Mathematics / Quantitative Aptitude: Formula-First Problem Solving
The quantitative aptitude section tests school-level arithmetic, algebra, mensuration and data handling under time pressure without a calculator. Most items are designed to be solved in two or three lines once the right formula is chosen, so the skill being tested is formula selection, not long calculation.
Core formulas and concepts
- Percentage: successive changes of a then b give a + b + ab/100.
- Profit and loss: profit percent is calculated on cost price unless the question says otherwise; discount is always calculated on the marked price.
- Interest: SI = PRT/100; CI = P[(1 + R/100)^T − 1]. For half-yearly compounding, halve the rate and double the time.
- Time and work: combined rate is 1/a + 1/b. Speed: S = D/T; upstream speed is u − v, downstream u + v.
- Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h; sphere volume 4/3 πr³.
Worked example
A shopkeeper marks goods 40 per cent above cost and then allows a 25 per cent discount. Find the profit percent. Reasoning: let cost price be 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 105 − 100 = 5 on a cost of 100, so profit is 5 per cent. The two percentages do not cancel each other, because they are calculated on different bases.
Traps that cost marks
- Applying discount on cost price or profit on selling price.
- Confusing percentage points with percent change.
- Using simple interest when the question says compounded annually.
- Mixing units - converting centimetres to metres before using a mensuration formula.