Directions: Read the following information carefully and answer the questions given below:
Ten persons—A, B, C, D, E, F, G, H, I, and J—live on different floors of a 10-storey building, where the ground floor is numbered 1, the floor above it is 2, and so on up to the top floor numbered 10.
B lives on an even-numbered floor below floor 5. Three persons live between B and F, who lives immediately below H. D lives on an even-numbered floor above H. Two persons live between H and C, who lives above D. The number of persons living above C is the same as the number of persons living below A. J lives three floors above F. E lives immediately below I and immediately above G.
The number of persons living above F is the same as the number of persons living below _____?
Correct Answer :
I
Solution :
The correct option is I.
Step-by-Step Explanation:
We are given a 10-storey building with floors numbered 1 to 10 from bottom to top, inhabited by 10 persons: A, B, C, D, E, F, G, H, I, and J.
1. Determining the positions of B, F, and H:
B lives on an even-numbered floor below Floor 5. The even floors below 5 are Floor 2 and Floor 4.
Three persons live between B and F, and F lives immediately below H.
- Case 1: If B lives on Floor 2, then F must live on Floor 6 (floors 3, 4, and 5 are between them). Since F is immediately below H, H lives on Floor 7.
- Case 2: If B lives on Floor 4, F would live on Floor 8 (floors 5, 6, and 7 between them), placing H on Floor 9.
2. Determining the positions of D and C:
D lives on an even-numbered floor above H, and two persons live between H and C, with C living above D.
- In Case 2 (H on Floor 9), two persons above H would put C on Floor 12 (which is invalid as there are only 10 floors). Placing C below H puts C on Floor 6, which is below D, violating the condition that C lives above D. Thus, Case 2 is eliminated.
- In Case 1 (H on Floor 7), two persons between H and C puts C on Floor 10. Since C (Floor 10) lives above D, and D is on an even floor above H (Floor 7), D must live on Floor 8.
3. Determining the positions of A and J:
The number of persons living above C (Floor 10) is 0. Therefore, the number of persons living below A must also be 0, which means A lives on Floor 1.
J lives three floors above F (Floor 6):
So, J lives on Floor 9.
4. Determining the positions of I, E, and G:
E lives immediately below I and immediately above G. This means I, E, and G occupy three consecutive floors in the order I (top), E (middle), and G (bottom).
The remaining empty floors are 5, 4, and 3. Therefore, I lives on Floor 5, E lives on Floor 4, and G lives on Floor 3.
Complete Floor Arrangement:
Floor 10: C
Floor 9: J
Floor 8: D
Floor 7: H
Floor 6: F
Floor 5: I
Floor 4: E
Floor 3: G
Floor 2: B
Floor 1: A
Solving the Question:
F lives on Floor 6, so the number of persons living above F (floors 7, 8, 9, 10) is 4.
We need to find the person who has 4 persons living below them. The floor with 4 persons living below it (floors 1, 2, 3, 4) is Floor 5.
The person living on Floor 5 is I.
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