Mathematics · 24 questions in the exam

Numbers

Q: Percentage basics

A percentage is a multiplier: +p% is ×(1 + p/100), −p% is ×(1 − p/100). Percentage change is (new − old) ÷ old, and percentage points are not percent. 120 → 150: +30/120 = +25%; 10% → 12% is +2 points but +20%

Q: Successive and reverse percentages

Successive changes multiply, so +20% then −20% is ×0.96. To undo a change, divide by its multiplier; in a mixture, hold the unchanged part fixed. old = new ÷ (1 + p/100); n periods of p%: ×(1 + p/100)ⁿ

Q: Unit conversions

Multiply by a fraction equal to 1 and cancel units. Each step is ×10 for length, ×100 for area and ×1000 for volume; km/h ÷ 3.6 = m/s. 1 m² = 10 000 cm²; 1 dm³ = 1 L; 0.1 h = 6 min

How the real numbers are ordered, percentages and unit conversions: the arithmetic every other topic leans on. Numbers is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 5 lessons, each with the rule that solves it and a diagram.

Number sets and the number line

ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ. A rational number is a fraction of integers, so its decimal stops or repeats; √2 and π are irrational. Compare fractions by cross-multiplying and roots by squaring.

Rulea/b < c/d ⇔ ad < bc (b, d > 0); [a, b] includes the ends, (a, b) does not

Order and operations

Adding keeps an inequality; multiplying by a negative flips it. Reciprocals flip the order of same-sign numbers, and between 0 and 1 squaring shrinks while the square root grows.

Rulea < b, c < 0 ⇒ ac > bc; 0 < x < 1 ⇒ x² < x < √x < 1/x

Percentage basics

A percentage is a multiplier: +p% is ×(1 + p/100), −p% is ×(1 − p/100). Percentage change is (new − old) ÷ old, and percentage points are not percent.

Rule120 → 150: +30/120 = +25%; 10% → 12% is +2 points but +20%

Successive and reverse percentages

Successive changes multiply, so +20% then −20% is ×0.96. To undo a change, divide by its multiplier; in a mixture, hold the unchanged part fixed.

Ruleold = new ÷ (1 + p/100); n periods of p%: ×(1 + p/100)ⁿ

Unit conversions

Multiply by a fraction equal to 1 and cancel units. Each step is ×10 for length, ×100 for area and ×1000 for volume; km/h ÷ 3.6 = m/s.

Rule1 m² = 10 000 cm²; 1 dm³ = 1 L; 0.1 h = 6 min

What is the Bocconi Test format?

Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.

Questions / time: 50 / 75 minutes
Distribution: 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
Scoring: +1 correct · 0 blank · −0.2 wrong
Question languages: English · Italian
Three-option questions: Some critical thinking questions have three options; a wrong answer there costs −0.33
Minimum score: Below 17 points the test is not considered for selection
AI degree: Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
Law test: A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring

Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)

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