Quantitative Aptitude and Basic Mathematics: Speed with Method
High-Yield Topics
Number system and divisibility, HCF and LCM, percentages, profit and loss, ratio and proportion, averages, simple and compound interest, time-speed-distance, time and work, mensuration, and data interpretation (tables, bar and pie charts).
Build a Toolkit
Memorise fractional equivalents of common percentages (12.5% = 1/8, 16.66% = 1/6, 20% = 1/5), squares up to 30, and cubes up to 15. These convert lengthy calculations into quick ones.
Method Over Muscle
For percentages, use the multiplier approach: a 20% increase followed by a 25% decrease is 1.20 × 0.75 = 0.90, a net 10% decrease. For time and work, take total work as the LCM of the given days. For successive discounts, multiply the factors rather than adding percentages.
Traps
- Percentage change base: a rise from 40 to 50 is a 25% rise, not 10%.
- Unit mismatch: minutes versus hours in speed questions.
- Successive changes: never add or subtract percentage points directly.
- Approximation drift: in data interpretation, round only after estimating the operation.
Rule of Thumb
Before computing, estimate the answer's rough magnitude. If your result is far from the estimate, an arithmetic slip has occurred.
Worked Example
A shopkeeper marks an item 40% above cost and gives a 25% discount. Profit percent? Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on 100, so 5%.