Chain Inequalities
Chain Inequalities problems present a single coded statement connecting 3 to 5 variables in a sequence (e.g., A @ B # C % D). You must decode the chain, understand the relationships between consecutive variables, and determine which conclusions about non-consecutive variables follow using the transitive property.
What You'll Learn
Introduction to Chain Inequalities
Chain Inequalities problems present a single coded statement connecting 3 to 5 variables in a sequence (e.g., A @ B # C % D). You must decode the chain, understand the relationships between consecutive variables, and determine which conclusions about non-consecutive variables follow using the transitive property.
Prerequisites
How to Solve Chain Inequalities Problems
Step 1: Note the symbol mapping provided
Step 2: Decode the entire chain by replacing each symbol with its meaning
Step 3: Write the decoded chain (e.g., A > B < C = D ≥ E)
Step 4: Identify the relationship between consecutive variables
Step 5: For conclusions about non-consecutive variables, trace the path through intermediate variables
Step 6: Apply transitive property only when all intermediate signs point in the same direction
Step 7: When signs change direction (e.g., > then <), no definite conclusion exists between the outer variables
Step 8: Evaluate each conclusion and select the correct answer option
Example Problem
Example: If @ = >, # = <, $ = =, % = ≥, decode: A @ B # C $ D % E. Which conclusions follow? Solution: Step 1: Decode: A > B < C = D ≥ E Step 2: Relationships: A > B, B < C, C = D, D ≥ E Step 3: For A and C: A > B < C → signs opposite → no definite relation Step 4: For A and E: A > B < C = D ≥ E → signs mixed → no definite relation Step 5: For B and D: B < C = D → B < D (follows by transitivity) Step 6: For C and E: C = D ≥ E → C ≥ E (follows) Answer: Conclusions stating B < D and C ≥ E follow
Pro Tips & Tricks
- Write the decoded chain with all variables and their relationships
- For transitive conclusions, the path must have consistent direction
- The '=' symbol preserves direction and can be included in any chain
- A path with mixed signs (e.g., > then <) yields no definite conclusion
- To check if A > C follows, the entire path must have only '>' and '=' signs
- To check if A < C follows, the entire path must have only '<' and '=' signs
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Chain Inequalities. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Chain Inequalities is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Chain Inequalities?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: