Quantitative Aptitude
What this domain tests
Quantitative Aptitude tests numerical accuracy and speed across number system, percentages, ratio and proportion, averages, time-work, time-speed-distance, interest, profit-loss, mensuration and data interpretation. Most items are short arithmetic; the challenge is choosing the fastest valid method.
Core rules and concepts
- Percentage: a change from A to B is ((B−A)/A)×100. Successive changes of x% and y% give a net change of x+y+xy/100 percent.
- Ratio: convert to parts; if a:b = 3:5, total 8 parts. Keep units consistent.
- Work: use LCM of days as total work. Efficiency is inversely proportional to time.
- Speed: average speed for equal distances is harmonic, 2xy/(x+y), not (x+y)/2.
- Interest: SI = PRT/100; CI = P(1+R/100)^T − P. For two years, CI − SI = P(R/100)^2.
- Mensuration: write formulae with units; convert cm/m before calculating.
Worked example
A can finish a job in 12 days and B in 18 days. How long together? Take total work = LCM(12,18) = 36 units. A does 3 units/day; B does 2 units/day; together 5 units/day. Time = 36/5 = 7.2 days, i.e. 7 1/5 days. The shortcut is 1/(1/12 + 1/18) = 1/(5/36) = 36/5.
Traps that cost marks
Do not subtract a discount from the marked price and then apply another percentage to the wrong base; successive discounts are not additive. Do not use the arithmetic mean for average speed over equal distances. In CI, do not add simple interest each year unless the question says so. Check whether the answer asks for days, hours or a fraction, and keep rupees, metres and percentages labelled.