Every topic
Pick any topic. Each one has a full lesson, a slide deck for class, and practice questions with worked solutions. New to aptitude? Start with the first card.
Start here
Three plain methods that crack most questions before you learn a single formula.
Speed maths
Vedic and Trachtenberg shortcuts: multiply, square and check answers in seconds.
Where these shortcuts come from
Most of these tricks have names. The Indian set is called Vedic Mathematics: 16 short Sanskrit rules (sutras) published by Bharati Krishna Tirthaji...
Multiply without long multiplication
Long multiplication writes every partial product and adds them at the end. Criss-cross does the same sums in your head, one answer digit at a time,...
Squares, cubes and roots in seconds
Almost every square you need is one of four patterns: ends in 5, near 50, near 100, or (a+b)2. Roots of perfect squares and cubes come from the last...
Percent-fraction table and quick checks
Half of percentage, profit, interest and DI questions get easy once 12.5% reads as 1/8 without thinking. The digit-sum check catches a wrong product...
Division, fractions and approximation under time pressure
Division is where time goes. Divide by 5, 25 and 125 by multiplying instead, compare fractions without dividing, and approximate when the options are...
Quantitative aptitude
Numbers, percentages, money, time, speed, shapes and chance.
Number System
Most number questions never need the full number. Divisibility wants the last few digits, unit digit wants the last digit, remainders want small...
Percentage
A percentage is a fraction with 100 underneath. Swap it for the fraction from the table and most questions become one division.
Profit and Loss
Profit and loss are always a % of cost price, never of selling price. Put CP = 100 and most questions solve themselves.
Discount
Discount is always on the marked price; profit is always on the cost price. Most questions are just connecting the two with CP = 100.
Ratio and Proportion
A ratio is a recipe, not an amount. Write amounts as 'parts', find what one part is worth, then multiply.
Partnership
Profit is split by capital × time, never by capital alone. Rupee-months is the only number that matters.
Simple Interest
SI is the same amount every year. If you know two year-end totals, their gap divided by the years between is one year's interest.
Compound Interest
CI is SI on a growing base. For 2 years the only extra over SI is interest on the first year's interest.
Time and Work
Never add days. Make the total work the LCM of the days, turn each person into units-per-day, then add those.
Pipes and Cisterns
Pipes are Time and Work with signs: filling pipes add, emptying pipes (and leaks) subtract.
Time and Distance
Distance = speed × time, and you can hold any one of the three fixed. When distance is fixed, speed and time trade in inverse ratio.
Problems on Trains
A train crossing something covers its own length plus that thing's length. A pole or a man counts as length zero.
Boats and Streams
Downstream the river helps, upstream it fights. Boat speed is the average of the two; stream speed is half the gap.
Averages
An average is the level everything would sit at if you evened it out. Work with deviations from that level instead of adding raw numbers.
Ages
The gap between two people's ages never changes. Anchor on the gap and every ratio question becomes counting units.
Mixtures and Alligation
Alligation is a see-saw: the mix price sits between the cheap and dear prices, and the quantities are in the inverse of the distances.
Mensuration
Areas scale with the square of lengths, volumes with the cube. A 10% longer side gives 21% more area and 33.1% more volume.
Probability
Probability = favourable / total, but only when every outcome is equally likely. List the sample space when in doubt; it is small more often than you...
Permutation and Combination
Order matters → permutation. Order does not matter → combination. Ask 'would swapping two picks give a different answer?'
Data Interpretation
DI is speed arithmetic on a table. Read the question first, then only the cells it needs; approximate with the fraction table.
Logical reasoning
Series, codes, directions, seating, puzzles and arguments.
Series
Every series is built from one of a handful of rules. Check them in order: differences, second differences, ratios, squares/cubes, two series...
Coding and Decoding
Find the rule from the one example, then test it on a second letter before you trust it. Most codes are a shift, a reversal, or a position-sum.
Directions
Draw it. Put a plus sign on paper and track every turn; right turn = clockwise. Distances are Pythagoras at the end.
Analogy
Say the relation in one sentence ('a doctor works in a hospital') and apply the same sentence to the second pair.
Ranking
Position from left + position from right = total + 1. Everything in this topic is that one line.
Syllogisms
Draw circles (Venn), never reason in words. A conclusion follows only if it is true in EVERY possible drawing.
Seating Arrangement
Place the most definite clue first (someone at an end, someone facing the centre), then fill around it. Draw every time.
Statements: Assumptions and Conclusions
An assumption is something the speaker must take for granted; a conclusion is something that must follow from the statement. Neither may add outside...
Puzzles
Make a grid (people × attributes) and fill ticks and crosses. A puzzle is solved by elimination, not inspiration.
Odd One Out / Classification
Find the rule that three share. The odd one breaks it. Check primes, squares, cubes, even/odd, vowels, letter gaps.
Blood Relations
Draw a family tree: + for male, - for female, horizontal line for couples, vertical for parent-child. Never hold it in your head.
Counting Figures
Count systematically by size: all 1-piece shapes, then all 2-piece shapes, and so on. Or use the formulas below for standard grids.
Cryptarithmetic
Start from the column that gives the most information: the leftmost carry, a letter that repeats, or a sum that must be 1.