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.
The number of cars bought between E and the one who purchased Hatchback is one more than the number of cars bought after the one who purchased _______.
- A.
Convertible
- B.
SUV
- C.
Coupe
- D.
Limousine
- E.
Sedan
Attempted by 7 students.
Show answer & explanation
Correct answer: B
Concept
In a linear (single-row) arrangement, six entities occupy six fixed positions (1 to 6, earliest purchase to latest). Every clue is a positional relationship — 'before/after' fixes order, 'immediately before' fixes adjacency, 'X persons between' fixes a gap, and 'as many before as after' equates two counts. The method is to translate each sentence into a position rule, anchor the most restrictive rules first, and let the remaining clues force the rest.
Setting up the order
Count clue: 'As many persons bought a car before F as after the Hatchback buyer' means (positions before F) = (positions after Hatchback). 'Sedan was bought three persons before F' places the Sedan buyer three steps ahead of F; the only consistent placement puts F at the 4th position, so 3 persons come before F and 3 come after Hatchback, fixing Hatchback at the 3rd position.
Gap clue: 'Two persons bought cars between the Hatchback buyer and the SUV buyer' means a gap of three positions. With Hatchback at 3, the SUV buyer sits at the 6th (last) position.
Adjacency clue: 'E is immediately before A' and 'E is before the SUV buyer'. The chain that satisfies the Coupe and Convertible clues forces E into the 1st position and A into the 2nd.
Coupe/Convertible clue: 'Coupe was bought two persons after A and immediately before Convertible' places Coupe at the 4th and Convertible at the 5th position.
Final clue: 'Convertible is after D and before B' places D at the 3rd and B at the 6th, leaving F at the 4th and C at the 5th.
The complete arrangement
Position | Person | Car |
|---|---|---|
1 | E | Sedan |
2 | A | Limousine |
3 | D | Hatchback |
4 | F | Coupe |
5 | C | Convertible |
6 | B | SUV |
Answering the blank
E is at position 1 and the Hatchback buyer is at position 3, so exactly one car was bought between them. The sentence needs this count (1) to be one MORE than the number of cars bought after some car X — that is, cars bought after X must equal zero. Only the car in the last (6th) position has zero cars after it.
The car at position 6 is the SUV, so the blank is SUV: cars between E and Hatchback (1) is one more than cars after SUV (0).
Cross-check
Convertible (position 5): one car after it, would need the count between E and Hatchback to be 2 — but it is 1, so it fails.
Coupe (position 4): two cars after it, would need a count of 3 — fails.
Limousine (position 2): four cars after it, would need a count of 5 — fails.
Sedan (position 1): five cars after it, would need a count of 6 — fails.
Only the last-position car gives zero cars after, matching 1 = 0 + 1.