Number System – Quantitative Aptitude
(For Dadra & Nagar Haveli & Daman & Diu Police Constable Exam)
Why this topic matters
The “Number System” section tests your ability to work with basic properties of numbers—integers, fractions, decimals, primes, and divisibility. It also covers quick mental calculations that are useful in daily policing tasks (e.g., estimating fines, calculating rates, etc.).
1. Simple Explanation
| Sub‑topic | What it is | Quick mental cue |
|---|---|---|
| Integer | Whole numbers, positive or negative, including zero. | “+ or –” |
| Fraction | Ratio of two integers where denominator ≠ 0. | “Numerator/Denominator” |
| Decimal | Number expressed in base‑10 with a point. | “Whole part . Fraction part” |
| Prime | Integer > 1 with exactly two positive divisors (1 and itself). | “Only two factors” |
| Composite | Integer > 1 that isn’t prime. | “More than two factors” |
| Power of 10 | Numbers like 10, 100, 1 000, … | “10ⁿ” |
| Divisibility Rules | Quick tests to determine if one number divides another. | “Look at last digits / sum” |
2. Key Points
| Concept | What to remember | Quick mental trick |
|---|---|---|
| Place Value | Each digit’s value grows by 10× as we move left. | “Hundreds, Tens, Ones” |
| Fraction Simplification | Divide numerator & denominator by GCD. | “Find GCD first” |
| Decimal to Fraction | Move decimal point right until whole, then divide by 10ⁿ. | “×10ⁿ / 10ⁿ” |
| Fraction to Decimal | Long division; detect repeating cycles. | “Divide until repeat” |
| Prime Check (≤ √n) | Test divisibility only up to √n. | “Check 2,3,5,7,…” |
| Divisibility Rules | 2 (last digit even), 3 (sum of digits divisible by 3), 4 (last two digits divisible by 4), 5 (last digit 0 or 5), 6 (divisible by 2 & 3), 9 (sum of digits divisible by 9), 10 (last digit 0). | “Rule list” |
| Powers of 10 | 10⁰ = 1, 10¹ = 10, 10² = 100, … | “Move decimal 0,1,2 places” |
| Number Patterns | Recognize arithmetic/geometric progressions. | “Find common difference/ratio” |
3. Worked Example
Problem
Find the sum of all two‑digit multiples of 7 that are also divisible by 5.
Step‑by‑Step
-
Identify the two‑digit multiples of 7
- Smallest 2‑digit multiple: 7 × 2 = 14
- Largest 2‑digit multiple: 7 × 14 = 98
-
Check which of these are divisible by 5
Divisible by 5 → last digit either 0 or 5.
Only numbers ending in 0 or 5 among the multiples of 7. -
List the candidates
14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
→ Those ending in 0 or 5: 35, 70. -
Sum them
35 + 70 = 105
Quick Mental Check
- Numbers divisible by both 7 and 5 must be divisible by LCM(7,5) = 35.
- Two‑digit multiples of 35: 35, 70.
- Sum = 35 + 70 = 105 (same answer).
4. Quick Revision Summary
| Topic | Key Take‑away |
|---|---|
| Integers | Positive, negative, zero. |
| Fractions | Simplify using GCD; convert to decimal via long division. |
| Decimals | Move decimal for fraction; use powers of 10 to shift. |
| Primes | Only two factors; test divisibility up to √n. |
| Composite | Any number > 1 not prime. |
| Divisibility | Memorize rules for 2,3,4,5,6,9,10. |
| Powers of 10 | 10ⁿ → shift decimal n places. |
| Patterns | Recognize AP/GP quickly; use formulas. |
Pro‑Tip: Practice converting between fractions and decimals, and solving divisibility questions in 10‑seconds. Flashcards for the divisibility rules are highly effective.
Good luck with your preparation!