Quantitative Aptitude – Tables
(For Himachal Pradesh PSC – Quantitative Aptitude Section)
Tables in quantitative aptitude refer to pre‑computed lists of numbers (squares, cubes, factorials, powers, logs, etc.) that help you answer questions quickly and accurately.
They are especially useful when a problem requires repeated or large calculations.
1. Simple Explanation
Tables are shorthand for “ready‑made data.”
Instead of doing a long multiplication, finding a square root, or computing a factorial from scratch, you look up the answer in a table.
For the PSC exam you may:
| Table | What it gives | Typical use |
|---|---|---|
| Multiplication tables (1–12) | Product of two numbers | Quick multiplication, solving word problems |
| Squares & Cube tables | (n^2), (n^3) | Finding squares, cubes, or working backwards |
| Factorial tables | (n!) | Permutations/combination calculations |
| Powers of 2, 3, 5, 10 | (2^n, 3^n, 5^n, 10^n) | Exponential growth questions |
| Logarithm tables | (\log_{10} n) | Solving problems involving logs or ratios |
| Trigonometric tables | (\sin, \cos, \tan) (in degrees) | Geometry, right‑triangle problems |
| Square‑root tables | (\sqrt{n}) | Estimating or exact root values |
Why tables?
• Saves time.
• Reduces arithmetic errors.
• Allows you to focus on logic rather than calculation.
2. Key Points
2.1 Types of Tables You Should Know
| Table | Key Facts | Memorisation Tips |
|---|---|---|
| 1–12 Multiplication Tables | 1×1 to 12×12 | Practice daily; use flashcards |
| Square Table (1–100) | (n^2) for 1–100 | Notice pattern ( (n+1)^2 = n^2 + 2n + 1) |
| Cube Table (1–20) | (n^3) for 1–20 | Use the identity ( (n+1)^3 = n^3 + 3n^2 + 3n + 1) |
| Factorial Table (1–10) | (n!) for 1–10 | Remember 5! = 120, 6! = 720, 7! = 5040 |
| Powers of 2 (2⁰–2¹⁰) | (2^n) | 2⁰=1, 2¹=2, 2²=4, …; double each step |
| Powers of 3 (3⁰–3⁸) | (3^n) | 3⁰=1, 3¹=3, 3²=9, … |
| Powers of 5 (5⁰–5⁶) | (5^n) | 5⁰=1, 5¹=5, 5²=25, … |
| Logarithm Table (1–10, 100) | (\log_{10} n) | 1→0, 10→1, 100→2; approximate others |
| Trigonometric Table (0°–90°, 15° increments) | (\sin, \cos, \tan) | Memorise key angles: 30°, 45°, 60° |
2.2 How to Use Tables Effectively
- Identify the needed quantity – e.g., “What is (7^3)?” → look at the cube table.
- Cross‑check – If the number isn’t in your small table, use a simple formula (e.g., (n^3 = n \times n^2)).
- Use patterns – Recognise that (n^2) ends in the same digit as (n) when (n) ends in 0 or 5.
- Approximate when necessary – For logs or roots not memorised, use nearby values and linear interpolation.
- Keep a pocket‑sized reference – If allowed, carry a small printed table or a mobile app.
2.3 Common Pitfalls
| Pitfall | Fix |
|---|---|
| Assuming pattern continues | Verify with a quick mental check or a small calculation. |
| Mixing up base | Remember that log tables are base‑10 unless otherwise stated. |
| Forgetting the index | Keep the index (e.g., (n)) aligned; otherwise you’ll pick the wrong value. |
| **Over‑ |