Read the given instructions carefully and answer the related questions: Six…
2025
Read the given instructions carefully and answer the related questions:
Six persons – A, B, C, D, E and F – bought six different types of cars – Sedan, SUV, Hatchback, Limousine, Coupe, and Convertible – one after the other, but not necessarily in the same order. The one who bought Sedan purchased it three persons before F. As many persons bought car before F as after the one who purchased Hatchback. Two persons bought cars between the ones who purchased Hatchback and SUV. E bought the car before the one who purchased SUV but immediately before A. Coupe was bought two persons after A but immediately bought before convertible. Convertible was bought before B but after D.
Sedan was purchased by who among the following person?
- A.
A
- B.
D
- C.
E
- D.
F
- E.
C
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept
In a linear-order puzzle each person occupies a fixed seat (1st to 6th). Convert every clue into a numeric position relation. "X is k persons before Y" means position(Y) = position(X) + k; "k persons between X and Y" means |position(X) − position(Y)| = k + 1. When a single clue still allows more than one placement, keep both branches alive and let a later clue eliminate the impossible one, rather than assuming the first reading.
Application
Translate and chain the clues:
Combine "Sedan is three persons before F" (Sedan = F − 3) with "persons before F equal persons after the Hatchback buyer" ((F − 1) = (6 − Hatchback)). Testing the seats where Sedan = F − 3 stays valid leaves two live branches: F at seat 4 (Sedan 1, Hatchback 3) and F at seat 6 (Sedan 3, Hatchback 1); the seat that would make Sedan and Hatchback collide is rejected.
Apply "two persons between Hatchback and SUV" (|Hatchback − SUV| = 3). In the F-at-4 branch this puts SUV at seat 6; in the F-at-6 branch it puts SUV at seat 4.
Apply "Coupe = A + 2" and "Coupe is immediately before Convertible" (Convertible = Coupe + 1) to the remaining open car seats in each branch. The F-at-6 branch forces Convertible onto the last seat, seat 6.
Test "Convertible is after D and before B." Convertible needs a seat strictly after it for B, so Convertible cannot be on the last seat — this eliminates the F-at-6 branch entirely. Only the F-at-4 branch survives: Sedan 1, Hatchback 3, SUV 6, Coupe 4, Convertible 5, Limousine 2.
Now place the people. "Coupe = A + 2" with Coupe at seat 4 puts A at seat 2; "E is immediately before A" puts E at seat 1, and "E before the SUV buyer" (seat 6) holds. "Convertible (5) after D, before B" with B needing the later seat puts D at seat 3, B at seat 6, and C at seat 5.
Final arrangement:
Seat | Person | Car |
|---|---|---|
1 | E | Sedan |
2 | A | Limousine |
3 | D | Hatchback |
4 | F | Coupe |
5 | C | Convertible |
6 | B | SUV |
Seat 1 holds the Sedan, and seat 1 is E, so E bought the Sedan.
Cross-check
Sedan (1) is three persons before F (4): 4 = 1 + 3. ✓
Persons before F = 3; persons after Hatchback (3) = 3. Equal. ✓
Between Hatchback (3) and SUV (6): seats 4 and 5 — two persons. ✓
E (1) is immediately before A (2) and before the SUV buyer (6). ✓
Coupe (4) = A (2) + 2, and Convertible (5) is immediately after Coupe. ✓
Convertible (5) is after D (3) and before B (6). ✓