Introduction

This guide covers the Number System topic for NDA NA aspirants. Master the concept, understand the tricks, and then test yourself with 10 practice MCQs.

Number System — Concept Guide

The Number System is the foundation of mathematics. Understanding types of numbers, divisibility rules, LCM, HCF, and number properties is essential for all competitive exams.

Types of Numbers

  • Natural numbers: 1, 2, 3... (counting numbers)
  • Whole numbers: 0, 1, 2, 3... (natural + zero)
  • Integers: ...-3,-2,-1,0,1,2,3...
  • Rational numbers: Can be expressed as p/q (q≠0)
  • Irrational numbers: Cannot be expressed as p/q (e.g., √2, π)
  • Prime numbers: Exactly 2 factors: 1 and itself
  • Composite numbers: More than 2 factors

Divisibility Rules (Quick Reference)

  • 2: Last digit even
  • 3: Sum of digits divisible by 3
  • 4: Last 2 digits divisible by 4
  • 5: Ends in 0 or 5
  • 9: Sum of digits divisible by 9
  • 11: Alternating sum of digits divisible by 11

⚡ Shortcuts & Tricks

  • LCM × HCF = Product of two numbers.
  • To find HCF: use prime factorisation or Euclidean division algorithm.
  • Sum of first n natural numbers = n(n+1)/2.
  • Sum of squares of first n naturals = n(n+1)(2n+1)/6.
  • Primes to 50: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 — memorise these!

Practice MCQs — Number System (10 Questions)

Now test your understanding with these 10 questions:

Q1. What is the LCM of 12 and 18?

  • A. 36
  • B. 24
  • C. 72
  • D. 18
Answer: A — LCM(12,18) = 36.

Q2. HCF of 48 and 72?

  • A. 24
  • B. 12
  • C. 36
  • D. 48
Answer: A — 48=2⁴×3, 72=2³×3². HCF=2³×3=24.

Q3. Which is a prime number?

  • A. 37
  • B. 39
  • C. 35
  • D. 33
Answer: A — 37 is prime. Others divisible by 3 or 5.

Q4. What is the value of 2⁸?

  • A. 256
  • B. 128
  • C. 512
  • D. 64
Answer: A — 2⁸=256.

Q5. Sum of first 10 natural numbers?

  • A. 55
  • B. 50
  • C. 45
  • D. 60
Answer: A — n(n+1)/2 = 10×11/2 = 55.

Q6. What is 15% of 200?

  • A. 30
  • B. 25
  • C. 35
  • D. 20
Answer: A — 15/100×200=30.

Q7. √144 = ?

  • A. 12
  • B. 11
  • C. 13
  • D. 14
Answer: A — 12²=144.

Q8. 3³ + 4² = ?

  • A. 43
  • B. 37
  • C. 41
  • D. 45
Answer: A — 27+16=43.

Q9. Which is not a factor of 36?

  • A. 8
  • B. 6
  • C. 9
  • D. 12
Answer: A — 36=4×9=6²=3×12. 8 is not a factor.

Q10. LCM of 5, 6, 9?

  • A. 90
  • B. 45
  • C. 30
  • D. 60
Answer: A — LCM(5,6,9)=90.

Summary

Number System is a scoring topic in NDA NA if you practise consistently. Focus on understanding the concept, apply the shortcut tricks, and practice regularly. Aim for 100% accuracy in this topic through regular revision.