The Quantitative Doctrine
SSC CGL TIER-I & TIER-II / THE CALCULATION ENGINE
Our goal is not merely "Finish SSC CGL Maths."
MAKE BASIC ARITHMETIC SO AUTOMATIC THAT YOUR BRAIN STOPS SPENDING CONSCIOUS TIME ON IT.
MAKE BASIC ARITHMETIC SO AUTOMATIC THAT YOUR BRAIN STOPS SPENDING CONSCIOUS TIME ON IT.
With a 15-minute Tier-I Quantitative Aptitude section, this matters enormously. A candidate who has to consciously calculate 17×8, 12.5%, or √784 repeatedly is burning time that should be spent on logic.
Layer 0: The Memory Engine
THE 25 PILLARS OF MENTAL INFRASTRUCTURE
0.1
Multiplication Tables
1 → 20
Don't cram vertically. Learn the network. Multiple routes to the same answer.
17 × 8 = (10×8) + (7×8) = 136
0.2
Squares
1² → 50²
A serious SSC asset. 1-30 instant; 31-50 rapid recall using algebraic patterns.
35² = (30+5)² = 900+300+25 = 1225
0.3
Cubes
1³ → 20³
Critical for simplification, compound interest, and number-based logic questions.
11³ = 1331 | 12³ = 1728
0.5
Reciprocals
1/2 → 1/20
Rapid recognition of repeating patterns. 1/6, 1/7, 1/9, 1/11, 1/14.
1/7 = 0.142857...
0.6
Multiples Composition
Mental Splitting
You don't need to memorize every multiple. Build from 2-10, derive the rest.
27 × 14 = 27 × (10+4) = 378
0.7
Prime Numbers
1 → 200
Foundational for divisibility, HCF, LCM, factorisation, and remainder problems.
2, 3, 5, 7, 11, 13, 17, 19...
0.8
Prime Factorisation
Instant Breakdown
Become comfortable breaking numbers immediately. Backbone for number systems.
360 = 2³ × 3² × 5
0.9
Divisibility Rules
2 → 20
Absolute core. Master 3, 4, 7, 8, 9, 11, 16.
11: Alternating digit-sum rule.
0.10
Common Factor Pairs
60, 72, 84...
Memorise factor pairs of common numbers to speed up quadratic splitting and simplifying.
72: 1×72, 2×36, 3×24, 4×18...
0.11
Square & Cube Roots
Estimation
Instantly identify perfect roots, and learn to bound imperfect roots tightly.
√700 lies between 26² and 27²
0.16
Ratio Fluidity
Part-to-Total
Foundational for partnership, mixture, averages, ages, and distribution.
Ratio 2:3 = Total 5 parts.
0.18
Order of Operations
BODMAS + Vinculum
Don't just memorize the acronym. Understand hierarchy including nested brackets.
The foundation of Simplification.
0.19
Algebraic Identities
The Big Seven
These should eventually become automatic language for Algebra and Simplification.
a³+b³ = (a+b)(a²−ab+b²)
0.21
Pythagorean Triples
Base + Multiples
Extremely valuable. Saves enormous time in Geometry and Trigonometry.
3-4-5 | 5-12-13 | 8-15-17
0.24
Complement Pairs
Base 100 / 1000
Powerful speed technique for mental arithmetic and percentage manipulation.
625 + 375 = 1000
0.4 Fraction ↔ Percentage
THE CORE CONVERSION MATRIX
Master the base, derive the rest (e.g., 3/8 = 37.5%, 5/8 = 62.5%). Massively accelerates Profit & Loss, SI/CI, and DI.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33⅓% |
| 1/6 | 0.166... | 16⅔% |
| 1/7 | 0.1428... | 14.28% |
| 1/8 | 0.125 | 12.5% |
| 1/9 | 0.111... | 11⅑% |
| 1/12 | 0.083... | 8⅓% |
| 1/16 | 0.0625 | 6.25% |
0.13 & 0.14 Power Bases
COMPUTATIONAL REASONING
Numbers that appear constantly in SSC logic and compound interest problems.
Powers of 2 (Absolute Memory)
2³=82⁴=162⁵=322⁶=642⁷=1282⁸=2562⁹=5122¹⁰=10242¹²=4096
Powers of 3 & 5
3³=273⁴=813⁵=2433⁶=729
5³=1255⁴=625
The CGL Syllabus Map
THE RECOMMENDED ASCENSION ORDER
PHASE B
Number System
Natural / Whole / Integers
Divisibility · HCF · LCM
Remainders · Unit Digit
Factors (Number & Sum)
Prime Numbers · Cyclicity
PHASE C
Arithmetic Core
Percentage → Ratio & Proportion → Average
Profit & Loss → Discount
Simple Interest → Compound Interest
Partnership → Mixture & Alligation
Time & Work → Pipes & Cisterns
Time, Speed & Distance → Trains → Boats
PHASE D
Algebra
Identities · Linear Equations
Simultaneous Equations
Surds · Indices
Algebraic Manipulation · Graphs
PHASE E
Geometry
Lines & Angles · Triangles
Congruence · Similarity · Centres
Quadrilaterals · Polygons
Circles · Chords · Tangents
PHASE F
Mensuration
2D: Square, Rectangle, Rhombus, Trapezium, Circle
3D: Cube, Cuboid, Prism, Cylinder, Cone, Sphere, Pyramid
PHASE G
Trigonometry
Ratios · Identities
Standard Angles · Complementary Angles
Heights & Distances
PHASE H
Data Representation
Tables · Bar Graphs · Pie Charts
Histograms · Frequency Polygons
Mixed Charts (Tier-II specific depth)
The Real Game
AFTER EVERY CHAPTER, EXECUTE THIS SEQUENCE:
CONCEPT
→
SHORTCUT
→
PYQ
→
TIMED DRILL
→
MIXED PYQ
The official syllabus is the map. Your PYQs are the evidence of what SSC actually asks. We will build pattern recognition: "SSC loves asking this" vs "Rare but legitimate."
Our First Lesson Starts Now
Quant 001: Speed Baseline
Don't use a calculator. 20 randomly ordered products. Enter your answers to establish your calculation reflex benchmark.
1.7 × 8
2.13 × 7
3.16 × 9
4.12 × 8
5.17 × 6
6.9 × 7
7.14 × 8
8.19 × 7
9.11 × 9
10.15 × 12
11.18 × 7
12.16 × 8
13.13 × 9
14.17 × 8
15.12 × 14
16.19 × 6
17.15 × 13
18.18 × 9
19.14 × 12
20.17 × 11
QUANTITATIVE APTITUDE ARCHIVE