Law School Discussion

New Games -(Dec99, sec1, q13)- try this (3)


New Games -(Dec99, sec1, q13)- try this (3)
« on: September 07, 2005, 05:22:46 PM »

Exactly five cars -- Frank's, Marquitta's, Orlando's, Taishah's, and Vinquetta's -- are washed, each exactly once. The cars are washed one at a time, with each receiving exactly one kind of wash: regular, suer, or premium. The following conditions must apply:

The first car washed does not receive a super wash, though at least one car does.
Exactly one car receives a premium wash.
The second and third cars washed receive the same kind of wash as each other.
Neither Orlando's nor Taishah's is washed before Vinquetta's.
Marquitta's is washed before Frank's, but after Orlando's.
Marquitta's and the car wahsed immediately before Marquitta's receive regular washes.

3. If the last two cars washed receive the same kind of wash as each other, then which one of the following could be true?

a) Orlando's car is washed third
b) Taishah's car is washed fifth
c) Taishah's car is washed before Marquitta's car.
d) Vinquetta's car receives a regular wash
e) Exactly one car receives a super wash


Re: New Games -(Dec99, sec1, q13)- try this (3)
« Reply #1 on: September 08, 2005, 06:41:14 AM »
Since the last spots 4 and 5 receive the same type of wash, M cannot go in 4. If it did, spots 4 and 3 would be the same type of wash. Furthermore, according to the rules, spots 2 and 3 would match too. So spots 2,3,4, and 5 would all be the same type of wash leaving us with one spot and two types of washes left. Since all types of washes are used, this cannot happen.

V     V
O-r   O - r
M-r   M - r
T     F
F     T

These are the two possible scenarios. Right off the bat, you can see A) can't happen nor can C).

With D), the first three would all get r and (according the question stem) the last two must be the same two. So this would exclude one of the types of washes making it wrong. Also this proves that p must go to V and F and T get s.

V - p           V - p
O - r           0 - r
M - r           M - r
T - s           F - s
F - s           T - s

E) as you see isn't true either, consider V gets either r or p and F and T must be the same.

So B), is the only one that's possible.