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OAT: Quantitative Reasoning

OAT · Work through your exam, one topic at a time.

All guide sections

Quantitative Reasoning

What the quantitative reasoning section tests

OAT quantitative reasoning covers arithmetic, algebra, geometry, trigonometry, probability and statistics, and data interpretation. The math is not advanced, but the section is timed and deliberately includes distractors, so setup and estimation matter as much as calculation.

Core rules

  • Percents: a 20% increase multiplies by 1.20; a 20% decrease multiplies by 0.80. Percent change is (new−old)/old×100.
  • Algebra: isolate the variable by inverse operations; for systems, use substitution or elimination. Check by substituting back.
  • Geometry: area of a circle = πr²; circumference = 2πr; triangle area = ½bh; Pythagorean theorem a²+b²=c².
  • Trigonometry: SOH-CAH-TOA; sin²θ+cos²θ=1.
  • Probability: P(A and B)=P(A)P(B) for independent events; without replacement changes the denominator.
  • Statistics: mean is sensitive to outliers; median is the middle value; mode is most frequent.

Worked example

How many liters of 60% saline solution must be mixed with 20% saline solution to make 40 L of 30% saline? Let x = liters of 60%, so 40−x = liters of 20%. Salt: 0.60x+0.20(40−x)=0.30(40). Simplify: 0.60x+8−0.20x=12, so 0.40x=4 and x=10 L. Check: 6 L salt from the 60% portion plus 6 L from the 30 L of 20% portion equals 12 L salt in 40 L, or 30%.

Traps

  • Adding percentages instead of weighting by volume.
  • Confusing percent increase with percent of.
  • Forgetting that probability without replacement changes the total.
  • Using the diameter as the radius.
  • Rounding too early and losing the answer choice.