SSC CGL Quant · Study & Practice

Number System & Simplification

AreaArithmetic DifficultyEasy–Moderate SSC weightage4–6 questions (Tier 1 & Tier 2)

Number System is the quiet workhorse of SSC Quant. Divisibility rules, HCF and LCM, unit-digit cycles and BODMAS simplification appear in almost every paper, and the speed you build here carries into percentages, ratios and the rest of arithmetic. The trick is to stop computing the long way: learn the rules, spot the pattern, and finish in seconds. This chapter takes you from the classification of numbers through surds and indices, with the exact short-cuts SSC rewards.

Topics

1 Classification of Numbers 4 worked · 5 practice · 8-Q test Start → 2 Divisibility Rules 4 worked · 5 practice · 8-Q test Start → 3 HCF & LCM 4 worked · 5 practice · 8-Q test Start → 4 Factors & Unit Digit 4 worked · 5 practice · 8-Q test Start → 5 BODMAS & Simplification 4 worked · 5 practice · 8-Q test Start → 6 Surds & Indices 4 worked · 5 practice · 8-Q test Start →

⚡ SSC shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Divisibility by 11: alternate-add the digits; difference 0 or 11 means divisible.
  • Number of factors: add 1 to each prime exponent and multiply.
  • Unit digit: reduce the power mod 4 and read the cycle.
  • HCF x LCM = product of the two numbers — finds a missing number fast.
  • BODMAS: division and multiplication rank equally — go strictly left to right.

⚠️ Common mistakes & traps

SSC is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Treating 1 as a prime number (it is not).
  • Doing addition before multiplication in simplification.
  • Forgetting LCM of fractions = LCM(numerators) / HCF(denominators).
  • Reading power mod 4 = 0 as the FIRST digit of the cycle instead of the LAST.

📈 SSC exam insight & PYQ analysis

SSC Tier 1 leans on quick divisibility, unit-digit and HCF/LCM word problems; Tier 2 adds layered simplification with fractions and surds. Bells/tiles/measuring-rod problems are LCM/HCF; remainder problems usually reduce to HCF of differences.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

HCF x LCM = ?Tap to reveal
Product of the two numbers
Factors of 2^2 x 3 x 5?Tap to reveal
(2+1)(1+1)(1+1) = 12
Unit digit of 7^53?Tap to reveal
7 (53 mod 4 = 1)
Is a recurring decimal rational?Tap to reveal
Yes
Divisibility by 9 rule?Tap to reveal
Digit sum is a multiple of 9

📌 Quick revision

Classify numbers, apply divisibility rules, factorise for HCF/LCM (HCF x LCM = product), count factors with (a+1)(b+1)..., find unit digits via the mod-4 cycle, and simplify strictly by BODMAS. These rules convert long arithmetic into one-line answers.

Chapter test

📝 Number System & Simplification — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
📊 My SSC analytics
Track scores, accuracy by topic and progress over time.
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🏆 Vidaara SSC success checklist

You have truly mastered Number System & Simplification when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (6 topics)6/6
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall5 cards