Quantitative Reasoning
Quantitative Reasoning on the OAT tests arithmetic, algebra, geometry, trigonometry, statistics, probability, and data interpretation. Items are often word problems that require setting up an equation before calculating.
Core rules
- Percent change = (new − old)/old × 100%. Percent increase and percent of are not the same operation.
- Average speed = total distance ÷ total time, not the average of separate speeds unless times are equal.
- Geometry formulas: circle area = πr²; circumference = 2πr; triangle area = ½bh; Pythagorean theorem a² + b² = c².
- Probability of independent events multiplies; without replacement changes the denominator and numerator for later draws.
- For a data set, mean is sensitive to outliers while median is resistant. Standard deviation measures spread around the mean.
Worked example
A jar has 5 red and 3 blue marbles. Two are drawn without replacement. Probability both are red = (5/8)(4/7) = 20/56 = 5/14 ≈ 0.357. The second fraction uses 4 red out of 7 remaining marbles.
Traps
Watch unit conversions; do not average rates without weighting by time; do not use the original denominator after a percent change; do not confuse permutation with combination; do not ignore that “without replacement” changes later probabilities.