Quantitative Reasoning: Arithmetic Through Precalculus
Content and constraints
Quantitative Reasoning is fast: about 40 questions in 45 minutes, roughly one minute each. Topics include fractions and percentages, ratios and proportions, rates and work problems, algebra (linear and quadratic equations, inequalities, functions), geometry (area, volume, similar triangles, circles), basic trigonometry, exponents and logarithms, probability and counting, and descriptive statistics. Speed comes from estimation and from recognizing problem templates, not from long computation.
Traps
- Percent change base. A 20% increase followed by a 20% decrease does not return to the original value; multiply factors (1.2)(0.8) = 0.96.
- Average speed. Averaging two speeds is wrong when the distances are equal and times differ; use total distance over total time.
- "Not" and "at least." Compute the complement and subtract from 1.
- Overlapping sets. Double-counting the intersection inflates totals; use Total = A + B − Both + Neither.
- Units. Convert before computing; mixed minutes and hours sink otherwise easy items.
Rule of thumb
Back-solve from the answer choices when the algebra looks messy, and estimate to eliminate. If choices differ by orders of magnitude, rounding to one significant figure is enough.
Worked example
A car travels 60 miles at 30 mph, then 60 miles at 60 mph. Times are 2 hours and 1 hour; total distance is 120 miles over 3 hours, so average speed is 40 mph - not the 45 mph you get by averaging 30 and 60. Always rebuild the definition (distance/time) rather than averaging rates.