Number System
Learning Objectives
- Understand the fundamental concepts of Number System
- Apply key formulas and techniques to solve problems
- Practice with exam-level questions to build speed and accuracy
Key Concepts
What is Number System?
The number system is the foundation of arithmetic. It covers types of numbers — natural, whole, integers, rational, irrational, prime, composite, co-prime, and their properties. SSC CGL Tier 1 frequently asks questions on divisibility rules, LCM & HCF, and unit digits.
Key Concepts
1. Divisibility Rules: A number is divisible by 2 if its last digit is even; by 3 if sum of digits is divisible by 3; by 4 if last two digits are divisible by 4; by 5 if last digit is 0 or 5; by 6 if divisible by both 2 and 3; by 9 if sum of digits is divisible by 9; by 11 if the difference between sum of digits at odd and even places is 0 or a multiple of 11.
2. LCM & HCF: LCM of two numbers is the smallest number divisible by both. HCF is the greatest number that divides both. For fractions, LCM = LCM of numerators / HCF of denominators; HCF = HCF of numerators / LCM of denominators.
3. Unit Digit Cyclicity: The unit digit of powers repeats in cycles of 4 for most digits. For example, 2^41 has the same unit digit as 2^1 = 2. Learn the cyclicity table: 2 → 2,4,8,6; 3 → 3,9,7,1; 4 → 4,6; 7 → 7,9,3,1; 8 → 8,4,2,6; 9 → 9,1.
Solved Examples
a) 12345 b) 12122 c) 13321 d) 14443
a) 3 b) 5 c) 7 d) 9
a) 124 b) 144 c) 164 d) 188
Shortcut Techniques
- For unit digit questions, only the unit digit of the base matters. Ignore the rest.
- For LCM of large numbers, divide all numbers by common prime factors and multiply the divisors and the final row.
- For divisibility by 7: double the last digit, subtract from the rest. Repeat until you get a small number divisible by 7.
- For HCF, use the difference trick: HCF(a,b) = HCF(a-b, b) for a > b.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.