Ranking & Order
Ranking & Order questions test your ability to calculate a person's absolute position inside a row or group, managing overlapping counts from both ends of the line.
Fundamental Principles
Total Identity Formula
The linear sorting equation establishing that the total count of a line equals a person's rank from the left plus their rank from the right minus one, written as: $$Total = Left + Right - 1$$.
Essential Formulation Tips
- Always remember to subtract one when adding a person's rank from both ends. If you don't, you end up counting that same individual twice.
- When two people swap places in a queue, use the person whose new position is fully known to calculate the line's total count before solving the rest of the problem.
Shortcut Execution Techniques
- The Double Count Adjuster: If a question asks for the total number of people standing *between* two ranks, use the formula: $$Between = (Higher Rank - Lower Rank) - 1$$, provided both ranks are measured from the same side.
Contextual Inquiries (FAQs)
Q: Why does the formula subtract one when calculating total row volume?
A: Because the targeted individual is included once in the left-side count and once in the right-side count. Subtracting one corrects this double-counting.
Example Breakdown: Resolving Overlapping Queue Positions
Demonstrates standard linear queue counting logic.Identify known positional indices: Left/Top rank = 15; Right/Bottom rank = 24.
Apply the Total Identity Formula: $$Total = 15 + 24 - 1$$
Perform arithmetic: 15 + 24 = 39; 39 - 1 = 38.
Conclusion: There are exactly 38 candidates in the row.
Queue Index Sorting
Practice adjusting overlapping positions and calculating linear queue volumes.
Q1. Kiran ranks 11th from the front of a queue and Sam ranks 18th from the rear. If they swap positions, Kiran becomes 21st from the front. What is the total number of people in the queue?