Number System & Simplification

Number System & Simplification

Concept

The number system is the backbone of SSC CGL Quant. It covers natural numbers, whole numbers, integers, rational and irrational numbers. Simplification means evaluating expressions correctly using BODMAS, while the number system portion tests your skills in divisibility, HCF/LCM, remainders, and finding missing digits in sums or products. In Tier 2, expect higher difficulty — questions often combine two concepts (e.g., LCM + remainder theorem).

Key sub-topics: divisibility rules (2, 3, 4, 5, 6, 8, 9, 11), unit digit cycles, cyclicity of remainders, and Euclidean algorithm for HCF.

Key Points

• Divisibility by 11: Difference between sum of digits in odd and even positions is a multiple of 11.
• Unit digit of 7^power cycles in 7, 9, 3, 1 (cycle length 4). Find power mod 4.
• For any two numbers a and b: a × b = HCF(a,b) × LCM(a,b) — one of the most used identities.
• Remainder theorem: When dividing by (a×b) where a and b are co-prime, remainders can be combined using the Chinese Remainder Theorem concept.
• Always reduce fractions to lowest terms before comparing.

Worked Example

Q: When a number is divided by 6, 8, and 12, it leaves the same remainder 3. If the number is between 300 and 350, find it. Approach: The number − 3 is divisible by LCM(6, 8, 12). LCM = 24. So number = 24k + 3. Between 300–350: 24 × 13 = 312, so 312 + 3 = 315. Answer: 315

SSC Pattern / Tips

• Most questions ask for the HCF/LCM of 3+ numbers — use the prime factor method or successive division.
• Remainder problems often give remainders 1 or 2 when dividing by small numbers — look for the LCM approach.
• For unit digit problems, always find exponent mod 4 (or mod 20 for larger bases).
• Always check if the numbers are co-prime before applying the HCF × LCM = product rule.