Reverse Direction
Reverse Direction problems present inequality chains that contain changes in direction (e.g., A > B < C). These mixed-sign chains create ambiguity about relationships between outer elements, but some conclusions may be definitely false. You must identify which conclusions contradict the given relationships.
What You'll Learn
Introduction to Reverse Direction
Reverse Direction problems present inequality chains that contain changes in direction (e.g., A > B < C). These mixed-sign chains create ambiguity about relationships between outer elements, but some conclusions may be definitely false. You must identify which conclusions contradict the given relationships.
Prerequisites
How to Solve Reverse Direction Problems
Step 1: Decode all given statements
Step 2: Identify where the inequality direction changes in the chain
Step 3: For outer elements with a direction change in between, no definite relationship exists
Step 4: However, some conclusions may be definitely false (contradict the given relationships)
Step 5: Test each conclusion by checking if it contradicts any established relationship
Step 6: A conclusion is definitely false if it violates a direct or transitive relationship
Step 7: Select the conclusion that cannot be true under any interpretation
Example Problem
Example: Statements: A > B, B < C. Which conclusion is definitely false? Solution: Step 1: Statements: A > B, B < C Step 2: Chain: A > B < C (direction changes at B) Step 3: A and C have no definite relation Step 4: Test conclusion 'A > C': Could be true or false depending on values → not definitely false Step 5: Test conclusion 'A < C': Could be true or false → not definitely false Step 6: Test conclusion 'A = C': Could be true or false → not definitely false Step 7: Test conclusion 'B > A': This contradicts A > B directly → definitely false Answer: B > A is definitely false
Pro Tips & Tricks
- A conclusion that reverses a directly given relationship is definitely false
- A conclusion that claims equality when inequality is strict may be false
- Outer elements with a direction change have no definite relation, so neither '>' nor '<' is definitely false
- Check each conclusion against the transitive closure of consistent-direction segments
- If a conclusion requires a direction change that doesn't exist, it may be false
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Reverse Direction. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Reverse Direction is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Reverse Direction?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: