Bocconi Graduate Test cheat sheet

Percentage change = (new − old)/old × 100; a 20% rise followed by a 20% fall leaves the original value at 0.96, a net 4% loss.

Successive percentage changes multiply: net factor = (1 + a)(1 + b); for a = +10% and b = −10% the factor is 0.99.

Compound interest: A = P(1 + r/n)^(nt); simple interest: A = P(1 + rt). Doubling time under continuous growth ≈ 70/r percent (rule of 70).

Quadratic roots: x = [−b ± √(b² − 4ac)]/(2a); the discriminant b² − 4ac gives two, one, or no real roots when positive, zero, or negative.

Arithmetic progression: aₙ = a₁ + (n − 1)d, sum = n(a₁ + aₙ)/2; geometric: aₙ = a₁r^(n−1), sum = a₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Ratios and mixtures: mixing parts a:b gives fraction a/(a+b); for three-part ratios use a common multiplier k so quantities are ak, bk, ck.

Work and rate: combined rate = 1/t₁ + 1/t₂; time together = t₁t₂/(t₁ + t₂). Distance = speed × time, with average speed = total distance / total time, not the mean of speeds.

Probability: P(A or B) = P(A) + P(B) − P(A and B); independent events multiply; conditional P(A|B) = P(A and B)/P(B).

Geometry essentials: area of triangle = ½bh, circle area = πr², circumference = 2πr, sphere volume = (4/3)πr³, Pythagoras a² + b² = c² for right triangles.

Deductive validity: an argument is valid if the premises cannot be true while the conclusion is false; validity is independent of whether premises are actually true.

Contrapositive is equivalent to the original conditional (if P then Q ⇔ if not Q then not P); the converse (if Q then P) and inverse are not equivalent.

Necessary vs sufficient: 'P is sufficient for Q' means P → Q; 'P is necessary for Q' means Q → P (equivalently not P → not Q).

Syllogism check: 'All A are B' plus 'All B are C' yields 'All A are C'; 'Some A are B' plus 'All B are C' yields 'Some A are C'.

Quantifier negation: not(all A are B) ⇔ some A are not B; not(some A are B) ⇔ no A are B.

Assumption questions: the correct answer is required for the conclusion to follow; test by negating it - if the argument collapses, it is the assumption.

Strengthen/weaken: identify the conclusion and the evidence link; the strongest option attacks or supports that specific link rather than a tangential claim.

Flaw types to recognize: circular reasoning, ad hominem, false dilemma, hasty generalization, confusing correlation with causation, and equivocation on a term.

Ordering and arrangement puzzles: draw a linear or table diagram, fix the most constrained element first, and eliminate options that violate a stated condition.

Main-idea questions: the answer must cover the whole passage, not one paragraph; reject options that are true but too narrow or too broad.

Inference questions: the correct choice is necessarily supported by the text; an option that is merely plausible in the real world is wrong.

Tone and attitude: watch qualifiers such as 'arguably', 'reportedly', 'unfortunately'; they signal the author's stance more reliably than isolated adjectives.

Scope words matter: 'all', 'only', 'never', 'primarily' change truth value; an option that overstates the passage's claim is incorrect.

Detail questions: locate the exact sentence, then compare each option's wording against it; paraphrases that add causes or comparisons not stated are traps.

Vocabulary in context: substitute each candidate meaning into the sentence and check that the surrounding logic still holds.

Paragraph function: classify sentences as claim, evidence, counterargument, or concession; this exposes the passage's structure for organization questions.

EXCEPT questions: three options are supported by the text; find the one that contradicts or is absent, and verify it against a specific line.

Read the axis labels and units first: charts may use thousands, millions, percentages, or index values (base year = 100).

Percentage of total: share = part/total × 100; when comparing shares across years, note that the total may change even if the part is constant.

Percentage points vs percent: a move from 20% to 25% is +5 percentage points but a 25% relative increase.

Index numbers: value in base-year terms = current index / 100 × base value; converting between index years uses the ratio of indices.

Growth rate over a period: CAGR = (end/start)^(1/n) − 1, where n is the number of intervals, not the number of data points.

Weighted averages: overall mean = Σ(weight × value)/Σweights; combining two groups gives a mean between the group means, closer to the larger group.

Estimation shortcut: round to two significant figures and check the option spacing; if options differ widely, exact arithmetic is unnecessary.

Ratios from tables: per-capita or per-unit figures require dividing the row value by the relevant denominator, not by the column total.

Table traps: a 'total' row may include categories not shown in the breakdown; confirm whether totals are additive before computing shares.