Number System Basics for Competitive Exams

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A Foundation Lesson for Quantitative Aptitude Aspirants

Hello future achiever! 👋 Welcome to Concept Studies, a place where we learn with clarity, confidence and real-life understanding. Today you are stepping into your very first chapter of Quantitative Aptitude — the Number System.

I still remember the first day I started preparing for competitive exams — banking, SSC, railways, insurance — and almost every topper I met told me the same thing:

“If your Number System is strong, 40% of Quant becomes simple.”

So today, let’s learn this chapter like a real aspirant — not just reading but understanding why every concept matters. Because concepts truly matter! 💙



🔢 1. What Are Numbers?

Numbers are not just digits written on paper. Numbers are the language of mathematics. Every calculation you do — profit, loss, interest, speed, average, Data Interpretation — everything starts here.

Let’s start with the simplest classification:

📌 Types of Numbers

  • Natural Numbers — 1, 2, 3, 4 …
  • Whole Numbers — 0, 1, 2, 3 …
  • Integers — … -3, -2, -1, 0, 1, 2, 3 …
  • Rational Numbers — fractions p/q
  • Irrational Numbers — √2, π (non-terminating & non-repeating)
  • Real Numbers — All rational numbers + irrationals numbers combined
Shortcut Trick: Every fraction p/q (q ≠ 0) is ALWAYS a rational number — even if its decimal looks long and confusing.

🧮 2. Understanding the Number Line (Visual Thinking)

Imagine a straight endless highway. That’s your number line. Left side is negative (cold side ❄), right side is positive (warm side 🔥), and 0 is the center.



This helps you understand ordering, comparison and future topics like inequalities.

✨ 3. Properties of Numbers (Small but Important!)

These apply everywhere — algebra, simplification, HCF-LCM, equations.

✔ Closure Property

If you add or multiply two whole numbers, the result is still a whole number.

✔ Commutative Property

a + b = b + a and a × b = b × a

✔ Associative Property

(a + b) + c = a + (b + c)

💥 4. Divisibility Rules

These rules are LIFESAVERS in exams. They reduce 30 seconds questions into 3 seconds.

📘 Divisibility Rules (Complete Updated List)

Number Rule
2 Last digit even (0,2,4,6,8)
3 Sum of digits divisible by 3
4 Last 2 digits divisible by 4
5 Last digit is 0 or 5
6 Number must be divisible by 2 and 3
7 Double last digit & subtract (special rule)
8 Last 3 digits divisible by 8
9 Sum of digits divisible by 9
10 Last digit is 0
11 (Sum of odd-position digits – even-position digits) divisible by 11
Super Shortcut: If a number is divisible by both 3 and 4 → it is automatically divisible by 12.

🌟 5. Prime & Composite Numbers (Simplified)

A prime number has only two factors — 1 and itself. Composite numbers have more than two factors.

Shortcut: You only need to check divisibility up to √n to test if a number is prime.

🧩 6. Remainders & Modular Thinking

This topic will be fully covered in future chapters, but here’s the basic idea:

Dividend = Divisor × Quotient + Remainder

If you divide 27 by 5 → remainder is 2

📝 7. Practice Questions (Solve & Learn!)

  1. Classify: √7, -12, 0, 4.25, 22/7
  2. Check whether 836 is divisible by 4, 6, 8, and 11.
  3. Find the remainder when 523 is divided by 7.
  4. Identify prime numbers from: 29, 57, 91, 97

🎯 8. What’s Coming Next?

This is just the first brick in your Quant foundation. Next post will be:

👉 Lesson 2: Divisibility Rules — With Advanced Tricks!

Make sure to follow the blog so you never miss the upcoming posts!

Remember: Concepts Matter. You Matter. Keep learning! 🚀

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