📚 Quantitative Aptitude – Tables
Puducherry Teacher Eligibility Test (TET) – Competitive Exam Focus
This note focuses on “Tables” as used in the quantitative aptitude section of competitive exams.
In the Indian context, “Tables” mainly refers to
- Circular arrangements (people around a table)
- Quick‑reference tables (multiplication, squares, binomials, etc.)
Both are covered here with rigorous derivations, useful formulae, common pitfalls, and a hard practice problem.
1. What is a “Table” in Aptitude?
| Interpretation | Typical Questions | Key Idea |
|---|---|---|
| Circular Table | “How many ways can 8 students sit around a round table?” | Seating is invariant under rotation. |
| Multiple Tables | “How many ways can 24 students be seated on 4 tables, each seating 6?” | Partitioning and arranging at each table. |
| Quick‑reference Tables | “Find 7×9, 12², 5C3” | Pre‑computed values to save time. |
Goal – Learn the combinatorial principles that underpin all these variants.
2. Circular Permutations
2.1 Basic Formula
For n distinct people around an unlabelled round table:
[ \boxed{P_{\text{circular}}(n) = (n-1)!} ]
Why (n‑1)!?
- Fix one person as a reference (break the symmetry).
- Arrange the remaining (n-1) people in a line: ((n-1)!) ways.
2.2 Derivation
- Start with linear permutations: (n!) ways to seat n people in a row.
- Identify equivalent seatings: A rotation by one seat turns one arrangement into another.
- Count rotations: For any arrangement, there are exactly n rotations (shift by 0,1,…,n−1).
- Divide: ( \frac{n!}{n} = (n-1)! ).
3. Circular Permutations with Identical Objects
If some people are indistinguishable (e.g., 2