Mathematics / Quantitative Aptitude
Topic spread
Simplification and approximation, number system (LCM, HCF, divisibility), percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, time-speed-distance, mensuration, and data interpretation from a small table or bar chart.
Shortcuts that pay
- Fraction-to-percentage anchors: 1/8 = 12.5%, 1/6 = 16.67%, 1/12 = 8.33%.
- Successive change: net = a + b + ab/100. Two successive discounts of 20% and 10% give a net 28% reduction.
- km/h to m/s: multiply by 5/18.
- If a price rises 25%, consumption must fall 20% to keep expenditure constant (25/125 × 100).
- Average of consecutive numbers = middle term = (first + last)/2.
Worked example
A trader marks an item 40% above cost and allows a 25% discount. Find the profit or loss percent. Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on 100 = 5%. Reasoning: work from a base of 100 and never add 40% then subtract 25% on the same base. The discount applies to the marked price while profit is measured on cost price - two different bases, and that is exactly where the trap sits.
Traps
- Applying a discount to cost price instead of marked price.
- Compound interest for two years equals SI plus interest on the first year's interest, not 2 × SI.
- Time and work: add reciprocals correctly (A in 10 days, B in 15 days → 1/10 + 1/15 = 1/6, so 6 days together).
- A percent increase followed by an equal percent decrease never returns to the original value.