Six friends, O, P, Q, G, H and I, live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on, till the topmost floor, which is numbered 6. Q lives on an odd-numbered floor. Only two people live between Q and O. H lives immediately above O. G lives immediately below P. How many people live between I and P?
Correct Answer :
Two
Solution :
Correct Answer: Option 4) Two
Let us analyze the given information step-by-step to determine the floor arrangement of the six friends (O, P, Q, G, H, and I):
1. Total Floors:
The building has 6 floors numbered 1 to 6 from bottom to top: 6, 5, 4, 3, 2, 1.
2. Positioning Q and O:
- "Q lives on an odd-numbered floor." So, Q can live on floor 1, 3, or 5.
- "Only two people live between Q and O."
- Case A: If Q is on floor 1, O must be on floor 4 (floors 2 and 3 between them).
- Case B: If Q is on floor 5, O must be on floor 2 (floors 3 and 4 between them).
- Case C: If Q is on floor 3, O cannot be placed because 2 floors above would be 6 (no room for O above Q with 2 between, wait, if Q is 3, 2 people below would mean O is at floor 0, which is invalid, or 2 people above would mean floors 4, 5 between and O on floor 6, but let's check H).
3. Positioning H:
- "H lives immediately above O."
- In Case A (O is on floor 4): H lives on floor 5.
- In Case B (O is on floor 2): H lives on floor 3.
- In Case C (if O is on floor 6): H cannot live above O since 6 is the top floor.
4. Positioning G and P:
- "G lives immediately below P" means P is directly above G (P on top, G directly below P).
- Let's test Case A (Q = 1, O = 4, H = 5):
Remaining empty floors are floor 6, floor 3, and floor 2.
To place P immediately above G, they need two consecutive vacant floors.
Floors 3 and 2 are vacant and consecutive! So, P is on floor 3 and G is on floor 2.
The remaining floor (floor 6) must be occupied by I.
Let's check the complete arrangement for Case A:
Floor 6: I
Floor 5: H
Floor 4: O
Floor 3: P
Floor 2: G
Floor 1: Q
All conditions are satisfied!
Now, let's count the number of people living between I and P:
- I is on Floor 6.
- P is on Floor 3.
- The people living between them (on Floors 5 and 4) are H and O.
Therefore, exactly 2 (Two) people live between I and P.
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