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Box Size Comparison

Box Size Comparison problems involve stacking boxes by size (larger below smaller) with additional inequality constraints. They often include removal scenarios where a box is taken out and you must determine the new arrangement.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 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 Box Size Comparison

Box Size Comparison problems involve stacking boxes by size (larger below smaller) with additional inequality constraints. They often include removal scenarios where a box is taken out and you must determine the new arrangement.

Prerequisites

Transitive inequalities Size ordering (larger/smaller) Stacking rule (larger below smaller) Removal and shifting
Why This Matters: Size Comparison problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test transitive ordering and scenario analysis.

How to Solve Box Size Comparison Problems

1

Step 1: Build complete size order using given inequalities

2

Step 2: Map size order to stack positions (largest at bottom)

3

Step 3: For removal questions, remove the specified box

4

Step 4: Remaining boxes shift up while maintaining size order

5

Step 5: Determine the box at the new position

6

Step 6: Verify all constraints

Pro Strategy: Build the complete size chain using transitive property. Stack order = reverse of size order (largest at bottom). For removal, shift boxes above the removed position down by one.

Example Problem

Example: Boxes A-E stacked (positions 1-5 bottom to top). Larger below smaller. A > B but A < C. D lightest. E > A but E < C. B > D. If D removed, which box at position 4? Solution: Step 1: Size chain: C > E > A > B > D Step 2: Original: 1=C,2=E,3=A,4=B,5=D Step 3: Remove D (position 5) Step 4: New stack: 1=C,2=E,3=A,4=B Step 5: Position 4 = B Answer: Box B

Pro Tips & Tricks

  • Complete size chain: heaviest > ... > lightest
  • Stack: position 1 = heaviest, position N = lightest
  • Removing a box: all boxes above shift down one position
  • The number of boxes decreases by 1 after removal
  • Size order remains the same among remaining boxes
  • If multiple boxes have equal size (rare), constraints may be ambiguous

Shortcut Methods to Solve Faster

Remaining stack order = original order with removed box omitted
New position of a box = original position - (1 if above removed, else 0)
The lightest box is at top, heaviest at bottom

Common Mistakes to Avoid

Not building the complete size chain before stacking
Placing heaviest at top (reverse of correct rule)
Forgetting that boxes above the removed box shift down
Keeping the removed box in the stack

Exam Importance

Box Size Comparison 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
INSURANCE
1-2 questions

Ready to Master Box Size Comparison?

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

20 practice questions
Detailed solutions
Step-by-step explanations
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