Quantitative Aptitude and Mathematics: Base-100 and LCM Models
Core areas
Quantitative aptitude rewards a small number of reliable techniques. Revise number system, HCF and LCM, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time and work, time–speed–distance, trains and boats, mensuration (2D and 3D), basic algebra, geometry, trigonometry, probability, and data interpretation. Learn tables up to 20, squares up to 30, cubes up to 15, and common fractions as percentages.
Traps
Unit mismatches are the biggest source of lost marks: metres vs kilometres, minutes vs hours, and 'per dozen' vs 'per unit'. Read whether profit is on cost price or selling price. Successive percentage changes are not additive. In time and work, remember that efficiency is inversely proportional to time. In compound interest, half-yearly compounding changes the rate and the number of periods. In data interpretation, check whether the question asks for a ratio, a percentage, or an absolute value.
Rule of thumb
Convert every problem into a single 'base = 100' or 'total work = LCM' model. For successive changes, multiply factors: a 20% increase followed by a 10% decrease is 1.20 × 0.90 = 1.08, i.e. an 8% net increase.
Worked example
A trader marks an item 40% above cost and allows a 25% discount. Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on 100, so 5%. Note that adding 40% and subtracting 25% would incorrectly suggest 15%.