Suppose that in addition to the original five cars Jabrohn's car is also washed. If all the other conditions hold as...

SarahA on June 3, 2019

any answer?

Victoria on June 3, 2019

Hi @msaber,

This question is quite confusing as Jabrohn is thrown into the mix with no conditions placed on position or wash, complicating the order of washes and types. This is an example of a question where an additional condition is added to the list of original conditions. We are given enough information to answer this question, but it requires quite a bit of work.

Let's start by mapping out the question based on the original conditions we are given.

Five cars are washed exactly once - Frank's, Marquitta's, Orlando's, Taishah's, and Vinquetta's.

Cars: F, M, O, T, V

The cars are washed one at a time, with each receiving exactly one kind of wash - Regular, Super, or Premium.

Washes: R, S, P

As the cars are washed one at a time, we can set up a sequence for this question as well.

1: _ 2: _ 3: _ 4: _ 5: _

Now let's go through the original conditions.

1) The first car washed does not receive a super wash, though at least one car does.

Therefore, the first car washed must receive a regular or premium wash. One or more cars in the sequence receive a super wash.

2) Exactly one car receives a premium wash.

If the first car that is washed receives a premium wash, no other cars can receive the premium wash.

3) The second and third cars washed receive the same kind of wash as each other.

Since only one car can receive the premium wash, the second and third cars must both receive either the super or regular wash.

Let's input these conditions into our sequence.

1: R/P 2: R/S 3: R/S 4: _ 5: _

Now let's get back to the conditions.

4) Neither Orlando's nor Taishah's is washed before Vinquetta's.

V > O and V > T

5) Marquitta's is washed before Frank's, but after Orlando's.

O > M > F

6) Marquitta's and the car washed immediately before Marquitta's receive regular washes.

The car immediately before Marquitta's car must be either O or T. This means that either O or T must receive a regular wash.

The chain we can build from this runs: V > O > M > F and V > T.

From this, we know:
V must be first, which means that V must either receive R or P.
M must fall 3rd or 4th.
O must fall somewhere between V and M.
T can fall in any position after V.
F must fall 4th or 5th.

There are four possible orders for the car washes which we can outline based on the conditions regarding the order of washes:
1) VOMTF
2) VOMFT
3) VOTMF
4) VTOMF

So, we know these four possible order scenarios and we can also map out the possible wash types as follows:

1: R/P 2: R/S 3: R/S 4: _ 5: _

The addition of Jabrohn throws a wrench into our mapped out scenarios above. The question adds another condition, but does not place any additional conditions on Jabrohn's position in the sequence or wash type. This means that J can fall anywhere in the chain and can receive any type of wash.

So, let's use this information as well as the possible scenarios we have outlined above to determine which of the answer choices could be true. Remember, we are looking for the answer choice that CANNOT be true, so any answer choice which could be true is incorrect. Therefore, if we can map out even a single scenario where the answer choice could be true, the answer is incorrect.

B) Vinquetta's car receives a super wash.

Based on the original conditions, this would not be possible as V has to fall 1st. However, the unconditional addition of J switches things up. There are no conditions which say that J cannot be washed first. If this is true, then V would be washed 2nd, meaning that it could receive R or S. This means that V could receive a super wash and, therefore, B is not the correct answer.

C) Four cars receive a regular wash.

We know that exactly one car receives a premium wash and at least one car receives a super wash. In the original question, this left only three cars which could receive a regular wash. However, the addition of J now means that there are four cars which could receive a regular wash as demonstrated by the potential scenario below:

1: JP 2: VR 3: TR 4: OR 5: MR 6: FS

This means that this answer choice could be true and, therefore, is not the correct answer.

D) Only the second and third cars washed receive a regular wash.

In order for this to be true, Marquitta's car must be washed third. Can this be true?

1: VP 2: OR 3: MR 4: TS 5: FS 6: JS

We can see from the possible scenario above that this could be true and, therefore, is not the correct answer.

E) Jabrohn's car is washed after Frank's car.

As there are no conditions placed on the order in which J is washed, it is entirely possible that J is washed last following F as we can see in the possible scenario outlined above under answer choice D.

A) Orlando's car receives a premium wash.

Exactly one car receives a premium wash. Could it be Orlando's?

The second and third cars washed receive the same kind of wash as each other and M and the car washed immediately before M receive R.

J does not largely impact the order of the cars as it could fall anywhere in the sequence. If we include J in the sequence, V can either fall 1st or 2nd and M cannot fall later than 5th or earlier than 3rd.

If M is in 5th, F must be in 6th. O cannot be 1st, so it must be 2nd, 3rd, or 4th. If O is 4th, it must receive R like M. If O is in 2nd or 3rd, it must receive the same type of wash as the other car in 3rd or 2nd. As only one car receives P, O cannot be P in this scenario.

If M is in 4th, then O must fall 2nd or 3rd and we run into the same problem as above.

If M is in 3rd, then V must fall in 1st (because V > O > M) and we run into the same problem as O falls 2nd.

Therefore, it cannot be true that Orlando's car receives a premium wash, making A the correct answer.

Sorry this is so long! I hope it was helpful. If you need any further clarification, please don't hesitate to ask!

SarahA on June 8, 2019

Victoria, this is great and thank you so much for taking your time to write such a clear and thorough explanation! I was utterly confused when I came to this question as I had not seen a game with a random variable thrown in at the end. Thanks to your explanation I can now recognize that this can be treated as an additional condition I am much better prepared to answer one of these wild-card questions :)

Ravi on June 9, 2019

@msaber, happy to hear you see it now! :) Keep up the awesome work, and let us know of any other questions you have!