Quantitative Reasoning
What the section tests
Quantitative Reasoning (QR) is 40 multiple-choice items in 45 minutes, covering algebra, geometry, trigonometry, statistics, probability, ratios, unit conversions, and data interpretation. The exam is designed to be solved without a scientific calculator, so estimation, backsolving, and clean setup are central. Expect word problems with real-world or science contexts and answer choices separated by enough distance that approximate arithmetic can eliminate three options.
Core rules and concepts
- Translate words into equations before calculating: define the unknown, write the relationship, then substitute.
- Use backsolving when answer choices are numerical and the equation is awkward; test the middle value and adjust.
- Use plugging in for percent or variable problems: choose 100 for an original price or a common denominator for fractions.
- Geometry: area, circumference, Pythagorean theorem, similar triangles, special right triangles (30-60-90, 45-45-90), and volume formulas.
- Trigonometry: sine, cosine, tangent, and the unit circle; know common values for 30, 45, and 60 degrees.
- Statistics: mean, median, mode, range, standard deviation as spread, and weighted averages. Probability: independent events multiply; mutually exclusive events add.
- Convert units by cancellation, and keep track of percent versus percentage points.
Worked example
How many liters of 20% saline solution must be added to 8 L of 50% saline to obtain a 30% mixture? Let x be liters of 20% solution. Salt: 0.20x + 0.50(8) = 0.30(x + 8). Then 0.20x + 4 = 0.30x + 2.4. Subtract: 1.6 = 0.10x, so x = 16 L. Check: 16 L at 20% contributes 3.2 L salt; 8 L at 50% contributes 4 L; total salt 7.2 L in 24 L, which is 30%. The common wrong answer, 8 L, comes from assuming equal volumes rather than equal salt.
Traps that cost marks
- Adding percentages directly instead of weighting by volume or amount.
- Mixing units (minutes with hours, centimeters with meters) before computing.
- Answering the value of x when the question asks for a total or a difference.
- Forgetting that percent increase then percent decrease does not return to the original value.
- Rounding too early; carry exact values until the final step, then compare with answer choices.