Aptitude
Quantitative aptitude and logical reasoning — percentages, algebra, time-speed-distance, probability, puzzles, and the shortcuts that crack timed tests.
Foundations & Number Sense
Number Systems and Divisibility
Types of numbers, divisibility rules for 2-12, factors, and multiples — the foundation everything else builds on.
HCF and LCM
Finding HCF and LCM using prime factorization and division, their relationship, and word problems.
Fractions, Decimals, and Surds
Converting between fractions and decimals, comparison tricks, and surds simplification.
Powers, Indices, and Roots
Laws of exponents, square and cube roots, and mental math shortcuts for common powers.
Unit Digits and Remainders
Cyclicity of unit digits, remainder theorem, and pattern recognition shortcuts for MCQs.
Simplification and Approximation
BODMAS mastery, approximation tricks for large numbers, and when to estimate vs compute exactly.
Arithmetic & Commercial Math
Percentages
Percentage-fraction equivalents, successive changes, and the shortcuts that save minutes in exams.
Profit, Loss, and Discount
Cost price, selling price, markup, discount, and the dishonest dealer problems that trip everyone up.
Simple and Compound Interest
SI and CI formulas, the 2-3 year shortcut for CI-SI difference, and installment problems.
Ratio and Proportion
Ratio basics, componendo-dividendo, and proportional division problems asked everywhere.
Averages
Weighted averages, average speed, and the 'adding/removing elements' problems that come up constantly.
Mixtures and Alligation
The alligation (cross) method, repeated dilution, and mixing problems that seem hard but have a simple trick.
Partnership
Simple and compound partnership, time-based profit sharing, and working vs sleeping partner problems.
Algebra & Equations
Linear Equations
Solving single and simultaneous linear equations, word problem translation, and substitution shortcuts.
Quadratic Equations
Factorization, discriminant, nature of roots, and the sign-based comparison trick for inequalities.
Inequalities
Linear and quadratic inequalities, modulus inequalities, and the wavy curve method for fast solving.
Arithmetic and Geometric Progressions
AP and GP nth term, sum formulas, and the word problems that use sequences without telling us.
Logarithms
Log laws, change of base, common values to memorize, and simplification problems.
Set Theory and Venn Diagrams
Union, intersection, complement, inclusion-exclusion for 2 and 3 sets, and maxima-minima problems.
Time, Speed & Work
Time and Work
Work-rate concept, the LCM method that makes everything easier, pipes and cisterns, and group work problems.
Time, Speed, and Distance
Unit conversions, average speed, relative speed, and the meeting point problems asked everywhere.
Trains
Crossing poles, platforms, and other trains — the formulas and the one concept that makes it all click.
Boats and Streams
Upstream, downstream, still water speed, and the standard problems that use these concepts.
Races and Circular Tracks
Head starts, dead heats, and the LCM method for finding when runners meet on circular tracks.
Clocks
Angle between clock hands, relative speed of hands, coincidences, and faulty clock problems.
Geometry & Mensuration
Lines, Angles, and Triangles
Angle properties, triangle types, congruence and similarity, Pythagoras, and area formulas for triangles.
Circles
Arc, chord, tangent properties, sector and segment areas, and the inscribed angle theorem.
Quadrilaterals and Polygons
Properties of parallelogram, rectangle, rhombus, square, trapezium — area formulas and diagonal relationships.
Mensuration: Areas and Perimeters
Area and perimeter of composite shapes, pathway problems, and carpet/painting word problems.
Mensuration: Volume and Surface Area
Cube, cuboid, cylinder, cone, sphere — volume, surface area, and melting/recasting problems.
Coordinate Geometry Basics
Distance formula, section formula, slope, equation of a line, and area of triangle from coordinates.
Counting & Probability
Permutations
Fundamental counting principle, nPr, arrangements with repetition, circular permutations, and word arrangement problems.
Combinations
nCr, selection problems, distribution, committee formation, and the difference between selection and arrangement.
Probability
Classical probability, addition and multiplication rules, conditional probability, and Bayes' theorem basics.
Dice, Coins, and Cards
Sample spaces for common objects, at-least/at-most problems, and the recurring templates for exam questions.
Data Interpretation Basics
Reading bar, line, and pie charts, calculating ratios and percentages from data, and spotting trends quickly.
Data Sufficiency
The framework for data sufficiency questions, common traps, and the systematic elimination strategy.
Logical Reasoning
Number and Letter Series
Identifying arithmetic, geometric, alternating, and mixed patterns in number and letter sequences.
Coding and Decoding
Letter shifting patterns, number-based coding, substitution ciphers, and reverse engineering the coding rule.
Blood Relations
Family tree construction, generation mapping, coded relationship problems, and the systematic approach.
Direction and Distance
Cardinal directions, turns, shortest distance using Pythagoras, and shadow-based direction problems.
Seating Arrangement and Puzzles
Linear and circular seating, floor-based arrangements, constraint satisfaction, and the elimination approach.
Syllogisms
Venn diagram method, all/some/no relationships, definite vs possibility conclusions, and the complementary pair shortcut.
Order, Ranking, and Sequencing
Position from top/bottom, interchanging positions, and alphabetical/chronological ordering puzzles.
Tips & Exam Strategy
Mental Math and Vedic Math Tricks
Multiplication shortcuts, squaring tricks, the fraction-percentage table, and digit sum verification.
Approximation and Option Elimination
When to approximate vs compute, using answer options to eliminate, back-substitution, and unit analysis.
Time Management in Aptitude Tests
Question triage, time-per-question budgeting, when to guess vs skip, and section-wise strategy.
Common Traps and Mistakes
The most frequent errors in aptitude tests — sign mistakes, misreading problems, ratio vs percentage confusion, and deliberate traps.