Numerical Aptitude: Arithmetic Shortcuts and Formula Discipline
Numerical Aptitude here is arithmetic rather than higher mathematics: number system, HCF and LCM, percentages, profit and loss, ratio and proportion, averages, simple and compound interest, time and work, speed and distance, and basic mensuration. Speed comes from converting percentages into fractions and writing the formula before touching the numbers.
Core rules
- Percentages: learn the fraction equivalents (12.5% = 1/8, 16 2/3% = 1/6, 20% = 1/5, 25% = 1/4). An increase of x per cent followed by a decrease of x per cent leaves a net loss of x squared divided by 100 per cent.
- Profit and loss: profit per cent is always on cost price; discount per cent is always on marked price. Selling price from cost price is CP(1 + p/100); from marked price it is MP(1 - d/100).
- Time and work: take the LCM of the individual days as total work, convert each worker into units per day, then add the rates. The combined time is never the average of the two times.
- Speed: average speed over equal distances is the harmonic mean 2xy/(x+y), not (x+y)/2.
- Mensuration: circle area is pi r squared, circumference is 2 pi r, cylinder volume is pi r squared h, and 1 litre equals 1000 cubic centimetres.
Worked example
A trader marks goods 40% above cost and allows a 25% discount. Let CP = 100, so MP = 140. SP = 140 x 0.75 = 105. Profit is 5 on a cost of 100, that is 5 per cent.
Traps that cost marks
- Dividing profit by selling price instead of cost price.
- Applying the discount to cost price rather than marked price.
- Mixing units, such as metres with centimetres or minutes with hours, before substituting.
- Using the simple-interest formula for the second year of a compound-interest question.