Mathematics and Quantitative Reasoning
Arithmetic and algebra
The quantitative section rewards clean setup more than speed. Translate words into an equation before calculating. Key relationships: part = percent × whole; percentage change = (new − old) ÷ old × 100; distance = rate × time; simple interest = principal × rate × time. In algebra, isolate the variable by doing the same operation to both sides, then substitute your answer back into the original equation.
Ratio, proportion, and geometry
A ratio compares parts, not necessarily the total. If a sum is divided in the ratio 3:5, the total is 8 parts. For geometry, keep formulas separate: area of a rectangle = length × width; triangle = ½ × base × height; circle area = πr²; circumference = 2πr. Convert units before combining measurements.
Worked example
A trader sells a bag for L$1,200 after a 20% discount. What was the marked price? Let the marked price be x. The selling price is 80% of x, so 0.80x = 1,200. Divide both sides by 0.80: x = 1,200 ÷ 0.8 = 1,500. The marked price was L$1,500. Check: 20% of 1,500 is 300, and 1,500 − 300 = 1,200. A common error is to add 20% of 1,200 to 1,200, which gives 1,440-wrong because the discount is calculated on the marked price, not the selling price.
Traps
Using the wrong base in percentage problems; mixing units (km with m, hours with minutes); forgetting that the median is the middle value after ordering; and rounding too early, which shifts the final answer.