Bocconi Test cheat sheet

Main-idea stems (primarily, mainly, chiefly, the passage is concerned with) require an answer covering the whole passage; an answer true of only one paragraph is a detail, not the main idea.

Stems such as 'according to the passage' or 'the author states' are literal-retrieval items: the credited answer paraphrases an explicit line, and outside knowledge is irrelevant.

An inference answer must follow necessarily from stated information; if it requires an assumption or real-world fact not in the passage, it is wrong.

Vocabulary-in-context items are solved by substituting each option into the original sentence and checking that meaning, tone, and grammar still fit.

Extreme scope words in options (all, never, only, must, entirely) usually exceed what the passage claims; the passage's own qualifiers set the ceiling.

EXCEPT/LEAST questions invert the task: four options are supported by the text and the credited answer is the one that is not; verify each option separately.

Contrast markers (however, although, yet, despite, but) mark a turn, and the author's actual position generally appears after the marker rather than before it.

Purpose is why the author wrote the passage (to argue, to describe, to refute, to reconcile); tone is the attitude conveyed by evaluative adjectives and adverbs.

Passage structure questions map function per paragraph: hypothesis, evidence, counterargument, rebuttal, implication - matching the role, not the topic, identifies the answer.

Every argument reduces to a conclusion plus premises: the conclusion is the claim the other statements support and typically follows therefore, thus, hence, or clearly.

An assumption is an unstated premise required for the conclusion to follow; the negation test confirms it - negate the statement and see whether the argument collapses.

Strengthen and weaken answers act on the evidence–conclusion link, making the required assumption more or less likely; options about the topic but off the link do no work.

A sufficient condition guarantees the outcome, a necessary condition is merely required; treating one as the other is the standard flaw in conditional arguments.

Recurring flaw patterns: correlation treated as causation, unrepresentative sample, circular reasoning, false dilemma, equivocation, and appeal to authority.

In causal arguments, weaken by supplying an alternative cause or reversing causation; strengthen by ruling out alternative explanations or showing a dose–response pattern.

A percentage change does not imply the same change in absolute numbers when the base shifts; options conflating rates with counts are standard traps.

Paradox and resolve-the-discrepancy items need an answer that explains both stated facts; explaining one while contradicting the other is disqualifying.

Options introducing new concepts, entities, or comparisons outside the argument's scope are usually wrong regardless of how reasonable they sound.

Percentage change = (new − old) ÷ old × 100; the denominator is the original value, and 'percentage points' measures an absolute difference between two percentages.

Successive changes of a% and b% multiply as (1 + a/100)(1 + b/100); they never simply add unless one change is zero.

To undo a p% increase, divide by (1 + p/100); to undo a p% decrease, divide by (1 − p/100) - subtracting the percentage is incorrect.

Average = total ÷ count, so total = average × count; a combined average is weighted by group size and lies between the two group averages, closer to the larger group.

Rates add for work done in parallel: 1/t = 1/a + 1/b, and time together is always less than the faster individual time.

For equal distances at speeds a and b, average speed = 2ab/(a + b); for equal times, the arithmetic mean applies instead.

Distance = speed × time; unit conversions (km/h to m/s) multiply by 1000/3600, i.e. divide by 3.6.

In tables and charts, check axis units, breaks, and per-capita or thousands qualifiers before computing; most errors here are unit errors, not arithmetic errors.

Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a; the discriminant b² − 4ac gives two real roots if positive, one if zero, none if negative.

Exponent rules: a^m · a^n = a^(m+n), a^m / a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1, and a^(−n) = 1/a^n.

Multiplying or dividing an inequality by a negative number reverses the sign; adding or subtracting a constant never does.

Combinations C(n,k) = n! / (k!(n−k)!) count unordered selections; permutations n!/(n−k)! count ordered arrangements - the divide-by-k! step is what removes order.

Inclusion–exclusion: |A ∪ B| = |A| + |B| − |A ∩ B|; for three sets subtract the three pairwise overlaps then add back the triple overlap.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); for independent events P(A ∩ B) = P(A) · P(B), and P(not A) = 1 − P(A).

Arithmetic sequence: a_n = a₁ + (n − 1)d, with sum S_n = n(a₁ + a_n)/2; geometric sequence: a_n = a₁r^(n−1).

Geometry essentials: triangle area ½bh, circle area πr², circumference 2πr, and interior angles of an n-gon sum to (n − 2)·180°.

Number series: test first differences, then ratios, then alternating sub-series at odd and even positions, then squares/cubes ± a constant.

Letter series use A = 1 … Z = 26; reversed or mirror-alphabet patterns (A↔Z, B↔Y) appear frequently with constant-step shifts.

Rotation preserves a figure's handedness, reflection reverses it; a change in chirality proves reflection rather than rotation.

Track rotation in explicit steps and direction (90° clockwise, 45° counterclockwise) and check whether the number of sides or dots changes at the same time.

Figure matrices usually follow a rule along rows first, then along columns, then across the whole grid; confirm the candidate rule on every row before applying it.

Countable properties carry rules: number of sides, enclosed regions, intersections, line segments, dots, and axes of symmetry often change by a constant increment.

'If A then B' is equivalent to its contrapositive 'if not B then not A'; the converse (if B then A) and inverse (if not A then not B) are not equivalent.

Syllogisms: All A are B plus All B are C gives All A are C; No A are B plus All C are A gives No C are B; 'some' statements do not convert.

Ordering and seating puzzles: draw a linear or circular diagram and fix the most constrained item first, then place items limited relative to it.