Logical & analytical reasoning

Answer: (c) Only III

'Some rats are cats' converts directly into 'Some cats are rats'. The other two conclusions are 'no' statements that would need a definite chain, but the links to cows and to rats run through 'some' statements, which settle nothing.

1. Statement 1 converts: some rats are cats → some cats are rats. Conclusion III follows.
2. Only the cats that are dogs are kept away from cows (no dog is a cow); the other cats may or may not be cows, so Conclusion I is not certain.
3. Rats reach dogs only through cats, by two 'some' links; a rat may or may not be a dog, so Conclusion II is not certain.
4. Only III follows.

• ✗ Conclusion I Cats that are not dogs could still be cows; nothing rules it out.
• ✗ Conclusion II Two 'some' statements give no definite link between rats and dogs, either way.
• ✓ Conclusion III It is the direct converse of 'Some rats are cats'.

Remember · A 'some' statement converts both ways; a 'no' conclusion needs an 'all' or 'no' chain — 'some' links never prove it.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) Only statement 3 is sufficient

All four colours are used on five floors, so exactly one colour repeats. If floors I and V are both red, red is that repeat, and floors II, III and IV must take the other three colours, one each — no two neighbours can match. Statements 1 and 2 leave the end floors free to copy a neighbour.

1. Five floors, four colours, all four used: one colour appears on two floors, the others once each.
2. Statement 3: I and V are red, so red is the repeated colour; II, III and IV take the other three colours, all different and none red.
3. Hence I–II, II–III, III–IV and IV–V all differ: statement 3 alone is sufficient.
4. Statement 1: II, III, IV differ, but floor I may copy floor II (e.g. blue, blue, green, yellow, red) — not sufficient.
5. Statement 2 (II ≠ IV) is already implied by statement 1, so 1 and 2 together are still not sufficient; 2 alone says nothing about any adjacent pair.

• ✗ 1. Not sufficient: it leaves the pairs I–II and IV–V unchecked.
• ✗ 2. Not sufficient: floors II and IV are not neighbours, so it controls no consecutive pair.
• ✓ 3. Sufficient: it forces II, III and IV to be the three non-red colours, all different.

Remember · 'Painted using four different colours' means all four are used; with five floors exactly one colour repeats — build from that count.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) 100 km

West and South are at right angles, so Q, P and R form a right triangle with the right angle at P. QR is the hypotenuse of a 60–80–100 triangle.

1. Q is due West and R due South of P, so angle QPR = 90°.
2. QR² = 60² + 80² = 3600 + 6400 = 10000.
3. QR = 100 km.
4. Check: 60 : 80 : 100 = 3 : 4 : 5.

Remember · Perpendicular directions make a right triangle; spot 3–4–5 multiples before squaring.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) 1, 2 and 3

The data fixes only the 40% who do not play cricket: they all play football and so all own two-wheelers. Nothing is said about whether cricketers own two-wheelers or also play football, so none of the three conclusions can be drawn.

1. Non-cricketers = 40%; all of them play football, so all of them have two-wheelers.
2. The 60% cricketers are not described: some may own two-wheelers, some may also play football.
3. Conclusions 1 and 2 need every cricketer to be without a two-wheeler — not given.
4. Conclusion 3 needs cricketers to avoid football — not given; the rule runs only from 'not cricket' to 'football'.
5. So 1, 2 and 3 all cannot be drawn.

• ✗ 1. Cannot be drawn: at most 60% lack two-wheelers; fewer do if any cricketer owns one.
• ✗ 2. Cannot be drawn: cricketers' vehicles are never mentioned.
• ✗ 3. Cannot be drawn: a cricketer may also play football; the data does not forbid it.

Remember · 'Whoever is not A does B' says nothing about the members of A; claims about that group cannot be drawn.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) 17 m

Plotting the walks from A's house, A's office is at (42, 2) and B's at (34, −13). They are 8 m apart east–west and 15 m apart north–south, so the straight-line distance is 17 m.

1. Take A's house as (0, 0), East as +x and North as +y.
2. 20 m + 10 m East: both reach (30, 0).
3. A turns left (North) 2 m → (30, 2), then right (East) 12 m → A's office at (42, 2).
4. B turns right (South) 8 m → (30, −8), left (East) 4 m → (34, −8), right (South) 5 m → B's office at (34, −13).
5. Separation: 42 − 34 = 8 m East–West and 2 − (−13) = 15 m North–South.
6. Distance = √(8² + 15²) = √289 = 17 m.

Remember · Use coordinates for direction puzzles; left and right depend on the direction currently faced.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) 1, 2 and 3

F is the father of B and D. G is F's widowed sister-in-law, so her late husband was F's brother, and C, B's cousin, is her child. The one slot left in the family — the mother of B and D — belongs to E, who is therefore F's wife, A's grandmother and C's aunt.

1. F is D's father; B and D are siblings, so F is B's father too, and A (B's daughter) is F's granddaughter.
2. G is a widow and F's sister-in-law, so her husband — F's brother — is no more.
3. C is B's cousin, so C is the child of G and F's late brother.
4. E completes the family as F's wife, the mother of B and D; the three females are then G, A and E.
5. So E is F's wife, A's grandmother and, as the wife of C's uncle, C's aunt.

• ✓ 1. E is the mother of B and D, hence F's wife.
• ✓ 2. A is the daughter of E's son or daughter B, so E is A's grandmother.
• ✓ 3. C is the child of F's brother; F's wife E is C's aunt.

Remember · Place each stated relation on a family tree; the leftover member usually fills the one slot the tree still needs.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) ‘Whose weight is greatest’ cannot be determined

S1 makes Sohan lighter than both Mohan and Rohan. S2 only says Mohan weighs less than twice Rohan, which allows Mohan to be heavier or lighter than Rohan. So the heaviest person cannot be fixed.

1. S1 (twice Sohan is below each of the others): 2S < M and 2S < R, so Sohan is the lightest.
2. S2: 2R > M and 2R > S — Mohan may be anything below twice Rohan.
3. Example 1: S = 10, R = 30, M = 50 → 20 < 50, 20 < 30, 60 > 50, 60 > 10; Mohan is heaviest.
4. Example 2: S = 10, R = 30, M = 25 → all conditions still hold; Rohan is heaviest.
5. The greatest weight cannot be determined.

Remember · Test inequality puzzles with two sets of numbers; if both fit the conditions but give different answers, it cannot be determined.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) Weight of Sohan is least

S1 says twice Sohan's weight is less than Mohan's and less than Rohan's. Since weights are positive, Sohan's own weight is even smaller, so Sohan is the lightest.

1. S1: 2S < M and 2S < R.
2. Weights are positive, so S < 2S; hence S < M and S < R.
3. Sohan is lighter than both others: Sohan's weight is the least.
4. S2 is not needed for this item.

Remember · If twice a quantity is below the others, the quantity itself certainly is — for positive values, x < 2x.

Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error