Quantitative Reasoning: DAT Study Guide
What the DAT Quantitative Reasoning section covers
Quantitative Reasoning (QR) is 40 questions in 45 minutes. It tests algebra, geometry, trigonometry, probability and statistics, ratios, percentages, unit conversions, and data interpretation. Questions include standard multiple-choice and quantitative comparison (QC) formats, so both calculation speed and comparison logic matter. Most items are designed for quick setup rather than lengthy computation.
Core rules and concepts
- Arithmetic: convert fractions, decimals, and percents; use benchmarks and estimation to eliminate.
- Algebra: solve linear and quadratic equations, systems, inequalities, exponents, and logs; check for extraneous or negative solutions.
- Geometry: area, volume, similar triangles, circles, coordinate distance/slope, and angle relationships.
- Trigonometry: unit-circle values, identities, law of sines and cosines, and right-triangle ratios.
- Probability/statistics: permutations vs combinations, 'without replacement,' mean/median/range, and qualitative standard deviation.
- QC: compare quantities A and B; test 0, 1, fractions between 0 and 1, and negatives before deciding.
- Data interpretation: check axis labels, units, and whether a graph shows totals or rates. Translate word problems into one equation or proportion before calculating; several choices differ only by a unit or sign. Know the area and volume formulas for circles, triangles, cylinders, and spheres.
Worked example
A bag contains 4 red, 5 blue, and 3 green marbles. Two are drawn without replacement. What is the probability both are red? First draw: 4/12. With one red removed, second draw: 3/11. Multiply: (4/12)(3/11) = 12/132 = 1/11. The 'without replacement' wording changes the denominator; with replacement the answer would be (4/12)^2 = 1/9.
Traps that cost marks
- Using the wrong denominator after a draw without replacement.
- Mixing units (minutes vs hours, centimeters vs meters) before computing.
- Forgetting a second solution to a quadratic or an absolute-value equation.
- In QC, assuming a variable is positive when the stem does not say so.
- Overcomputing: many items can be solved by estimation or by eliminating impossible answer choices.