Puzzles, arrangements & general mental ability

Answer: (a) 100 m

After the first turn the two run in opposite directions, so they end up 60 + 40 = 100 m apart on one line. The next turns send both of them 50 m in the same direction, which does not change the gap.

1. Take the common first run as 50 m north, ending at a point O.
2. X turns right (east) and runs 60 m; Y turns left (west) and runs 40 m. They are now 60 + 40 = 100 m apart on an east–west line.
3. X, facing east, turns left and so runs north 50 m; Y, facing west, turns right and so also runs north 50 m.
4. Both moved 50 m north, so they are still 100 m apart.

Remember · Equal moves in the same direction never change the distance between two people; only the unequal or opposite legs count.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) 7

Count odd days from the end of 2000: 31 December 2098 falls on a Wednesday, and January to May 2099 add 4 more odd days, so 31 May 2099 is a Sunday. One week later, 7 June 2099, is also a Sunday.

1. 2000 years contain 0 odd days, so 31 December 2000 was a Sunday.
2. From 2001 to 2098 there are 98 years, of which 24 are leap years (2004, 2008, …, 2096). Odd days = 98 + 24 = 122, and 122 ÷ 7 leaves 3.
3. So 31 December 2098 is Sunday + 3 = Wednesday.
4. 1 January to 31 May 2099 (2099 is not a leap year): 31 + 28 + 31 + 30 + 31 = 151 days; 151 ÷ 7 leaves 4.
5. 31 May 2099 is Wednesday + 4 = Sunday, so 1 June 2099 is a Monday and 7 June 2099 is a Sunday.
6. Check: 5 June 2022 (the day of this exam) was a Sunday. Up to 5 June 2099 there are 77 years and 19 leap days: 96 days, which leaves 5 on division by 7. So 5 June 2099 is a Friday and 7 June a Sunday.

Remember · Calendar items: 400 years give 0 odd days; add ordinary years plus leap years, reduce mod 7, then add month days.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) 22

C is 12th from the front, so B is 4th or 20th, and A is then 9th, 15th or 25th. With 13 people behind A, the queue has A’s place + 13 people, which is smallest when A is 9th: 22.

1. 11 persons are ahead of C, so C is 12th from the front.
2. 7 persons between B and C means B is 8 places from C: 4th or 20th.
3. 4 persons between A and B means A is 5 places from B: if B is 4th, A is 9th; if B is 20th, A is 15th or 25th.
4. 13 persons are behind A, so the queue has (A’s place + 13) persons: 22, 28 or 38.
5. The minimum is 22, with B 4th, A 9th and C 12th.
6. Check: between B (4th) and A (9th) stand places 5–8, i.e. 4 persons; between B (4th) and C (12th) stand places 5–11, i.e. 7 persons; behind A (9th) stand places 10–22, i.e. 13 persons.

Remember · Queue items: ‘k persons between’ means a gap of k + 1 places; list the cases and take the minimum.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) None of the above

The conditions allow more than one seating. In one valid seating C faces G but E does not face F; in another E faces F but C does not face G; and B can never sit beside A. So none of (a), (b) and (c) is definitely correct.

1. A sits between E and D, so E, A, D occupy three adjacent seats; F sits between B and H, so B, F, H occupy three adjacent seats. C and G take the two seats left.
2. A’s two neighbours are E and D, so B can never sit next to A — (a) is never true.
3. Valid seating 1 (clockwise): A, D, G, B, F, H, C, E. B and D are neither next to nor opposite C. Here C is opposite G, but E is opposite B, not F.
4. Valid seating 2 (clockwise): A, D, H, F, B, G, C, E. Again B and D are neither next to nor opposite C. Here E is opposite F, but C is opposite H, not G.
5. (b) fails in seating 2 and (c) fails in seating 1, so none of the statements is definitely correct.

Remember · For ‘definitely correct’, build two valid arrangements; any option that fails in either one is out.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) Both 1 and 2

The hour and minute hands meet 16 4/11 minutes after 3 o’clock, i.e. between 3:16 and 3:17. The second hand catches the minute hand about 58.98 seconds after 4:58, i.e. before 4:59. Both statements are correct.

1. At 3:00 the hour hand is 90° ahead of the minute hand. The minute hand moves 6° a minute and the hour hand 0.5°, so the minute hand gains 5.5° a minute.
2. It catches up after 90 ÷ 5.5 = 180/11 = 16 4/11 minutes, about 3:16:22 — between 3:16 and 3:17. Statement 1 is correct.
3. t seconds after 4:58, the minute hand is at the 58 + t/60 minute mark and the second hand at the t mark. They meet when t = 58 + t/60, i.e. t = 58 × 60/59 ≈ 58.98 s.
4. That is before 4:59, so statement 2 is also correct.

• ✓ 1. The hands coincide at 3:16 4/11, inside the stated minute.
• ✓ 2. The second hand passes the minute hand about 58.98 seconds after 4:58, before 4:59.

Remember · Clock overlaps: gap ÷ relative speed. Minute hand gains 5.5° per minute on the hour hand.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error