Quantitative Reasoning: Multiplicative Percentages, Rates, and Estimation
What this domain tests
Quantitative Reasoning is 40 items in 45 minutes with no calculator, roughly 65–70 seconds each. Content runs from arithmetic and percentages through algebra, geometry, trigonometry, probability and statistics, rates and ratios, and data interpretation from tables and graphs. The mathematics is not hard; the pace and the design of the distractors are.
Core rules
- Percent change is multiplicative. A 25% increase multiplies by 1.25; a 20% decrease multiplies by 0.80. Never add or subtract percentages across successive changes.
- Average speed is total distance divided by total time, not the mean of the two speeds.
- Probability: multiply along independent events, add across mutually exclusive ones. Without replacement, the denominator shrinks each draw.
- Geometry: circle area πr², circumference 2πr, triangle angles sum to 180°, and similar triangles give proportional sides. Watch radius versus diameter.
- Convert units before computing; mixing minutes with hours is the single most common arithmetic error.
- Estimate first: round to numbers that cancel, then compare with the answer choices.
Worked example
A jacket priced at $80 is marked up 25%, then later discounted 20%. What is the final price?
Apply each change to the running price. Markup: 80 × 1.25 = 100. Discount: 100 × 0.80 = 80. The final price is $80, a net change of 0%. The trap answer, 5% (25 − 20), comes from subtracting percentages; successive percent changes compound on different bases, so they neither add nor cancel.
Traps that cost marks
- Adding percentages instead of multiplying factors.
- Averaging two speeds over equal distances; for 60 and 40 mph the correct average is the harmonic mean, 48 mph.
- Using diameter where radius is required in area and volume formulas.
- Forgetting that drawing without replacement changes the denominator.
- Misreading a graph's axis scale, especially when it starts at a nonzero value.
- Solving for x and stopping without answering what the question actually asked, such as x + 3.