Quant Basics Refresher for CAT & IPMAT

Quick Revision of Arithmetic, Algebra, and Numbers

Presented by Career Launcher South Ex, Delhi

Introduction

Quantitative Aptitude (QA) is a make-or-break section for CAT and IPMAT aspirants. Though challenging, it’s highly manageable — not because it’s easy, but because it’s predictable. Arithmetic, Algebra, and Numbers form the core of the QA syllabus and often account for over 70% of the questions.

Whether you’re revising late in the season or starting your focused prep, this is your quick yet thorough refresher, structured for clarity, retention, and effective practice.

Why Focus on Quant Basics?

Based on recent trends:

• Arithmetic: 35–40% in CAT | 40%+ in IPMAT

• Algebra: 25–30% in CAT | 25%+ in IPMAT

• Numbers: 15–20% in both exams

• Others (Geometry, Modern Math, etc.): 10–15%

Mastering these three areas covers 75–80% of the Quant paper.

Part 1: Arithmetic – The Scoring Stronghold

Key Topics Covered

• Percentages

• Profit & Loss

• Simple and Compound Interest

• Ratio and Proportion

• Time, Speed, and Distance

• Time and Work

• Mixtures and Alligations

• Averages

Core Concepts Recap

• Percentages: % change = (New – Old)/Old × 100
  Tip: Convert percentages into fractions for quick calculations.

• Profit & Loss: SP = CP × (1 ± Profit/Loss %)
  Tip: Use a base value of 100 for easier calculations.

• Simple & Compound Interest:

  • SI = (P × R × T)/100

  • CI = P(1 + R/100)^T – P
    Tip: Understand and memorize the difference between SI and CI.

• Ratio & Proportion:
  If A:B = 2:3 and B:C = 4:5, then A:C = 8:15
  Tip: Always make the common term (B here) equal.

• Time, Speed & Distance: Distance = Speed × Time
  Tip: Use unitary method before applying formulas.

• Time & Work:
  Work = Rate × Time
  Total Work = LCM of efficiencies
  Tip: Use the “1-day work” concept.

• Mixtures & Alligations:
  Use: C = (Q1×P1 + Q2×P2)/(Q1 + Q2)
  Tip: Apply when two components are mixed.

• Averages: Avg = Sum / Count
  Tip: Weighted averages are essential for mixtures.

Sample Practice

• Question 1 (CAT):
  A man spends 30% of income on rent and 20% of remaining on groceries. If ₹28,000 is left, what was his income?
  → Let income = x
  → Rent = 0.3x → Remaining = 0.7x
  → Groceries = 0.14x → Final = 0.56x = 28,000
  → x = ₹50,000

• Question 2 (IPMAT):
  Train crosses 200m bridge in 25 sec, 300m platform in 35 sec. Find speed.
  → 100m in 10s → Speed = 10 m/s
  → Train length = 250 – 200 = 50m

Part 2: Algebra – The Concept Builder

Key Topics Covered

• Linear Equations

• Quadratic Equations

• Polynomials

• Inequalities

• Functions

• Progressions (AP/GP)

• Algebraic Identities

Core Concepts Recap

• Linear Equations:
  ax + by = c
  Tip: Elimination and substitution work best.

• Quadratics:
  x = [-b ± √(b² – 4ac)] / 2a
  Tip: Discriminant (b² – 4ac) shows root type.

• Identities:
  (a + b)² = a² + 2ab + b²
  Tip: Use for expression simplification.

• Inequalities:
  Reverse signs when multiplying/dividing by negative.
  Tip: Plot values for modulus inequalities.

• Functions:
  f(x) means replace x with value.
  Tip: Try test values to verify results.

• AP/GP:

  • AP nth = a + (n–1)d

  • GP nth = arⁿ⁻¹
    Tip: Memorize sum formulas.

Sample Practice

• Question 1 (CAT):
  If a + b = 7 and ab = 10, find a² + b².
  → a² + b² = (a + b)² – 2ab = 49 – 20 = 29

• Question 2 (IPMAT):
  If x + 1/x = 4, find x² + 1/x².
  → = (x + 1/x)² – 2 = 16 – 2 = 14

Common Pitfalls

• Sign errors in inequalities and squaring

• Forgetting domain restrictions (like x ≠ 0)

• Misapplying quadratic conditions

Part 3: Number System – The Foundation Block

Key Topics Covered

• Divisibility Rules

• HCF & LCM

• Factorization

• Remainders (Euler’s and Fermat’s Theorems)

• Base Systems

• Digital Root

• Cyclicity

• Prime Numbers

Must-Know Rules

• HCF & LCM:
  HCF × LCM = Product of numbers (for 2 numbers)

• Divisibility Shortcuts:

  • Div by 3 → Sum of digits

  • Div by 4 → Last 2 digits

  • Div by 11 → Alternating sum

• Remainders:
  Use mod n or Euler’s theorem

• Digital Root:
  Add digits repeatedly till one remains

• Cyclicity:
  Observe the pattern in powers (e.g., 2ⁿ, 3ⁿ)

Sample Practice

• Question 1 (CAT):
  Find remainder of 7⁴⁸ ÷ 100
  → Cycle = [7, 49, 43, 1]; 48 mod 4 = 0 → Ans = 1

• Question 2 (IPMAT):
  How many trailing zeros in 100!?
  → 100/5 + 100/25 = 20 + 4 = 24

Self-Testing Prompts

Arithmetic

• Mixtures: Mix 2L of 10% acid with 3L of 30% → Answer: 22%

• Speed: Travel 60km at 40 kmph, next 60 at 60 → Avg Speed: 48

• Work: A in 10 days, B in 15 → Together: 6 days

Algebra

• Roots of x² – 5x + 6 = 0 → Answer: 2, 3

• If x – 1/x = 3, find x² + 1/x² → Answer: 11

• 5th term of AP: 2, 4, 6... → Answer: 10

Numbers

• 13⁴ mod 10 → Answer: 1

• No. of factors of 120 → Answer: 16

• LCM of 12 and 18 → Answer: 36

Weekly Quant Target Plan

• Monday: Percentages & Ratios – Concepts + 10 MCQs (1.5 hrs)

• Tuesday: Quadratics & Identities – Video + 15 MCQs (2 hrs)

• Wednesday: Divisibility & LCM – Worksheet + Review (1.5 hrs)

• Thursday: Mixtures & Averages – Sectional Test (2 hrs)

• Friday: Functions & Inequalities – Drill 10 questions (1.5 hrs)

• Saturday: Mixed Mock Section – 30 MCQs (2 hrs)

• Sunday: Error Review – Log mistakes, revisit weak areas (1 hr)

Final Takeaways

• Revise with structure, not randomly

• Maintain an error log

• Master fundamentals first — they cover most real exam questions

• Use a 7-day sprint format for consistency

At Career Launcher South Ex, Delhi, we specialize in making Quant less intimidating. With focused modules, personalized mentorship, and performance analytics, you’ll gain both confidence and competence.

Ready for Practice?

Want a custom PDF with 100 Quant basics questions or a printable weekly planner? Just let us know your level (CAT or IPMAT) — we’ll send a version tailored just for you.

Stay focused. Start small. Build confidence.
Quant mastery is built on depth, not just speed.