OEA Admission Exam cheat sheet

Percent change = (new − old) ÷ old × 100; a 20% decrease followed by a 20% increase yields a net 4% decrease, not zero.

Successive percentage changes multiply: combined factor = (1 + a)(1 + b); for two changes of r%, net = 2r + r²/100 percent.

Average speed over equal distances = harmonic mean = 2xy/(x + y), not the arithmetic mean (x + y)/2.

Work rates add: if A finishes in a days and B in b days, together they take ab/(a + b) days.

Compound interest: A = P(1 + r/n)^(nt); simple interest: I = Prt. Doubling time under continuous growth ≈ 70 ÷ percent rate.

Ratio scaling: keep units consistent and cross-multiply; for a:b = c:d, ad = bc. Part-to-whole vs part-to-part must be distinguished before solving.

In data tables, compute the required quantity directly from the stated columns; never infer a total from a subset unless the problem states the subset is exhaustive.

Weighted mean = Σ(wᵢxᵢ) ÷ Σwᵢ; a simple average of group averages is valid only when group sizes are equal.

Median is positional (middle of ordered data) and resistant to outliers; mean shifts with extreme values. Mode is the most frequent value.

Main idea = the claim the whole passage supports; a true but narrow detail is a trap answer, not the main idea.

Inference answers must be necessarily true given the text; if the passage only allows 'possibly', the answer choice saying 'must' is wrong.

Tone and attitude words (qualified, unequivocal, skeptical, ambivalent) must match the author's hedges such as 'arguably' or 'in most cases'.

Scope check: an answer that adds a comparison, cause, or time frame absent from the passage is out of scope even if plausible.

EXCEPT and NOT questions invert the task: eliminate the four choices the passage supports and keep the unsupported one.

Analogy questions require matching the logical relationship (part-to-whole, cause-effect, degree), not surface topic similarity.

Para-jumble strategy: find the opening sentence (no backward-referring pronouns like 'this' or 'these'), then track pronoun and connector chains.

Vocabulary in context: substitute each option into the original sentence and test whether the passage's logic still holds.

Contrapositive is valid: from 'if P then Q' infer 'if not Q then not P'. The converse ('if Q then P') and inverse ('if not P then not Q') are invalid.

'Only if' introduces the necessary condition: 'P only if Q' means P → Q, so Q is necessary and P is sufficient.

'Unless' means 'if not': 'P unless Q' translates to 'if not Q then P'.

Necessary vs sufficient: sufficient guarantees the outcome; necessary is required but may not guarantee it. Confusing them is the most common flaw.

Syllogism validity: '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'.

For seating/ordering puzzles, fix the most constrained element first, then propagate; draw a linear or circular diagram rather than reasoning verbally.

If-then rules in grouping puzzles: treat each rule as a constraint and test answer choices by violation rather than constructing full solutions.

Correlation is not causation; post hoc, ad hominem, circular reasoning, and false dilemma are the standard flaw labels to check first.

Numerical series: test differences, then ratios, then alternating sub-series; check squares, cubes, and primes before assuming a complex rule.

Subject-verb agreement: the verb agrees with the head noun, not a prepositional phrase ('The list of items is'), and with neither/nor the verb matches the nearer subject.

Pronoun case: after 'than' or 'as', supply the implied verb to choose ('She is taller than I [am]', not 'than me').

Dangling modifier rule: an introductory participial phrase must describe the subject of the main clause.

Semicolon joins two independent clauses; a colon must follow a complete clause and introduces an explanation or list.

Comma splice and run-on are errors; fix with a period, semicolon, or coordinating conjunction.

Parallel structure: items in a series and elements joined by and/or/but must share grammatical form (all infinitives, all gerunds).

Affect is usually a verb (to influence); effect is usually a noun (result). 'Between' takes two items; 'among' takes three or more.

Prefer the concise, active construction: eliminate redundancy ('return back', 'reason because') and wordy expletives ('there is').

Modifiers like 'only' and 'almost' must sit adjacent to the word they limit; placement changes meaning.

Order of operations: parentheses, exponents, multiplication/division left to right, addition/subtraction left to right.

Break multi-step word problems into stated givens, the target quantity, and the unit of the answer; convert units before computing.

Estimation check: round to one significant figure to bound the answer, then verify the exact result falls inside that bound.

Pigeonhole principle: placing n items into k containers guarantees at least one container holds ⌈n/k⌉ items.

Permutations count ordered arrangements (n!/(n−r)!); combinations count unordered selections (n!/(r!(n−r)!)).

Probability of at least one = 1 − probability of none; independent events multiply, mutually exclusive events add.

Set problems: |A ∪ B| = |A| + |B| − |A ∩ B|; extend with inclusion-exclusion for three sets.

Calendar and clock reasoning: a clock's hands overlap 11 times in 12 hours; the minute hand gains 5.5° per minute on the hour hand.

For 'which assumption is required' items, negate the choice: if negation destroys the argument, it is a necessary assumption.