Mathematics / Quantitative Aptitude
Quantitative aptitude rewards formula recall plus calculation speed. High-yield areas are percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, pipes and cisterns, time–speed–distance, trains and boats, mensuration, basic trigonometry, and data interpretation from tables, bar graphs and pie charts.
Formulas worth memorising
- Successive percentage change: net = a + b + ab/100.
- Profit% = (SP − CP)/CP × 100; discount is always calculated on the marked price.
- SI = PRT/100; CI amount = P(1 + r/100)^t.
- Train passing a pole: time = length ÷ speed; convert km/h to m/s by multiplying by 5/18.
- Average of 1 to n = (n+1)/2; average speed for equal distances = 2xy/(x+y).
Worked example
A trader marks goods 40% above cost and allows a 25% discount. Find his profit percent. Take CP = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 105 − 100 = 5 on a cost of 100, so profit = 5%. The reasoning hinges on the base: the discount is applied to the marked price, not to the cost price, and the profit is finally expressed on the cost price.
Traps
- Applying the discount to CP instead of MP - the single biggest source of error here.
- Assuming SI and CI give the same amount beyond the first year.
- Mixing units: cm² with m², minutes with hours.
- Over-calculating in data interpretation when the options are far apart; approximate deliberately.
- Forgetting that in time and work, efficiency is inversely proportional to days taken.