Ranking & Ordering
Ranking and ordering questions describe positions from the front, back, top, bottom, or relative to other people. The key is to represent positions consistently and use simple rank formulas or a short ordered chain rather than trying to visualize the entire group mentally.
Common patterns
- Converting a rank from the front to a rank from the back
- Finding the total from ranks at both ends
- Counting people between two known positions
- Updating ranks after two people swap
- Building a relative order from pairwise comparisons
Worked example
Question: Riya is 7th from the front in a line of 20. What is her rank from the back?
Answer: 14th
Back rank = 20 − 7 + 1 = 14.
How to approach Ranking & Ordering
- Fix the reference end — Write each given rank with its direction — front/back or top/bottom — so positions from opposite ends are not mixed.
- Use the rank formula or chain — For opposite-end ranks use total − rank + 1 or top + bottom − 1; for comparisons, write a clear left-to-right or high-to-low chain.
- Recheck inclusive counting — Remember that the ranked person is counted at both ends and that people “between” two positions exclude both endpoints.