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 ? (below is the attached image)

(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.

OA is A

Is this correct approach ?

(1) Let the rate for Lisa 1/2

Let the rate for Paul 1/3

Both started at the same time. So, the equation is

(1/2 + 1/3) * t = 18

Hence, sufficient

(2). rate of Lisa 1/(x - 10)

rate of Paul 1/x

[1/(x - 10) + 1/x ] * t = 18

2 variables one equation. So, insufficient.

Is this approach correct ?

## The figure above represents the floor plan of an art gallery

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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? (below is the attached image)

OA is A

Let's take each statement one by one.

(1) Lisa spends 2x minutes in each room and Paul spends 3x minutes in each room.

Say they meet at the room when Paul moved from y rooms; thus, Lisa must have moved from (18 - y) rooms.

Time spent by Paul = Time spent by Lisa

3x*y = 2x*(18 - y)

y = 7.2

y= 7.2 means that Paul is at the 8th room and so is Lisa

The 8th room = K room. Sufficient.

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

Dealing with Statement 1, we know that it's important that we know the ratio of time Paul and Lisa spent in each room. Given, "Lisa spends 10 minutes less time in each room than Paul does," will not serve the purpose. Say if Paul spent 11 minutes in each room, then Lisa would spend 1 minute in each room. The ratio of times = 11/10. However, say if Paul spent 30 minutes in each room, then Lisa would spend 20 minutes in each room. The ratio of times = 3/2 â‰ 11/10.

Insufficient.

The correct answer: A

Hope this helps!

-Jay

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Jay,

Thanks for your approach. Appreciate it. So, is it

Thanks for your approach. Appreciate it. So, is it

**another approach**which gives me**another**thought process ? Or Is my approach above completely wrong ?