Quantitative Reasoning: Arithmetic and Its Shortcuts
This section applies school-level mathematics quickly: percentages, ratio and proportion, averages, work and rate, speed–distance–time, simple and compound interest, elementary algebra, basic geometry (area, perimeter, angles, Pythagoras) and simple probability. The mathematics is easy; marks are lost to misreading and unit errors. Set up the relationship before computing.
Setup rules
- Percentage change: always divide by the original value. A rise from 80 to 100 is 25%, not 20%.
- Successive changes: multiply factors, never add percentages. A 40% mark-up followed by a 25% discount gives 1.40 × 0.75 = 1.05, a 5% gain.
- Ratios: convert to a common unit, then to parts of a total. If A:B = 2:3 and the total is 45, one part is 45 ÷ 5 = 9.
- Work and rate: add rates, not times. Two pipes filling in 6 and 12 hours together take 1/(1/6 + 1/12) = 4 hours.
- Averages: total = average × count. Never average two averages unless the counts are equal.
Worked example
A trader marks an item 40% above cost and then allows a 25% discount. What is the profit percentage? Take cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on a cost of 100, so 5%. The tempting answer, 15%, comes from subtracting 40 − 25; it fails because the discount applies to the marked price, not the cost.
Traps that cost marks
- Taking the percentage of the wrong base (marked price instead of cost).
- Mixing km/h with metres and seconds in the same calculation.
- Using compound interest where the question says simple, or vice versa.
- Choosing an option that is arithmetically neat but answers a slightly different question.