📚 Jammu & Kashmir Patwari / Lekhpal – Quantitative Aptitude
Topic: Tables
Tables in quantitative aptitude usually refer to the multiplication tables (1 – 12) and the tables of powers, factors, LCM/HCF, and common multiples.
Mastering these tables helps in solving a wide range of problems quickly and accurately, which is essential for the Patwari/Lekhpal exam.
1️⃣ Simple Explanation
- Multiplication Tables: A grid that lists the products of two numbers (usually 1 to 12).
- Example: 7 × 9 = 63.
- Powers & Roots Tables: 2² = 4, 3³ = 27, 10¹⁰ = 10,000,000,000.
- Factor & Multiple Tables: For a given number, list all its factors or multiples up to a certain limit.
- LCM/HCF Tables: Quickly find the least common multiple or highest common factor of two numbers.
Why tables matter?
- Speed: Reduces calculation time.
- Accuracy: Minimises mental mishaps.
- Confidence: Allows you to tackle problems that require quick mental arithmetic, e.g., “Find the 7th multiple of 12.”
2️⃣ Key Points to Master
| Aspect | Tips & Tricks |
|---|---|
| Memorisation | • Memorise 1–10 tables fully. • Memorise 11–12 tables partially (key patterns). |
| Patterns | • 9’s table: digit sum = 9 (9×4=36, 3+6=9). • 5’s table: ends with 5 or 0 (5×7=35). • 10’s table: add a zero. |
| Using Tables for Quick Multiplication | • Break numbers into parts: 27×13 = (20+7)×13 = 20×13 + 7×13. Use 13’s table for 20×13 and 7×13. |
| Finding LCM/HCF | • Use prime factor tables or factor tables. • LCM of 12 and 15 = 60 (use multiples table). |
| Powers & Roots | • Powers of 2 grow fast; memorize up to 2¹⁰. • 10’s powers are simple (10, 100, 1000...). |
| Factors | • For a number N, list all divisors ≤ √N. • Use factor tables for quick LCM/HCF. |
| Multiples | • For 3, multiples end in 3, 6, 9. • For 4, last two digits divisible by 4. |
| Table‑Based Problem Solving | • “Find the 9th term of the series: 3, 6, 9, …” → use 3’s table. • “What is 5 × 8?” → 5’s table: 40. |
3️⃣ Worked Example 1 – Quick Multiplication Using Tables
Problem: Calculate ( 27 \times 13 ) quickly.
Solution:
- Break 27 into 20 + 7.
- Use the 13’s table:
- 13 × 20 = 13 × 2 × 10 = 26 × 10 = 260
- 13 × 7 = 91 (from table)
- Add the parts: 260 + 91 = 351.
✅ Result: (27 \times 13 = 351)
4️⃣ Worked Example 2 – LCM Using Multiples Table
Problem: Find LCM of 12 and 18.
Solution:
- Write the multiples of each up to 36:
- 12: 12, 24, 36
- 18: 18, 36
- The first common multiple is 36.
- LCM = 36.
5️⃣ Worked Example 3 – Factors Using Factor Table
Problem: List all factors of 48.
Solution:
- Prime factorise: 48 = 2³ × 3.
- Generate factor combinations:
- 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
- Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
6️⃣ Quick Revision Summary
| Topic | What to Remember |
|---|---|
| Multiplication Tables | Full memorisation of 1–10; 11–12 by pattern. |
| Patterns | 9’s digit sum, 5’s end digit, 10’s zero append. |
| Quick Multiplication | Break complex numbers into sums; use part‑table. |
| LCM/HCF | Use multiples/factors tables; prime factorisation if needed. |
| Powers | 2¹–2¹⁰, 3³, 10ⁿ; use for exponential problems. |
| Factors | List up to √N; pair |