2.3 Verbal Logic, Percentages & Vocabulary

2.3 Verbal Logic, Percentages & Vocabulary

Quick Answer: Treat verbal logic as constrained deduction, percentages as careful translation into arithmetic, and vocabulary as meaning-in-context. On a timed PAF-style intelligence paper, these items are won by avoiding extra assumptions—not by writing long explanations.

Section 2.3 gathers the remaining high-frequency verbal-intelligence tools: logical deduction (statements and conclusions), simple percentages, and synonyms/antonyms, including engineering-context wording. Together with analogies and coding/series, they cover the usual verbal surface of initial tests for AE entry. Pace expectations remain the same hedge as earlier: candidates often mention on the order of 100 items in ~35 minutes for intelligence sittings—plan for brevity; do not invent pass percentages or sectional minima.

Verbal Logic — Only What Follows

Typical formats:

1. Two statements → conclusions (which conclusion follows?)
2. All / some / no categorical statements (basic syllogism)
3. If–then conditionals (modus ponens / denying the consequent carefully)
4. Seating / order micro-puzzles with three to five people (less common but same discipline)

Rules That Prevent Wrong “Common Sense”

• “All A are B” does not mean “all B are A.”
• “Some A are B” means at least one; it does not prove “some A are not B.”
• From “If P then Q”, given P, conclude Q. Given Q alone, do not conclude P.
• From “If P then Q”, given not Q, conclude not P. Given not P, do not conclude not Q.

Worked example — categorical

Statements: (1) All turbines are engines. (2) All engines need fuel.

Valid conclusion: All turbines need fuel. Invalid: “All engines are turbines.” Invalid: “Some fuel is a turbine” (not forced).

Worked example — conditional

“If the warning light is on, the circuit is open.” The warning light is on. Conclusion: the circuit is open. If instead you only know the circuit is open, you cannot conclude the light is on.

Worked example — “some”

“Some alloys are conductors. All conductors are tested.” Conclusion that follows: Some alloys are tested (the overlapping some that are conductors). “All alloys are tested” does not follow.

How to Attack Options

1. Underline quantifiers: all, some, no, only, unless.
2. Reject any option that adds a fact (cost, safety, PAF policy) not in the stem.
3. Prefer the option that is a logical consequence, even if it sounds narrower than a flashy alternative.

Simple Percentages — Translate, Then Compute

Intelligence-paper percentages are rarely multi-chapter commerce problems. They are usually:

• Find x% of N
• Express A as a percentage of B
• Successive percentage change
• Percentage increase/decrease between two values

Core conversions:

x% of N = (x/100) × N

A as % of B = (A/B) × 100

Increase from A to B = ((B − A)/A) × 100%

Worked example — direct

15% of 240 = 0.15 × 240 = 36.

Worked example — “what percent”

36 is what percent of 240? (36/240) × 100 = 15%.

Worked example — successive change (classic trap)

A quantity increases by 20% then decreases by 20%. Net factor = 1.20 × 0.80 = 0.96 → 4% net decrease, not a return to the original. If a stem says a metal rod’s recorded length rises 10% then falls 10%, the final reading is 99% of the original recorded value.

Worked example — AE dressing

“30% of 50 rivets failed inspection.” Failed count = 0.30 × 50 = 15. Remaining = 35. If a follow-up asks what percent of the remaining are later rejected when 7 more fail, that percent uses base 35, not 50.

Percentage Shortcut Habits

On a fast paper, convert 35% of 80 as 10% = 8, so 30% = 24, plus 5% = 4 → 28.

Vocabulary — Synonyms, Antonyms, Context

Synonym = nearest meaning; antonym = opposite meaning. Engineering-context items still test English, with science words as the payload.

High-yield pairs for AE / FSc-adjacent stems:

Worked example — context

“The wing surface must remain smooth to reduce drag.” Closest synonym among rough, even, porous, jagged → even (regular/level), not a materials-science essay on roughness height.

Worked example — antonym

Antonym of opaque in “opaque canopy section” → transparent (or clear), not dark (dark can still be opaque).

Worked example — near-synonym trap

Velocity vs speed: in casual English they blur; in physics stems, velocity is vector. If options are pure vocabulary without vector language, the paper may treat them loosely—read the option set before forcing a textbook objection.

Putting Logic, %, and Words on One Timeline

A realistic mixed drill (aim ~20–25 seconds average if your sitting matches the commonly reported density):

1. Logic: All sparrows are birds; some birds are migratory → some sparrows being migratory is not forced; do not pick it.
2. Percent: A tank is 40% full; 30 litres are added and it becomes 55% full. Capacity? Let C be capacity. 0.40C + 30 = 0.55C → 30 = 0.15C → C = 200 litres.
3. Vocab: Synonym of corrode → rust / eat away / oxidise (best available option); antonym orientation → protect / coat only if options support it.

Engineering-Context Verbal Items — Stay Inside the Stem

PAF AE candidates sometimes over-answer:

• A question about pitch in a vocabulary list may mean tar or musical pitch, not aircraft attitude, unless nearby words are aeronautical.
• A percentage item about fuel is still arithmetic; do not adjust for density or temperature unless numbers are given.
• A logic item about cadets in a hangar is a people-set puzzle; hangar knowledge does not add premises.

Study Plan for Section 2.3

• Daily: 5 syllogism/conclusion items, 5 percentage translations, 10 synonym/antonym flash checks.
• Keep an error notebook with three columns: added an assumption, % base wrong, near-miss synonym.
• Rehearse successive percentage change until the 20% up / 20% down → 4% down reflex is automatic.
• Review Sections 2.1–2.2 weekly so analogy, coding, and logic share the same “rule first” instinct.

Verbal intelligence for the Aeronautical Engineering Initial Test is a speed-and-precision craft. Official cut-offs are not asserted here; what you can control is method quality on every stem type in this chapter.