Quantitative reasoning / Mathematics
Quantitative reasoning / Mathematics on the Bocconi Specialized Masters Test assesses numerical fluency and multi-step problem solving. Questions assume arithmetic, ratios, percentages, elementary algebra, geometry, counting/probability, and data interpretation; advanced calculus is rarely needed. The section rewards clean translation from words to equations and careful unit control.
Core rules and concepts
- Translate words into equations: define the unknown, write units, and keep part-to-part ratios separate from part-to-whole ratios.
- Percent change is (new − old)/old; successive changes multiply, so +20% then −25% is 1.20 × 0.75 = 0.90, a 10% net decrease.
- Rate problems add work rates; average speed over equal distances is harmonic: 2ab/(a+b), not (a+b)/2.
- Counting: use permutations when order matters, combinations when it does not; probability via the complement 1 − P(no event) often shortens work.
- Geometry: similar figures scale lengths by k, areas by k², and volumes by k³; keep π exact until the final step.
Worked example
A shirt costs €80. Its price rises 15%, then falls 20%. Final price? Multiply: 80 × 1.15 × 0.80 = 80 × 0.92 = €73.60. The net change is −8%, not −5%; adding percentages is valid only when both changes are calculated from the same base.
Traps that cost marks
Common traps: confusing percentage points with percent; reading “increased to” as “increased by”; using an arithmetic average for speeds; ignoring unit conversions; and choosing an answer without checking whether it satisfies every condition.
Key points
- Define variables and units before calculating.
- Multiply successive percentage changes; never simply add them.
- Distinguish part-to-part from part-to-whole ratios.
- Use harmonic mean for equal-distance average speed.
- Check the final answer against all stated conditions.