Quantitative Aptitude – Number System
Master the Fundamentals. Score the Easy Marks. Win the Section.
1. What Is the Number System?
The Number System is the foundation of Quantitative Aptitude. It includes:
2. Types of Numbers
| Type | Examples | Notes |
|---|---|---|
| Natural | 1, 2, 3, ... | Counting numbers |
| Whole | 0, 1, 2, 3, ... | Natural + 0 |
| Integers | ..., -3, -2, -1, 0, 1, 2, ... | No decimals |
| Rational | 2/3, 0.75 | Can be written as \( \frac{p}{q} \) |
| Irrational | \( \pi \), \( \sqrt{2} \) | Non-repeating, non-terminating |
| Prime | 2, 3, 5, 7, 11... | Only divisible by 1 and itself |
| Composite | 4, 6, 8... | More than 2 factors |
Tip: Memorize prime numbers up to 50. 1 is neither prime nor composite.
3. Divisibility Rules
Exam Tip: Eliminate options quickly using these rules.
4. HCF and LCM
Use the identity:
\( \text{HCF} \times \text{LCM} = \text{Product of Numbers} \)
Apply via prime factorization or ladder method.
5. Factors and Multiples
6. Remainders and Modular Arithmetic
Apply the identity:
\( a = nq + r \Rightarrow a \mod n = r \)
Use power cycles and Euler’s/Fermat’s theorems for large powers.
Example: \( 7^{103} \mod 5 \): Cycle is 7, 9, 3, 1 → 103 mod 4 = 3 → Answer = 3
7. Unit Digits of Powers
Find repeating cycle of last digits:
Use \( n \mod \text{cycle length} \) to find position.
8. Trailing Zeros in Factorials
Formula:
\( \left\lfloor \frac{n}{5} \right\rfloor + \left\lfloor \frac{n}{25} \right\rfloor + \left\lfloor \frac{n}{125} \right\rfloor + \cdots \)
Example: 100! → 100/5 = 20, 100/25 = 4 → Total = 24 zeros
9. Base Conversions
10. Exam Strategy and Speed Tips
11. Final Revision Checklist
Summary: Understand the logic, learn the shortcuts, and practice with time limits. That’s the formula to crack Number System questions in competitive exams.