Quantitative Reasoning and Mathematics
What this section tests
Arithmetic (fractions, ratio, percentage, averages, profit and loss, simple and compound interest, time–work, speed–distance–time), elementary algebra (linear equations, exponents, factorisation), basic geometry (angles, triangles, circles, area and perimeter, Pythagoras), and data interpretation from tables and charts (mean, median, mode).
Concepts to master
Percent means per hundred: always name the base before computing a change. Successive percentage changes do not add. Ratio sharing works on total parts. Average speed is total distance over total time. Simple geometry facts - angle sum of a triangle is 180°, the exterior angle equals the sum of the two remote interior angles, area of a circle is πr² - solve many items faster than algebra.
Traps that repeat
- Wrong base: percent change is (new − old) ÷ old, never ÷ new.
- Successive changes: a 25% rise then a 20% fall is not a 5% change.
- Average speed: never the arithmetic mean of two speeds.
- Unit mismatch: cm versus m, minutes versus hours, grams versus kilograms.
- Over-precision when the question asks for an approximation.
- Misreading percent of as percent more than.
Rule of thumb
Write the given quantities with their units and the unknown's symbol before substituting. Convert every comparison into per-hundred terms and state the base explicitly. If two methods disagree, the unit or base is usually the culprit.
Worked example
A price rises 25% and then falls 20%. Start at 100: after the rise it is 125; 20% of 125 is 25, so it returns to 100 - a net change of zero, not the tempting 5%.