SOF IEO cheat sheet

Word order: standard declarative order is Subject + Verb + Object + Manner + Place + Time (SVOM place time). Adverbs of frequency go before the main verb but after 'be': 'She is always late', 'She always arrives late'.

Inversion rule: after a negative or restrictive adverbial at the start of a clause, invert subject and auxiliary - 'Never have I seen...', 'Rarely does he complain', 'Not only did she win, but she also broke the record'.

Conditionals: zero = present + present (general truth); first = if + present simple, will + base (real future); second = if + past simple, would + base (unreal present); third = if + past perfect, would have + past participle (unreal past). Mixed: 'If I had studied, I would be a doctor now'.

Modal meaning map: must = strong obligation or logical certainty; have to = external obligation; should/ought to = advice or expectation; can = ability or permission; may/might = possibility or formal permission; could = past ability or tentative possibility; needn't = absence of obligation vs mustn't = prohibition.

Modal past forms: modal + have + past participle expresses a judgement about the past - 'must have left' (certainty), 'can't have known' (impossibility), 'should have called' (unfulfilled duty or regret), 'might have been' (past possibility).

Collocations: fixed verb-noun pairs must be memorised, not logically derived - make a decision, take responsibility, do harm, pay attention, draw a conclusion, keep a promise, raise an issue, meet a deadline, heavy rain, strong argument.

Phrasal verbs: meaning shifts with the particle and transitivity matters. Separable (object may sit between verb and particle): turn the light off / turn off the light - 'pick up', 'give away'. Inseparable: 'look after', 'run into', 'call on'. Three-part verbs are always inseparable: 'put up with', 'get away with', 'look forward to'.

Idioms: meaning is non-compositional, so decode from context. Common exam sets - 'a blessing in disguise' (hidden benefit), 'bite the bullet' (endure something unpleasant), 'break the ice' (start a conversation), 'hit the nail on the head' (be exactly right), 'once in a blue moon' (very rarely), 'the last straw' (final tolerable limit).

Language and people: register and tone carry social meaning. Formal register uses full forms and Latinate vocabulary; informal uses contractions, phrasal verbs and idioms. Politeness is marked by hedging ('I was wondering whether...'), indirect questions (word order reverts to statement order: 'Could you tell me where the station is?').

Work rate formula: rate = work / time; combined rate adds - 1/a + 1/b = 1/t. If A finishes in 6 h and B in 3 h, together they take t where 1/6 + 1/3 = 1/2, so t = 2 h.

Successive percentage changes multiply, they do not add: a 20% rise then a 20% fall gives 1.20 × 0.80 = 0.96, a net 4% decrease. Reverse a percentage change by dividing: price after +25% is 1.25 × original.

Average speed is total distance divided by total time, never the mean of the speeds. Equal distances at speeds a and b give harmonic mean 2ab/(a+b).

Ratio and mixture rule: when two solutions of concentrations p% and q% are mixed to give r%, the ratio of their amounts is (q − r) : (r − p). This is the alligation cross and solves most mixture questions directly.

Logical structure: a conditional 'If P then Q' is equivalent to its contrapositive 'If not Q then not P'. The converse ('If Q then P') and inverse ('If not P then not Q') are NOT equivalent - the classic trap in syllogism and inference items.

Quantifier logic: 'all A are B' does not imply 'all B are A'. Negation of 'all A are B' is 'some A are not B'; negation of 'some A are B' is 'no A are B'. One counterexample is enough to falsify a universal claim.

Seating and ordering puzzles: fix the most constrained item first, then apply each clue as an elimination constraint. Write 'A immediately left of B' as a single block (AB); 'A is not adjacent to B' as a forbidden pair, not a position.

Number series and coding: check differences, then ratios, then alternating sequences (two interleaved series). For letter-shift codes, convert letters to positions 1–26 and test a constant shift before a positional or reverse-alphabet rule.

Data sufficiency and assumption spotting: for 'sufficient' questions, test each statement alone before combining. For argument questions, the assumption is the unstated premise needed to make the conclusion follow - reject options that merely restate the evidence or weaken the claim.