Art Gallery Race

[smclean23]

The figure above represents the floor plan of an art gallery that has a lobby and 18 rooms. If Lisa goes from the lobby into room A at the same time that Paul goes from the lobby into room R, and each goes through all of the rooms in succession, entering by one door and exiting by the other, which room will they be in at the same time ?

(1) Lisa spends 2x minutes in each room and Paul spends 3x minutes in each room.
(2) Lisa spends 10 minutes less time in each room than Paul does.


Answer is A....

[treker]

Can someone please explain the answer for this question, please?

Thanks...

[mohitsharda]

The figure above represents the floor plan of an art gallery that has a lobby and 18 rooms. If Lisa goes from the lobby into room A at the same time that Paul goes from the lobby into room R, and each goes through all of the rooms in succession, entering by one door and exiting by the other, which room will they be in at the same time ?

(1) Lisa spends 2x minutes in each room and Paul spends 3x minutes in each room.
(2) Lisa spends 10 minutes less time in each room than Paul does.


Answer is A....

Statement 1:
Lisa is ahead of paul. As she leaves the lobby, paul enters it.I am going to solve this as a speed problem.
Lisa spends 2x minutes in a room and paul spends 3x minutes.
=> Lisa is faster than paul.
Now, lisa is ahead of paul so, for them to meet, we can say that lisa will catch up to paul.
Let us say that paul covers D rooms by the time that he and lisa meet.
=> Lisa covers (d + 18) rooms as lisa was 1 room ahead of paul in the beginning and there are a total of 18 rooms.
We get the equation:
(d+18)/ (3x) = d / (2x) which can be solved for d as x cancels out.
So, condition is sufficient

Statement 2:
10 minutes less is all relative and will not help us to get a definite answer. so insufficient.


So, A

I know its a bit difficult to understand. (especially the way i explained above)