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RRB NTPC Number System Full Explanation (5-Day Plan)

 

RRB NTPC Number System Full Explanation (5-Day Plan)

Hello!Number System for RRB NTPC, to be covered in a 5-day learning plan. The Number System is a key topic in the RRB NTPC CBT 1 and CBT 2 Maths section, with 2-4 questions typically appearing in the 30-mark Quantitative Aptitude part. I’ll break it down simply, step-by-step, from basics to advanced, with examples, tricks, and RRB-style practice questions.

What is the Number System? It’s about how numbers work, their types, and operations. Key topics for RRB NTPC include:

  • Types of Numbers: Natural, Whole, Integers, Rational/Irrational, Real.
  • Divisibility Rules: Rules to check if a number is divisible by another.
  • HCF & LCM: Highest Common Factor (HCF) and Least Common Multiple (LCM).
  • Factors & Multiples: Finding factors, multiples, and total number of factors.
  • Unit Digit & Remainders: Calculating unit digits and remainders (e.g., Remainder Theorem).
  • Fractions & Decimals: Operations on fractions and decimal conversions (sometimes included in Number System).

5-Day Learning Plan: Study 1-2 hours daily. Solve 5-10 practice questions at the end of each day. If you want feedback on your answers, share them in the comments, and I’ll check them!

Day 1: Basics & Types of Numbers

  • Explanation: The Number System is based on the decimal system (base 10). Types of numbers:
    • Natural Numbers (N): 1, 2, 3, ... (positive counting numbers).
    • Whole Numbers (W): 0, 1, 2, 3, ... (natural numbers + 0).
    • Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ... (whole + negative numbers).
    • Rational Numbers: In the form p/q (q ≠ 0), e.g., 1/2, 0.5 (terminating or repeating decimals).
    • Irrational Numbers: Not rational, e.g., √2, Ï€ (non-terminating, non-repeating decimals).
    • Real Numbers: All numbers on the number line (rational + irrational).
  • Example: 3/4 is rational (decimal: 0.75, terminates). √3 ≈ 1.732 (non-terminating, irrational).
  • RRB Trick: Quickly identify positive/negative and rational/irrational for MCQs.
  • Practice Questions (5):
    1. What type is 0? (a) Natural (b) Whole (c) Integer (d) All.
    2. Is √4 rational? (Yes/No, why?).
    3. What type is -5/2?
    4. What type is π?
    5. Do real numbers include all numbers? (Yes/No).

Day 2: Divisibility Rules & Factors/Multiples

  • Explanation: A number is divisible if division leaves no remainder (remainder = 0).
    • Divisibility Rules:
      • 2: Last digit is even (0, 2, 4, 6, 8).
      • 3: Sum of digits divisible by 3.
      • 4: Last two digits divisible by 4.
      • 5: Last digit is 0 or 5.
      • 6: Divisible by both 2 and 3.
      • 9: Sum of digits divisible by 9.
      • 10: Last digit is 0.
    • Factors: Numbers that divide a given number (e.g., factors of 12: 1, 2, 3, 4, 6, 12).
    • Multiples: Multiples of a number (e.g., multiples of 12: 12, 24, 36, ...).
    • Total Factors: For a number n = p^a × q^b, total factors = (a+1)(b+1).
  • Example: Is 456 divisible by 3? Sum = 4+5+6 = 15, 15/3 = 5 (Yes). Factors of 900: 900 = 2² × 3² × 5², total = (2+1)(2+1)(2+1) = 27.
  • RRB Trick: Practice quick digit-sum calculations for 3 and 9.
  • Practice Questions (5):
    1. Is 1234 divisible by 2? (Yes/No).
    2. How many factors does 567 have? (567 = 3³ × 3 × 7, calculate).
    3. Is 999 divisible by 9?
    4. What are common multiples of 12 and 18?
    5. Total factors of 48? (48 = 2⁴ × 3, (4+1)(1+1) = 10).

Day 3: HCF & LCM (Highest Common Factor & Least Common Multiple)

  • Explanation:
    • HCF: Largest number dividing two or more numbers (use Euclid’s Algorithm: divide larger by smaller, take remainder, repeat).
    • LCM: Smallest common multiple.
    • Formula: HCF × LCM = product of two numbers (a × b).
    • Prime Factorization: HCF = lowest power of common primes, LCM = highest power.
  • Example: HCF(12, 18): 12 = 2² × 3, 18 = 2 × 3², HCF = 2 × 3 = 6. LCM = 2² × 3² = 36. Check: 6 × 36 = 216 = 12 × 18.
  • RRB Trick: Use Euclid’s for 2-3 numbers to save time.
  • Practice Questions (5):
    1. HCF(24, 36)? (Answer: 12).
    2. LCM(8, 12)? (24).
    3. HCF and LCM of 45 and 60?
    4. HCF of three numbers 15, 25, 30?
    5. For a = 20, b = 28, find HCF × LCM.

Day 4: Unit Digit & Remainders

  • Explanation:
    • Unit Digit: Last digit of a number. Powers follow cycles: 2 (2, 4, 8, 6), 3 (3, 9, 7, 1), 4 (4, 6), 5 (5), 6 (6), 7 (7, 9, 3, 1), 8 (8, 4, 2, 6), 9 (9, 1).
    • Remainder Theorem: a^n mod m = (a mod m)^n mod m. Use cyclic patterns.
  • Example: Unit digit of 7^100? Cycle = 4 (7, 9, 3, 1), 100 mod 4 = 0 → 1. 123 mod 5 = 3 (last digit 3).
  • RRB Trick: Memorize power cycles (4 or 10) for quick calculations.
  • Practice Questions (5):
    1. Unit digit of 3^50?
    2. 25 mod 7 = ?
    3. Unit digit of 9^20?
    4. 456 mod 10?
    5. 2^10 mod 5 = ?

Day 5: Fractions/Decimals & Revision

  • Explanation:
    • Fractions: Proper (numerator < denominator), Improper (opposite), Mixed. Operations: +, -, ×, / (use common denominator).
    • Decimals: Terminating (e.g., 1/2 = 0.5), non-terminating (repeating: 1/3 = 0.333..., or non-repeating: √2).
    • Rational = terminating or repeating decimal.
  • Example: 3/8 = 0.375 (terminating). 1/3 = 0.333... (repeating). 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
  • RRB Trick: Convert decimals to fractions by multiplying by 1000 for quick checks.
  • Practice Questions (10 – Mixed Revision):
    1. HCF(100, 150)?
    2. Unit digit of 4^15?
    3. 1/6 + 1/4 = ?
    4. Is 789 divisible by 9?
    5. Is √9 rational?
    6. LCM(9, 12)?
    7. 5^20 mod 10?
    8. Decimal of 2/5?
    9. Number of factors of 36?
    10. What type is -3/7?

Additional Tips:

  • Review the previous day’s content at the end of each day.
  • Practice RRB NTPC previous papers (e.g., odd divisors of 900900 = 36).
  • Recommended Book: R.S. Aggarwal Quantitative Aptitude (available in English).
  • Share any doubts in the comments! After 5 days, I can provide a mock test. Best of luck for your RRB NTPC prep! 🚂
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