Number System – Concepts, Shortcuts & Solved MCQs (2025)

The Number System is one of the most important topics in Quantitative Aptitude. It forms the base for many questions in exams like SSC, Banking, CAT, GATE, and campus placements.
In this guide, we’ll cover definitions, formulas, tricks, and practice questions to help you master the Number System.

Types of Numbers

1. Natural Numbers (N): Counting numbers → 1, 2, 3, 4…
2. Whole Numbers (W): Natural numbers + Zero → 0, 1, 2, 3…
3. Integers (Z): Positive & negative numbers + zero → … -2, -1, 0, 1, 2 …
4. Rational Numbers (Q): Numbers expressed as p/q, where q ≠ 0 (e.g., 3/4, -7/2).
5. Irrational Numbers: Cannot be expressed as p/q (e.g., √2, π).
6. Real Numbers (R): Combination of rational + irrational numbers.
7. Prime Numbers: Numbers greater than 1 that have only 2 factors (1 and itself).
   Examples: 2, 3, 5, 7, 11…
8. Composite Numbers: Numbers with more than two factors (e.g., 4, 6, 8…).

Important Formulas & Shortcuts

• Even Number: 2n
• Odd Number: 2n + 1
• Prime Number Check: Divisible only by 1 & itself
• HCF × LCM = Product of numbers (for 2 numbers)
• Sum of first n natural numbers:
  S=n(n+1)2S = \dfrac{n(n+1)}{2}S=2n(n+1)​
• Sum of first n odd numbers:
  S=n2S = n^2S=n2
• Sum of first n even numbers:
  $S=n(n+1)$

Solved Examples

Q1. Find the sum of first 20 natural numbers.
Formula: n(n+1)/2 = 20 × 21 / 2 = 210

Q2. Which of the following is a prime number?
A) 15
B) 17 ✅
C) 21
D) 25

Q3. Find the LCM of 12 and 18.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM = 2 × 2 × 3 × 3 = 36 ✅

Q4. Find HCF of 36 and 48.
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
HCF = 2 × 2 × 3 = 12 ✅

Q5. Find the 10th odd number.
Formula = 2n – 1
= 2(10) – 1 = 19 ✅

Practice Questions (MCQs)

Q1. Which is the smallest prime number?
A) 0
B) 1
C) 2 ✅
D) 3

Q2. What is the sum of first 15 odd numbers?
A) 120
B) 200
C) 225 ✅
D) 250

Q3. What is the HCF of 72 and 108?
A) 18 ✅
B) 24
C) 36
D) 54

Q4. What is the LCM of 8, 12, and 20?
A) 60
B) 120 ✅
C) 240
D) 480

Q5. Which of the following is an irrational number?
A) 22/7
B) 3.5
C) √5 ✅
D) 0.75

The Number System is the foundation of Quantitative Aptitude. If you understand the concepts, formulas, and tricks, you can easily solve questions in exams within seconds.
Keep practicing with more MCQs to improve speed and accuracy.

Next Topic: Algebra – Concepts & MCQs