Quantitative Reasoning
What this domain tests
Quantitative Reasoning asks you to work with rates, ratios, proportions, percents, unit conversions, and multi-step word problems. You are not just computing-you are deciding which relationship applies. Core concepts: proportional reasoning (direct vs. inverse), percent change, average rate, density and scaling, and estimation to check plausibility.
Traps to watch
- Percent of vs. percent change. "20% of 50" is 10; "increased by 20%" multiplies by 1.20. Mixing these is the most common error.
- Inverse relationships. If workers double, time halves. Do not apply direct proportion to rate problems.
- Unit mismatch. Minutes vs. hours, cents vs. dollars. Convert before you compute.
- Successive percents do not add. A 20% discount then a 10% discount is not 30% off.
- Answering the wrong quantity. The question may ask for the remainder, not the total.
Rule of thumb
Set up a proportion with labeled units and cancel them like fractions. If the units of your answer are wrong, your setup is wrong.
Worked example
A machine fills 180 bottles in 12 minutes. At this rate, how many in 45 minutes? Rate = 180/12 = 15 bottles per minute. Then 15 × 45 = 675 bottles. Check plausibility: 45 minutes is nearly four times 12, so the answer should be a bit under 4 × 180 = 720. 675 fits.
For percent change, use (new − old)/old × 100. If a price rises from $40 to $50, that is 10/40 = 25% increase-not 20%.