Quantitative Reasoning: Rates, Percentages, and Data Checks
Quantitative reasoning tests practical math under time pressure: percentages, ratios, rates, averages, and quick estimation from tables or word problems. The math is rarely advanced; the challenge is setup and avoiding careless errors.
Concepts to understand
- Percent change: change divided by the original value. A rise from 40 to 50 is +25%, not +10%.
- Percent of vs. percent more: "20% of 80" is 16; "20% more than 80" is 96. Read the wording twice.
- Successive percentages: a 10% increase then a 10% decrease does not return to the start; it lands slightly lower (multiply by 1.10 × 0.90 = 0.99).
- Ratios and rates: set up a proportion and keep units consistent. Distance = rate × time; work problems combine rates as reciprocals.
- Averages: total divided by count. To find a missing value, use the total: sum = average × count.
- Estimation: round aggressively to eliminate answer choices, then compute precisely only if two remain close.
Traps
- Using the new value as the base for percent change.
- Mixing units (minutes vs. hours, cents vs. dollars).
- Averaging averages of unequal groups without weighting.
- Answer choices that reflect the right method with one arithmetic slip-always re-check the final step.
Rule of thumb
Write the formula before you compute, label every unit, and sanity-check whether the answer is plausible in size and direction.
Worked example: A team of 4 completes a job in 12 days. How long for 6 workers at the same rate? Total work = 4 × 12 = 48 worker-days; 48 ÷ 6 = 8 days.