Quantitative Reasoning
What the quantitative section tests
Quantitative items mix arithmetic, algebra, geometry, and data interpretation. High-yield topics: percentages and successive changes, ratios and proportions, averages, rates and work, linear equations, angle and area rules, divisibility and primes, and reading values from tables or charts.
Two habits decide most scores. First, translate the words into an equation or a multiplication factor before computing. Second, check units and the exact quantity requested - many wrong choices are correct answers to a slightly different question.
Frequent traps:
- Percent changes do not add. A 20% rise then a 20% fall give 1.2 × 0.8 = 0.96, a 4% net decrease, not 0%.
- Averages of averages. You cannot average two group means unless the groups are equal in size; weight each mean by its group size.
- Average speed. For equal distances at speeds a and b, average speed is 2ab/(a+b), not (a+b)/2.
- Geometry figures are not to scale. Use given lengths and angle facts, never appearance.
- Percent of what? "Increased by 25%" multiplies by 1.25; "increased to 25%" does not.
Worked example. A car covers 60 km at 60 km/h and returns at 40 km/h. Time is 1 + 1.5 = 2.5 hours for 120 km, so average speed is 48 km/h. The tempting 50 km/h is the trap.
Rule of thumb: convert every percent change to a factor (increase 1 + r, decrease 1 − r) and multiply the factors in sequence.