Question Details

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.
Only two people live between O and H. O lives above P. Only two people live between Q and P. Only one person lives between G and P. G lives on floor numbered 1.

How many people live above I?

Options

A

One

B

Three

C

Two

D

None

Show Answer

Correct Answer :

Option C

Two

Two

Solution :

To find the number of people living above I, we can determine the exact floor arrangement of the six friends (O, P, Q, G, H, and I) on the six floors (numbered 1 to 6 from bottom to top) by analyzing the given clues step-by-step:

1. G lives on floor numbered 1:
Let us represent the floors from 6 down to 1. We place G on floor 1:
Floor 6: [ ]
Floor 5: [ ]
Floor 4: [ ]
Floor 3: [ ]
Floor 2: [ ]
Floor 1: G

2. Only one person lives between G and P:
Since G is on floor 1, the person living between G and P must be on floor 2. Therefore, P must live on floor 3:
Floor 6: [ ]
Floor 5: [ ]
Floor 4: [ ]
Floor 3: P
Floor 2: [ ]
Floor 1: G

3. Only two people live between Q and P:
P is on floor 3. We cannot place Q below P because there are only two floors below floor 3 (floors 1 and 2). Thus, Q must live above P, with two floors in between (floors 4 and 5). This places Q on floor 6:
Floor 6: Q
Floor 5: [ ]
Floor 4: [ ]
Floor 3: P
Floor 2: [ ]
Floor 1: G

4. O lives above P, and only two people live between O and H:
P is on floor 3. Since O lives above P, O must be on either floor 4 or floor 5 (since floor 6 is occupied by Q).
- If O lives on floor 4, placing two people between O and H would mean H lives on floor 1. But floor 1 is occupied by G. So O cannot be on floor 4.
- Therefore, O must live on floor 5. If O is on floor 5, then the two people between O and H must be on floors 4 and 3. This places H on floor 2:
Floor 6: Q
Floor 5: O
Floor 4: [ ]
Floor 3: P
Floor 2: H
Floor 1: G

5. Place the remaining person, I:
The only vacant floor left is floor 4, so I must live on floor 4:
Floor 6: Q
Floor 5: O
Floor 4: I
Floor 3: P
Floor 2: H
Floor 1: G

6. Determine how many people live above I:
I lives on floor 4. The floors above floor 4 are floor 5 (O) and floor 6 (Q).
Therefore, there are exactly two people (O and Q) living above I.

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