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Comparison Chains

Comparison Chains problems involve a series of linked comparisons (e.g., A > B, B > C, C > D) that together form a complete ordering. These problems test your ability to chain comparisons using the transitive property and fill in missing links.

10Worksheets
200+Practice Questions
Easy to 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 Comparison Chains

Comparison Chains problems involve a series of linked comparisons (e.g., A > B, B > C, C > D) that together form a complete ordering. These problems test your ability to chain comparisons using the transitive property and fill in missing links.

Prerequisites

Understanding of transitive property Basic inequality chaining Logical deduction Comparative terms
Why This Matters: Comparison Chains are fundamental to ranking puzzles. You can expect 2-3 questions in SSC CGL and Banking exams.

How to Solve Comparison Chains Problems

1

Step 1: List all given comparison statements

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Step 2: Arrange them to form a continuous chain when possible

3

Step 3: Use transitive property: If A > B and B > C, then A > C

4

Step 4: Identify missing links in the chain

5

Step 5: Determine the complete order from highest to lowest

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Step 6: Answer questions about specific positions

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Step 7: Verify all given comparisons are satisfied

Pro Strategy: Convert all statements to use the same inequality direction (e.g., always use > for 'greater than'). Use transitive property to connect statements. Look for the person who is greater than everyone else (top) and less than everyone else (bottom).

Example Problem

Example: A > B, C < B, D > A, E < C. Arrange in descending order. Solution: Step 1: Rewrite all with > direction: A > B, B > C, D > A, C > E Step 2: Chain: D > A > B > C > E Step 3: Descending order: D, A, B, C, E Answer: D > A > B > C > E

Pro Tips & Tricks

  • Convert 'A is less than B' to 'B > A'
  • Chain statements by finding common terms
  • If A > B and B > C, then A > C (transitive)
  • The longest chain often gives the complete order
  • If no direct comparison exists, check indirect through intermediates
  • Multiple chains may need to be merged

Shortcut Methods to Solve Faster

If A > B and B > C, then A > C automatically
The tallest person has no one above them in the chain
The shortest person has no one below them
The complete order is a total ordering of all items

Common Mistakes to Avoid

Reversing inequality direction when chaining
Assuming transitivity across non-linear relationships
Missing intermediate connections that complete the chain
Creating circular comparisons (A > B > C > A)

Exam Importance

Comparison Chains is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Comparison Chains?

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