Compound Inequality
Compound Inequality problems present two or three independent inequality statements that share common variables. You must combine information across statements to determine which conclusions logically follow. These problems test your ability to integrate information from multiple sources and apply transitive property across statements.
What You'll Learn
Introduction to Compound Inequality
Compound Inequality problems present two or three independent inequality statements that share common variables. You must combine information across statements to determine which conclusions logically follow. These problems test your ability to integrate information from multiple sources and apply transitive property across statements.
Prerequisites
How to Solve Compound Inequality Problems
Step 1: Decode each statement individually using the given symbol mapping
Step 2: List all relationships from all statements
Step 3: Identify common variables that appear in multiple statements
Step 4: Combine relationships through common variables to form longer chains
Step 5: Apply transitive property across the combined information
Step 6: If no common variable exists between statements, treat them independently
Step 7: Evaluate each conclusion using all available information
Example Problem
Example: Statements: A > B, B < C. Which conclusion follows? Solution: Step 1: Decode: A > B, B < C Step 2: Combine: A > B < C Step 3: Signs are opposite ( > then < ) → no direct relation between A and C Step 4: Conclusion 'A > C' does not follow Step 5: Conclusion 'B < C' follows directly from second statement Step 6: Conclusion 'A > B' follows directly from first statement Answer: Conclusions that are directly stated follow; transitive conclusions may not follow if signs are mixed
Pro Tips & Tricks
- Statements without common variables cannot be combined
- When statements share a variable, chain them together
- If A > B and B > C, combine to A > B > C
- If A > B and B < C, combine to A > B < C (no A-C relation)
- Write all relationships in a single place for easy reference
- Check if conclusions can be derived directly from any single statement
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Compound Inequality. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Compound Inequality is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Compound Inequality?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: