Multiple Statements
Multiple Statements problems present 2 or 3 independent coded inequality statements. These statements may share common variables, allowing you to combine information across statements. You must determine which conclusions logically follow from the combined information.
What You'll Learn
Introduction to Multiple Statements
Multiple Statements problems present 2 or 3 independent coded inequality statements. These statements may share common variables, allowing you to combine information across statements. You must determine which conclusions logically follow from the combined information.
Prerequisites
How to Solve Multiple Statements 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
Step 8: Determine which conclusions must be true
Example Problem
Example: If @ = >, # = <, decode: Statement 1: A @ B, Statement 2: B # C. Which conclusion follows? Solution: Step 1: Decode S1: A > B, S2: B < C Step 2: Combine: A > B < C Step 3: A and C have opposite signs → no direct relation Step 4: Conclusion 'A > C' does not follow Step 5: Conclusion 'B < C' follows (directly from S2) Step 6: Conclusion 'A > B' follows (directly from S1) 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, you can 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 Multiple Statements. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Multiple Statements is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Multiple Statements?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: