Rank-based Ordering: Scores
Rank-Based Ordering problems involve ranking people by scores or marks (1st = highest score). Clues include direct comparisons (A scored more than B), range statements (A scored less than B but more than C), and extreme position statements (A scored the least).
What You'll Learn
Introduction to Rank-based Ordering: Scores
Rank-Based Ordering problems involve ranking people by scores or marks (1st = highest score). Clues include direct comparisons (A scored more than B), range statements (A scored less than B but more than C), and extreme position statements (A scored the least).
Prerequisites
How to Solve Rank-based Ordering: Scores Problems
Step 1: Determine total number of people to rank
Step 2: Translate clues into inequalities (e.g., 'A > B' means A scored more than B)
Step 3: Build a chain from highest to lowest using transitivity
Step 4: Place people with known extreme ranks (highest, lowest)
Step 5: Use 'between' constraints to place others
Step 6: Fill remaining ranks by elimination
Step 7: Answer questions about specific ranks
Example Problem
Example: Six people scored distinct marks. A scored more than B. C scored less than D but more than E. F scored the least. Find third highest scorer. Solution: Step 1: Rank 1 (highest) to 6 (lowest) Step 2: A > B, D > C > E, F = 6 Step 3: Build chain: D > C > E, A > B, F lowest Step 4: Combine and determine order Step 5: Third highest is rank 3 Answer: Person at rank 3 identified
Pro Tips & Tricks
- Rank 1 = highest score, Rank N = lowest score
- 'More than' means higher rank (smaller rank number)
- 'Less than' means lower rank (larger rank number)
- Transitive: If A > B and B > C, then A > C
- If X scored between Y and Z, then Y > X > Z or Z > X > Y
- Draw a vertical ranking ladder (top = highest)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Rank-based Ordering: Scores. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Rank-based Ordering: Scores is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Rank-based Ordering: Scores?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: