Puzzle Test Questions and Answers

Answer: C

The order of arrival works out uniquely as:

Why: Rajiv's couple has the Garments couple just before it and Rupu's couple just after it, so Rajiv is second or third. Ashutosh's couple is followed by Rinku's, which is followed by the Jewellery couple, so Ashutosh is first or second. Prem comes just before Rosy, so Prem cannot be last.

If Rajiv were second, Ashutosh would be first, Rinku would be Rajiv's wife and the third couple would deal in Jewellery. Prem would then be third and Pappu fourth with Books, leaving Furniture for Rajiv and Rinku, which clue (iv) forbids. So Rajiv is third and Rupu's couple fourth. Ashutosh cannot then be second, because Rinku would be third and the fourth couple, Pappu's, would have to deal in Jewellery though Pappu deals in Books. So Ashutosh is first, Rinku's couple second (Garments), Rajiv's third (Jewellery) and Pappu's fourth (Books). Prem must be second, with Rosy in the third couple as Rajiv's wife, and Nitu is Ashutosh's wife.

The arrival right after Ashutosh's couple was Prem and Rinku, as clue (iv) states directly. Rajiv and Rosy came third and Pappu fourth, so none of them came immediately after Ashutosh.

Answer: C

The tasks run as follows: A from 9 to 11 a.m. (2 h); B after A, from 11 a.m. to 12 noon (1 h); C after A and B, from 12 noon to 1 p.m. (1 h); D alongside B and C, so from 11 a.m., for 3 h, to 2 p.m.; and E only after A, B, C and D are all done.

So the earliest completion of C is 1 p.m. 11 a.m. is when A ends, and 12 noon is when B ends and C can begin. 2 p.m. is when D ends; C does not have to wait for D, because D runs alongside it.

Answer: C

The integer assigned to N is 6.

P is 4. T differs from P by 5, so T is 9 or −1; only 9 lies between 1 and 9, so T = 9.

N differs from T by 3, so N is 6 or 12. Only 6 is in range, so N = 6.

4 is already taken by P, so it cannot also belong to N. 5 and 7 differ from T = 9 by 4 and 2, not 3.

Answer: C

The ages are 9, 2, 2.

The sets of three ages with product 36, and their sums, are: 1, 1, 36 (38); 1, 2, 18 (21); 1, 3, 12 (16); 1, 4, 9 (14); 1, 6, 6 (13); 2, 2, 9 (13); 2, 3, 6 (11); 3, 3, 4 (10).

The agent knew the sum, the number of shops, yet still could not tell, so the sum must be shared by two sets: 13, from 1, 6, 6 and 2, 2, 9. The clue that John has an 'eldest son' rules out 1, 6, 6, where the two oldest would be twins of the same age. That leaves 9, 2, 2.

The sets 9, 4, 1 and 6, 3, 2 have unique sums, so the agent would not have needed more data, and 6, 6, 1 has no single eldest.

Answer: C

The subject before Science is Economics.

The course runs 22 to 29 July with 23 July a holiday, leaving seven days for seven subjects: 22, 24, 25, 26, 27, 28 and 29. Psychology is on 22 July (I), Philosophy on 24 July, right after the holiday (V), and Mechanics on 29 July (IV). That leaves Sociology, Economics, Science and Engineering for 25 to 28 July.

Science is the day before Engineering (III), Economics and Engineering have one day between them (VI), and Sociology and Economics have two days between them (VII). Sociology and Economics must then be on 25 and 28. If Sociology were on 25, Economics on 28 would push Engineering to 26 and Science to 25, a clash. So Economics is on 25, Science on 26, Engineering on 27 and Sociology on 28.

Economics comes immediately before Science.

Answer: B

The city with no industry, no university and no hill station is N.

Work out the cities. N and O are not industrial, so the three industrial cities are L, M and P. M is a port, and an industrial city with a university has no port, so M has no university; the two industrial cities with universities are L and P. O is the hill station with a university, so the three university cities are L, O and P. The ports are M and one more: not O (not a port), not L or P (they have universities), so N. Summary: L is industrial with a university, M is industrial with a port, N has a port only, O is the hill station with a university, P is industrial with a university.

N is not industrial, has no university and is not the hill station (that is O). M is industrial, and L and P are industrial and have universities.

Answer: B

The two port cities are M and N.

Work out the cities. N and O are not industrial, so the three industrial cities are L, M and P. M is a port, and an industrial city with a university has no port, so M has no university; the two industrial cities with universities are L and P. O is the hill station with a university, so the three university cities are L, O and P. The ports are M and one more: not O (not a port), not L or P (they have universities), so N. Summary: L is industrial with a university, M is industrial with a port, N has a port only, O is the hill station with a university, P is industrial with a university.

L and P cannot have ports because they are industrial cities with universities, and O is stated not to be a port, so the ports are M and N.

Answer: A

The two women arrived in the order 1 and 2.

The order of arrival is: 1 Ashutosh and Nitu (Furniture), 2 Prem and Rinku (Garments), 3 Rajiv and Rosy (Jewellery), 4 Pappu and Rupu (Publishing, the "Books" of the paper).

The clues give three chains of couples in a row of four: the Garments couple, then Rajiv, then Rupu's couple; Prem, then Rosy's couple; Ashutosh, then Rinku's couple, then the Jewellery couple. If Rajiv were second he would clash with Ashutosh in the third chain unless both sat in the first two places, and that leaves Rinku with Rajiv in Furniture, which the clues forbid. So Rajiv is third and Ashutosh first. The Garments couple is then second and is Rinku's, and the Jewellery couple is Rajiv's. Prem, who must come just before Rosy, is second, so Rosy is Rajiv's wife. Pappu (Books) is fourth with Rupu, and Nitu is with Ashutosh in Furniture.

Furniture is the first couple (Nitu) and Garments is the second couple (Rinku), so the two women come in the order 1 and 2. 2 and 1 reverses them, and 3 is the Jewellery couple.

Answer: C

The true statement is Rosy is the wife of Rajiv.

The order of arrival is: 1 Ashutosh and Nitu (Furniture), 2 Prem and Rinku (Garments), 3 Rajiv and Rosy (Jewellery), 4 Pappu and Rupu (Publishing, the "Books" of the paper).

The clues give three chains of couples in a row of four: the Garments couple, then Rajiv, then Rupu's couple; Prem, then Rosy's couple; Ashutosh, then Rinku's couple, then the Jewellery couple. If Rajiv were second he would clash with Ashutosh in the third chain unless both sat in the first two places, and that leaves Rinku with Rajiv in Furniture, which the clues forbid. So Rajiv is third and Ashutosh first. The Garments couple is then second and is Rinku's, and the Jewellery couple is Rajiv's. Prem, who must come just before Rosy, is second, so Rosy is Rajiv's wife. Pappu (Books) is fourth with Rupu, and Nitu is with Ashutosh in Furniture.

Rupu is married to Pappu and deals in Books (Publishing), not Garments. Prem deals in Garments, not Jewellery. Nitu deals in Furniture, not Books. Only the third statement fits.

Answer: C

E can start at 2 p.m.

A takes 9 to 11 a.m. With B now taking 2 hours, B runs 11 a.m. to 1 p.m., and C, which needs A and B done, runs 1 to 2 p.m. D runs alongside B and C, from 11 a.m., for 3 hours, which ends at 2 p.m. E needs A, B, C and D all complete, so it starts at 2 p.m., when both C and D end.

12 noon and 1 p.m. are too early, since B or C are still running. 3 p.m. would add an hour of idle time that nothing in the information requires.