Section 4, days 1–2

Beginner’s toolkit

Most CAT arithmetic is solved with five tools: fraction–percent conversions, multiplying factors, assumed values, the LCM trick and alligation. Make them automatic in the first two days; every later chapter leans on them.

Fraction ↔ percentage table

Memorise these.

  • 1/250%
  • 1/333.33%
  • 1/425%
  • 1/520%
  • 1/616.67%
  • 1/714.29%
  • 1/812.5%
  • 1/911.11%
  • 1/1010%
  • 1/119.09%
  • 1/128.33%
  • 1/156.67%
  • 1/166.25%
  • 1/205%

Also learn the multiples

  • 3/837.5%
  • 5/862.5%
  • 2/728.57%
  • 3/742.86%
  • 5/683.33%
  • 4/944.44%
  • 5/1241.67%

Fraction → percent drill

Type the percentage; two decimals is enough. 10 seconds a card, 20 cards a round. Enter submits, Enter again moves on.

Multiplying factors

An increase of r% means multiply by (1 + r/100); a decrease of r% means multiply by (1 − r/100). Prefer fractions:

  • +25% = ×5/4
  • −20% = ×4/5
  • +12.5% = ×9/8
  • +33.33% = ×4/3
  • −16.67% = ×5/6
  • +14.29% = ×8/7

Powers that keep appearing:

  • 1.1² = 1.21
  • 1.1³ = 1.331
  • 1.1⁴ = 1.4641
  • 1.05² = 1.1025
  • 1.2² = 1.44
  • 1.2³ = 1.728
  • 1.08² = 1.1664
  • 0.9² = 0.81
  • 0.9³ = 0.729

Squares, cubes and powers

Squares 11–30

  • 11²121
  • 12²144
  • 13²169
  • 14²196
  • 15²225
  • 16²256
  • 17²289
  • 18²324
  • 19²361
  • 20²400
  • 21²441
  • 22²484
  • 23²529
  • 24²576
  • 25²625
  • 26²676
  • 27²729
  • 28²784
  • 29²841
  • 30²900

Cubes 1–12

  • 1³1
  • 2³8
  • 3³27
  • 4³64
  • 5³125
  • 6³216
  • 7³343
  • 8³512
  • 9³729
  • 10³1000
  • 11³1331
  • 12³1728

2¹⁰ = 1024, 3⁵ = 243, 3⁶ = 729, 5⁴ = 625.

Five methods used in every chapter

  1. 1

    Assume a convenient value

    Take 100 for percentages, the LCM of the days for work, the LCM of the times for speed.

  2. 2

    Hold one quantity fixed

    If distance is fixed, speed and time are inversely proportional; if time is fixed, distance and speed are directly proportional. The same logic covers price × quantity and rate × time.

  3. 3

    Write equations before calculating

    One unknown per sentence of the question, then solve.

  4. 4

    Alligation (weighted average)

    If A (value a) and B (value b) mix to give an average m, then A : B = (b − m) : (m − a). Section 10 teaches it fully.

  5. 5

    Use the options

    Backsolve and eliminate (see Exam day).

Daily mental-math drill, 15 minutes

Multiply by 5
Multiply by 10, then halve. Multiply by 25: multiply by 100, then divide by 4.
Two-digit number × 11
34 × 11 = 3 | (3 + 4) | 4 = 374.
Percent of a number by pieces
17% of 240 = 24 (10%) + 12 (5%) + 4.8 (2%) = 40.8.
Near-square products
49 × 51 = 50² − 1 = 2499.

Every day: 20 fraction-to-percent conversions, 20 squares, 10 successive-percentage calculations.