Quantitative Reasoning: Rates, Percents, Averages, and Word Problems
What the section tests
Quantitative Reasoning emphasizes applied arithmetic: percents, ratios and proportions, rates, weighted averages, basic algebra, and data described in text or tables. Calculator-free fluency with fractions and estimation matters more than advanced math.
Core concepts
- Percent change = (new − old) ÷ old. A 20% decrease then a 20% increase does not return you to the start (0.8 × 1.2 = 0.96).
- Percent of vs. percent more than: "20% of 50" is 10; "20% more than 50" is 60.
- Ratios: convert to parts of a total. A 3:5 split of 40 gives 15 and 25.
- Weighted averages: total the quantities, then divide by the total count - never average the averages.
- Rates: distance = rate × time; combined work rates add as reciprocals of completion times.
Traps that cost points
- Unit mismatch (minutes vs. hours, cents vs. dollars).
- Average speed confused with the average of two speeds.
- Answering a partial step - the choice equals an intermediate value, not the requested one.
- Percent of a changed base, e.g., discount applied after tax.
- Misreading "percent" as "percentage points."
Worked example
A courier drives 60 miles at 30 mph and returns at 60 mph. What is the average speed for the round trip?
Time out = 60 ÷ 30 = 2 h; return = 60 ÷ 60 = 1 h. Total distance = 120 mi, total time = 3 h. Average speed = 120 ÷ 3 = 40 mph - not 45, which is the trap answer from averaging the speeds.
Rule of thumb: for any average-rate or weighted-average item, convert to total quantity ÷ total count before dividing.