Directions: Read the given passage carefully and answer the questions given below.

Six executives – A, B, C, D, E, and F – live on different floors of a six-storey building where the lowermost floor is numbered as 1, the floor immediately above it is numbered as 2, and so on up to the topmost floor numbered as 6. Each of them prefers a different fruit among Apple, Banana, Grape, Mango, Orange, and Papaya, but not necessarily in the same order.

E lives on the lowermost floor and prefers Grape. C lives on an odd-numbered floor immediately below F. Exactly two floors are between C and the one who prefers Mango, who lives on an even-numbered floor. F prefers Papaya. The one who prefers Orange lives immediately below the one who prefers Papaya. The number of floors above A is equal to the number of floors below B. A prefers Apple, while B prefers Banana.

Which of the following statements is/are true?

I. F lives on an even-numbered floor.
II. C prefers Grape.
III. C lives on the floor immediately below F.

The correct option is Both I and III.

Step-by-Step Explanation:

1. Lowermost floor: E lives on floor 1 and prefers Grape.
2. Positions of C and F: C lives on an odd-numbered floor immediately below F. Since floor 1 is occupied by E, C must live on floor 3 (making F live on floor 4) or floor 5 (making F live on floor 6).
3. Fruit preference of F and C: F prefers Papaya. The person living immediately below the one who prefers Papaya prefers Orange. Since C lives immediately below F, C prefers Orange.
4. Position of Mango: Exactly two floors are between C and the person who prefers Mango, who lives on an even-numbered floor.
- If C is on floor 3, two floors above C is floor 6. Floor 6 is an even-numbered floor, so the person on floor 6 prefers Mango.
- Floor 1 = E (Grape)
- Floor 3 = C (Orange)
- Floor 4 = F (Papaya)
- Floor 6 = D (Mango)
5. Positions of A and B: The remaining vacant floors are floors 2 and 5. The number of floors above A equals the number of floors below B. Placing A on floor 5 (1 floor above) and B on floor 2 (1 floor below) satisfies this condition. A prefers Apple, and B prefers Banana.

Final Floor Arrangement (from Top to Bottom):
• Floor 6: D - Mango
• Floor 5: A - Apple
• Floor 4: F - Papaya
• Floor 3: C - Orange
• Floor 2: B - Banana
• Floor 1: E - Grape

Evaluating the Statements:
I. F lives on an even-numbered floor: True (F lives on floor 4).
II. C prefers Grape: False (C prefers Orange; E prefers Grape).
III. C lives on the floor immediately below F: True (C lives on floor 3, immediately below F on floor 4).

Therefore, statements I and III are true.