Question Details

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.

Who bought the car three persons after that person who bought the car immediately before D?

Options

A

C

B

B

C

F

D

A

Show Answer

Correct Answer :

Option A

C

C

Solution :

To find the correct answer, we can analyze the clues step-by-step and determine the order of purchases for the six persons (A, B, C, D, E, F) and their cars (Sedan, SUV, Hatchback, Limousine, Coupe, Convertible).

Let the purchase positions be 1, 2, 3, 4, 5, and 6 from first to last.

Step 1: Determine the positions of Sedan, F, and Hatchback
- Clue: "The one who bought Sedan purchased it three persons before F." This means Sedan is at position p and F is at position p + 3.
- Clue: "As many persons bought car before F as after the one who purchased Hatchback."
Let's analyze the possible positions:
If F is at position 4, Sedan is at position 1. There are 3 persons before F, so there must be 3 persons after Hatchback, which places Hatchback at position 3.
If F is at position 5, Sedan is at position 2. There are 4 persons before F, which would place Hatchback at position 2. Since two cars cannot be at the same position, this case is invalid.
If F is at position 6, Sedan is at position 3. There are 5 persons before F, which would place Hatchback at position 1. Let's see if this works with the next clue.

Step 2: Determine the position of SUV
- Clue: "Two persons bought cars between the ones who purchased Hatchback and SUV."
If Hatchback is at position 3 (from our first valid case), SUV must be at position 6 (since there are two positions, 4 and 5, between them). This is valid.
If Hatchback is at position 1 (from our second case), SUV must be at position 4. However, in this case, Sedan is at position 3, F is at 6. Let's check the next clues to see which case holds.

Step 3: Analyze the position of E, A, Coupe, and Convertible
- Clue: "E bought the car before the one who purchased SUV but immediately before A." This means E and A purchased consecutively as (E, A).
- Clue: "Coupe was bought two persons after A but immediately bought before convertible." This means Coupe is at posA + 2, and Convertible is at posA + 3.
Let's test the case where Sedan is 1st, Hatchback is 3rd, F is 4th, and SUV is 6th:
Since E and A are adjacent, and E is before SUV (6th):
If E is at 1st and A is at 2nd:
Coupe is at 2 + 2 = 4th (bought by F).
Convertible is immediately after Coupe, which puts Convertible at 5th.
This arrangement is valid. The remaining car, Limousine, must be at position 2 (bought by A).

Step 4: Place the remaining persons
- Clue: "Convertible was bought before B but after D."
Convertible is at position 5, so B must be at position 6.
D must be before position 5. Since positions 1 and 2 are taken by E and A, and position 4 is taken by F, D must be at position 3.
This leaves C to be placed at position 5.

Summarizing the final arrangement:
1. E (Sedan)
2. A (Limousine)
3. D (Hatchback)
4. F (Coupe)
5. C (Convertible)
6. B (SUV)

Step 5: Answer the final question
We need to find who bought the car three persons after the person who bought the car immediately before D.
- The person who bought the car immediately before D (position 3) is A (position 2).
- Three persons after A (position 2) is the person at position
2 + 3 = 5.
- The person at position 5 is C.

Therefore, C bought the car three persons after the person who bought the car immediately before D.

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