Logical & analytical reasoning

Answer: (d) Neither I nor II

A comparison is certain only when every sign between the two letters points the same way. B and E are separated by a change of direction at C, and S = T ≤ U = V allows S to equal V, so neither conclusion is always true.

1. Statement I: between B and E the chain reads B > C < D > E. The direction changes at C, so B and E cannot be compared.
2. Example: B = 5, C = 1, D = 10, E = 8 fits the chain, and here B is less than E. So I is not always true.
3. Statement II: between S and V the chain reads S = T ≤ U = V, which gives only S ≤ V.
4. If T = U, then S = V, so S is not always less than V. II is also not always true.
5. Neither statement is correct.

• ✗ I B > C and D > E, but C < D breaks the chain; B can be smaller than, equal to or larger than E.
• ✗ II S = T ≤ U = V gives S ≤ V, so S may equal V; 'always less than' does not follow.

Remember · Trace the signs between the two letters: a change of direction means no conclusion; any ≤ or ≥ rules out strict < or >.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) Cannot be concluded

The item gives no rule about who tells the truth. Even if we assume every innocent person speaks the truth, both 'P stole' and 'Q stole' fit all the statements, so the thief cannot be identified.

1. The item says only one person is guilty but gives no rule on who tells the truth or lies.
2. Test the most helpful assumption: innocent people speak the truth. If R stole, innocent P's claim 'Q stole it' would be false — so R is ruled out.
3. If P stole: innocent Q says R and Q did not steal (true), and innocent R says he did not steal (true). Consistent.
4. If Q stole: innocent P says he did not steal and Q stole it (true), and innocent R's statements are true. Consistent.
5. Both P and Q remain possible, so the thief cannot be concluded.

Remember · In truth-and-lie puzzles, test each suspect as culprit for consistency; if more than one survives, the answer is 'cannot be concluded'.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) Only four

As siblings, P, Q and R share S as mother and T as father, so S and T are a couple. Only P's gender is known, so the statements that need Q to be male or R to be female are not definite; the other four are.

1. P, Q and R are siblings, so R's mother S and P's father T are the parents of all three — and a couple.
2. P is male (a brother). The genders of Q and R are not given.
3. Definitely true: I (S and T are a couple), III (T is Q's father), IV (S is P's mother), VI (P is S's son).
4. Not definite: II (Q may be a daughter) and V (R may be a son).
5. So four statements are definitely true.

• ✓ I S is the mother and T the father of the same siblings, so they are a couple.
• ✗ II Q's gender is not given; Q could be T's daughter.
• ✓ III T is P's father and Q is P's sibling, so T is Q's father.
• ✓ IV S is R's mother and R is P's sibling, so S is P's mother.
• ✗ V R's gender is not given; R could be T's son.
• ✓ VI P is male and S is his mother, so P is S's son.

Remember · Note every gender actually given; a statement that needs an unknown gender is never 'definitely true'.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) 399000

The code multiplies the alphabet positions of the letters: 14 × 15 = 210, then × 20 = 4200, then × 5 = 21000. Adding S (19) gives 21000 × 19 = 399000.

1. Alphabet positions: N = 14, O = 15, T = 20, E = 5, S = 19.
2. NO = 14 × 15 = 210. NOT = 210 × 20 = 4200. NOTE = 4200 × 5 = 21000. The code is the product of the positions.
3. NOTES = 21000 × 19 = 399000.
4. Check: 4200 ÷ 210 = 20 (T) and 21000 ÷ 4200 = 5 (E), confirming the rule.

Remember · When a code grows as letters are added, divide consecutive codes: the ratio gives each new letter's value (here its alphabet position).

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) 71813

Each letter keeps a fixed digit across both words: Y = 7, E = 1, M = 8 and N = 3. So YEMEN is 7-1-8-1-3, i.e. 71813.

1. From FRANCE = 654321: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1.
2. From GERMANY = 9158437: G = 9, E = 1, R = 5, M = 8, A = 4, N = 3, Y = 7 (E, R, A, N agree with the first word).
3. YEMEN = Y, E, M, E, N = 7, 1, 8, 1, 3 = 71813.

Remember · For letter-to-digit codes, build a lookup table from the given words and read off the new word; check shared letters agree.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 31 km

Plotting the places on a grid shows two road routes from D to F: via C, A and B (6 + 10 + 6 + 9 km) and via E and G (5 + 14 + 12 km). Both total 31 km.

1. Put A at (0, 0), with east = +x and north = +y.
2. B = (0, 6); C = (10, 0); D = 6 km south of C = (10, −6); E = 5 km west of D = (5, −6); F = 9 km west of B = (−9, 6); G = 12 km south of F = (−9, −6).
3. Route D → C → A → B → F: 6 + 10 + 6 + 9 = 31 km.
4. Route D → E → G → F: 5 + 14 + 12 = 31 km (E to G runs from x = 5 to x = −9).
5. Either way the distance is 31 km.

Remember · For direction-and-road items, fix one place as the origin and write coordinates; route lengths then follow by simple addition.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (b) 1331

Both examples turn a cube n³ into (n + 3)³: 4³ becomes 7³ and 6³ becomes 9³. So 512 = 8³ becomes 11³ = 1331.

1. 64 = 4³ and 343 = 7³; 216 = 6³ and 729 = 9³.
2. The rule: n³ is written as (n + 3)³.
3. 512 = 8³, so it is written as 11³ = 1331.

Remember · Recognise squares and cubes at sight (up to 20² and 12³); number codes often shift the base.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error