Syllogism & Logical Deduction: previous-year questions

Answer: (C) Some white X-brand cars with radial tyres are parked here.

Statement 1 says every X-brand car parked here is white, and statement 2 says some of these cars have radial tyres; together they give 'some white X-brand cars with radial tyres are parked here' (C). The statements say nothing about the tyres of other brands, so A and D (which are identical in the booklet) cannot be concluded, and they say only that the X-brand cars here are white, so B ('only white cars are parked here') does not follow, since cars of other brands and colours may also be parked. 'All cars are not X-brand' simply means that some cars are of other brands. Rule: a valid conclusion must not go beyond the group the statements actually speak about.

Answer: (A) A quadrilateral cannot be square unless it has four equal sides, but having four equal sides doesn't guarantee a quadrilateral to be a square.

A necessary condition is one without which the result cannot happen; a sufficient condition is one that by itself guarantees the result. Every square has four equal sides (necessary), but four equal sides do not make a square, because a rhombus also has four equal sides; right angles are needed as well (so the condition is not sufficient). Option A says exactly this. Options B and C reverse the meaning by denying that squares have equal sides, and D denies any connection. In symbols, 'P is necessary for Q' means Q implies P, and 'P is sufficient for Q' means P implies Q.

Answer: (D) All persons with high education has good earnings.

The statement has the form 'if P then Q' (highly educated implies earns well). Option D, 'all highly educated persons have good earnings', is the same statement in other words, so it must be true. Options A and C are the converse ('if Q then P'), the error called affirming the consequent, since a person may earn well without being highly educated. Option B is the inverse ('if not P then not Q'), which also does not follow. The only other statement that is logically equivalent to the original is its contrapositive: 'a person who does not earn well is not highly educated'.

Answer: (A) Only '1' is strong.

PSC's final key 'A' treats only argument 1 as strong: making seniority the only criterion would deny promotion to more deserving and suitable juniors, which bears directly on merit and efficiency. Argument 2 is weak because it appeals to feelings (humiliation) rather than to any principle; argument 3 is treated as weak because experience alone does not prove suitability, and 'must be rewarded' does not justify making seniority the sole criterion. In such questions a strong argument is directly related to the issue, factual and significant; a weak one is emotional, trivial or merely restates an opinion.

Answer: (C) Tapas is rich and so he has a lot of influence.

The statement 'If a person is rich, he has a lot of influence' is a conditional (rich implies influence). The only valid inference is to affirm the condition for a particular case: Tapas is rich, therefore he has a lot of influence (modus ponens). Option (A) reverses the conditional - influence may come from other sources (the fallacy of affirming the consequent); options (B) and (D) deny the condition and conclude the opposite (the fallacy of denying the antecedent). The valid contrapositive would be: a person without much influence is not rich.

Answer: (C) Smoking may lead to cancer.

The given statement is a particular one - 'many' smokers, not all or most, get cancer - so the only safe conclusion is the cautious, possibility-type one: smoking may lead to cancer. Option (A) wrongly turns it into a claim about cancer patients, option (B) strengthens 'many' into 'most', and option (D), though true in life, speaks of health in general and goes beyond what is stated. Rule: from 'some/many A are B' you may infer only a possibility, never a universal or majority claim.

Answer: (A) Only '1' and '3' are strong.

PSC's final key 'A' treats arguments 1 and 3 as strong: argument 1 gives a comparative, fact-based reason (the maximum number of holidays among countries) and argument 3 a direct practical benefit (faster work and clearance of pending jobs). Argument 2 defeats itself - it calls the practice a British legacy that 'should be carried forward', which supports keeping the holidays, not reducing them; argument 4 is treated as weak because 'ample spare time' is vague and employees already have weekly offs and leave. Since options (B) and (C) both include argument 2, they can be eliminated first.

Answer: (B) Many students are not genius.

'All students are not genius' is logically the denial of 'all students are genius': it asserts that at least some students are not genius. The option that preserves this sense is 'Many students are not genius'. Option (A), 'Every student is not genius', would mean that no student is a genius, which is too strong; option (C) is something the statement may suggest but does not assert; option (D), about non-students, has no basis. In standard logic, 'All S are not P' is read as the particular negative 'Some S are not P'.

Answer: (C) D > A

Chaining the given inequalities gives $A>B>C>D$, meaning A is the greatest and D is the smallest of the four. "D > A" directly contradicts this chain and is therefore definitely wrong, while $A>D$, $A>C$ and $B>D$ all follow validly from the chain.

Answer: (A) (ii), (iii), (i), (iv), (v)

The natural real-world sequence of a medical episode runs: Illness occurs, one visits a Doctor, has a Consultation, receives Treatment, and finally experiences Recovery — i.e., (ii), (iii), (i), (iv), (v).

Answer: (D) (i), (v), (iv), (ii), (iii), (vi)

Following the broad biological hierarchy from most general to most specific gives: Animal, Vertebrate, Mammal, Feline (the cat family), then narrowing to the specific example Leopard, and finally the most familiar and specific everyday example, Cat — i.e. (i), (v), (iv), (ii), (iii), (vi).

Answer: (D) banks

By definition, every river flows within banks; a delta or tributaries are common but not universal features (some rivers have neither), and boats are entirely incidental to a river's existence.

Answer: (A) lens

Every camera, by definition, requires a lens to focus light onto its recording medium; film reels are absent in digital cameras, and a flash or stand are optional accessories, not defining features.

Answer: (D) d

From 'Tanushree is a dancer' and 'Dancers are young ladies' it follows that Tanushree is a young lady who is a dancer, i.e. conclusion (d), the answer the key takes. Conclusion (a) is the invalid converse (all dancers are young ladies does not mean all young ladies are dancers), and (c) contradicts the statements. Conclusion (b) only repeats the second statement; the key prefers (d) because it combines both statements.

Answer: (C) Harry

Hard-working: Tom, Brown, Jack. Ambitious: Tom, Dick, Jack. Harry is in neither list (he is only intelligent and honest), so he is neither hard-working nor ambitious. Brown is hard-working but not ambitious, and Dick is ambitious but not hard-working; Brown is not among the options anyway.