Shortcut Tricks

• Count folds → calculate layers (2ⁿ)
• Visualize symmetry clearly
• Track direction of folds carefully
• Practice mental unfolding

Questions

Q1. Paper folded 4 times, one hole punched. Total holes?

2⁴ = 16 holes

Q2. Paper folded twice, two cuts made. Total cuts after unfolding?

4 layers × 2 cuts = 8 cuts

Exam Tips

• Always count folds first
• Use 2ⁿ formula for layers
• Focus on symmetry and position
• Avoid guesswork, visualize properly

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