A circular sheet of paper is folded along the lines in the directions shown.
The paper, after being punched in the final folded state as shown and
unfolded in the reverse order of folding, will look like
Options:
(A) Symmetric 4-quadrant punched circle pattern (matching unfolded quadrant perforations)
(B) Asymmetric dual punch pattern
(C) Single central hole pattern
(D) Diagonal 2-corner punch pattern
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.4)**
**1. Governing Concept**:
- **Topic**: Spatial Aptitude & Paper Folding and Unfolding
- A circular paper is folded in half (semi-circle) and then folded in half again (quadrant of $90^\circ$).
- A circular punch is made through the folded quadrant.
- When unfolded in reverse sequence:
- Unfolding back to the semi-circle reflects the punch across the second fold line.
- Unfolding to the full circle reflects both punches across the diameter fold line.
- This generates a symmetric array of 4 circular holes arranged symmetrically across the four quadrants of the circular sheet.
**2. Option Analysis**:
- **Option (A) is CORRECT**: Shows the 4 symmetrically disposed holes matching the quadrant fold reflections.
- **Option (B) is INCORRECT**: Lacks 4-fold radial reflection.
- **Option (C) is INCORRECT**: Depicts a single central hole.
- **Option (D) is INCORRECT**: Asymmetric 2-hole pattern.
**3. Final Answer**:
- **Correct Choice**: **A**
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