📚 Number System – Study Notes
Program: Insurance (LIC / GIC)
Subject: Quantitative Aptitude
Topic: Number System
1️⃣ Simple Explanation
The number system is the set of numbers we use to count, measure, and do arithmetic. In quantitative aptitude, we mainly deal with:
| System | Symbols | Range | Typical Use |
|---|---|---|---|
| Natural Numbers (ℕ) | 1, 2, 3 … | Positive integers | Counting objects |
| Whole Numbers (ℤ⁺∪{0}) | 0, 1, 2 … | Non‑negative integers | Money, marks |
| Integers (ℤ) | …, –3, –2, –1, 0, 1, 2 … | All whole numbers + negatives | Balancing accounts |
| Rational Numbers (ℚ) | Fractions (p/q where q≠0) | All numbers that can be expressed as a fraction | Discounts, rates |
| Irrational Numbers | √2, π, e | Non‑fractional, non‑repeating | Constants in formulas |
| Real Numbers (ℝ) | Rational + Irrational | All possible numbers on the number line | All calculations |
| Complex Numbers (ℂ) | a + bi (i² = –1) | Not used in basic LIC/GIC problems | Advanced mathematics |
In LIC/GIC quantitative tests, you’ll mainly use integers, rationals, and real numbers. You need to quickly determine the type of a number, perform simple operations, and solve problems involving divisibility, parity, and basic arithmetic properties.
2️⃣ Key Points to Remember
| # | Concept | Quick Note |
|---|---|---|
| 1 | Divisibility Rules | 2 → 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 |
| 2 | Parity | Even numbers: divisible by 2; Odd numbers: not divisible by 2. |
| 3 | Prime Numbers | Numbers >1 with only two divisors: 1 and itself. |
| 4 | Multiples & Factors | A multiple of n is n·k. A factor of n divides n exactly. |
| 5 | Greatest Common Divisor (GCD) | Largest number dividing two numbers. Use Euclid’s algorithm. |
| 6 | Least Common Multiple (LCM) | Smallest number divisible by both. LCM × GCD = product of numbers. |
| 7 | Decimal Representation | Finite decimals (e.g., 0.5) are rational. Repeating decimals (e.g., 0.333…) are also rational. |
| 8 | Scientific Notation | 4.2 × 10⁵ → 420,000. Useful for very large or very small numbers. |
| 9 | Negative Numbers | Keep track of signs in addition/subtraction. Multiplying two negatives gives a positive. |
| 10 | Number Properties | - Even + Even = Even - Even + Odd = Odd - Odd + Odd = Even - Even × Any = Even - Odd × Odd = Odd |
3️⃣ Worked Example
Problem (LIC style):
A sum of money is invested for 3 consecutive years.
- Year 1: interest rate = 10% (simple interest).
- Year 2: interest rate = 12% (compound interest on the amount at the end of Year 1).
- Year 3: interest rate = 15% (simple interest on the amount at the end of Year 2).
If the principal was ₹10,000, what is the total amount after 3 years?
Step‑by‑Step Solution
| Year | Type | Rate | Amount at start | Interest | Amount at end |
|---|---|---|---|---|---|
| 1 | Simple | 10 % | ₹10,000 | 10 % of 10,000 = ₹1,000 | ₹11,000 |
| 2 | Compound | 12 % | ₹11,000 | 12 % of 11,000 = ₹1,320 | ₹12,320 |
| 3 | Simple | 15 % | ₹12,320 | 15 % of 12,320 = ₹1,848 | ₹14,168 |
Total amount after 3 years = ₹14,168.
Why This Uses Number System Concepts
- Percentages are fractions: 10 % = 10/100 = 0.1.
- Multiplication of fractions and whole numbers.
- Rational numbers (0.1, 0.12, 0.15).
- Addition of different monetary amounts.
- Rounding: No rounding needed, but if required, keep track of decimal places.
4️⃣ Quick Revision Summary
| Topic | What to Check |
|---|---|
| Divisibility | Use quick rules for 2, 3, 4, 5, 6, 9, 10 |
| Parity | Remember even + odd = odd |
| Prime Check | Trial division up to √n |
| GCD & LCM | Euclid’s algorithm; LCM = (a·b)/GCD |
| Decimals & Fractions | Convert repeating decimals to fractions if needed |
| Scientific Notation | Move decimal point correctly |
| Negative Numbers | Watch sign changes in multiplication/division |
| Operations | Add/subtract with same/different signs; multiply/divide with fractions |
Practice Problems for You
- Divisibility: Is 1,234,568 divisible by 6?
- GCD & LCM: Find GCD and LCM of 48 and 180.
- Interest Calculation: ₹5,000 at 8% simple interest for 4 years.
- Fraction to Decimal: Convert 17/25 to decimal.
- Scientific Notation: Write 0.00042 in scientific notation.
Answer the above and compare with the solutions below.
5️⃣ Solutions to Practice Problems
| # | Question | Answer |
|---|---|---|
| 1 |