Inequality Puzzle

Inequality Puzzle problems present comparative clues about a set of elements (e.g., A > B, B < C, C > D). You must use these clues to arrange all elements in order and answer questions about which element is largest, smallest, or in a specific position. These problems test your ability to build a complete ordering from partial comparative information.

10Worksheets
200+Practice Questions
HardDifficulty
2-3 hoursHours to Master

Introduction to Inequality Puzzle

Inequality Puzzle problems present comparative clues about a set of elements (e.g., A > B, B < C, C > D). You must use these clues to arrange all elements in order and answer questions about which element is largest, smallest, or in a specific position. These problems test your ability to build a complete ordering from partial comparative information.

Prerequisites

Comparative reasoning Transitive property Ordering and ranking Logical deduction from partial information
Why This Matters: Inequality Puzzle problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test ordering and arrangement skills.

How to Solve Inequality Puzzle Problems

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Step 1: List all elements mentioned in the clues

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Step 2: Translate each clue into an inequality (e.g., 'A is taller than B' → A > B)

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Step 3: Build a chain or network of relationships using transitivity

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Step 4: Identify the largest element (no element greater than it)

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Step 5: Identify the smallest element (no element less than it)

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Step 6: Arrange all elements in order from largest to smallest

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Step 7: Answer the specific question (largest, smallest, middle, or position)

Pro Strategy: Start with the strongest relationships. Use transitivity to combine clues into a single chain when possible. If the clues create a partial order (not fully connected), identify the extremes by finding elements that are never less than any other (for largest) or never greater than any other (for smallest).

Example Problem

Example: Arrange A, B, C, D, E using clues: A > B, C < B, D > E, C > D. Which is largest? Solution: Step 1: Elements: A, B, C, D, E Step 2: Clues: A > B, C < B (means B > C), D > E, C > D Step 3: Combine: A > B > C > D > E Step 4: Chain: A > B > C > D > E Step 5: A is greater than all others → largest is A Answer: A is the largest

Pro Tips & Tricks

  • Draw a vertical line with largest at top, smallest at bottom
  • Place elements with known relationships first
  • Use transitivity to fill gaps in the ordering
  • If a chain cannot be fully determined, identify the known extremes
  • Elements that appear only on the 'greater than' side are candidates for largest
  • Elements that appear only on the 'less than' side are candidates for smallest

Shortcut Methods to Solve Faster

Largest = element with no incoming 'greater than' relationships from others
Smallest = element with no incoming 'less than' relationships from others
If a complete chain is formed, the first is largest, last is smallest
Count how many elements each element is greater than to determine relative position

Common Mistakes to Avoid

Misreading the direction of inequalities (A > B means A is greater)
Forgetting to use transitive property to connect separate clues
Assuming all elements can be ordered when clues may be incomplete
Missing that some clues may be redundant or contradictory

Exam Importance

Inequality Puzzle 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
1-2 questions
GMAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Inequality Puzzle?

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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