Quantitative Aptitude and Mathematics
The concept map
Almost every question is built from a small set of cores: percentages and their conversion to fractions; ratio and proportion; averages and weighted averages; profit, loss and discount; simple and compound interest; time–speed–distance; time and work (including pipes and cisterns); mensuration of standard figures; permutations, combinations and probability; number system (LCM/HCF, divisibility, remainders); and data interpretation from tables, bar and pie charts.
Traps built into the paper
- Percentage asymmetry: a 20% rise followed by a 20% fall does not return to the original value.
- Average speed: for equal distances, speed is the harmonic mean 2xy/(x+y), not (x+y)/2.
- Successive discounts never add: two 10% discounts give 19%, not 20%.
- 'By what percent' vs 'what percent': the denominator is always the base named after 'than' or 'of'.
- Unit mismatch in speed/time questions (km/h against minutes) and in mensuration (cm against m).
- Work problems: a leak or an outlet pipe is negative work; add it with a minus sign.
Worked example (successive percentage change)
A price rises 20%, then falls 10%. Net change = a + b + ab/100 = 20 + (−10) + (20 × −10)/100 = 10 − 2 = 8% increase. This one formula covers successive discounts, successive price rises, and population growth.
Rule of thumb
Convert percentages to fractions early (12.5% = 1/8, 16.66% = 1/6, 33.33% = 1/3). Approximation with clean fractions is faster and safer than long division, and DI answers are usually spaced widely enough to permit it.