# If all the new cars in the exhibition are research models, then which one of the following statements must be true?

natnabila on May 10, 2020

Video Explanation

Can you please do an explanation of this logic game, and not just the set up?

SamA on May 14, 2020

Hello @natnabila,

Of course!

A key term here is "all." Remember that all of the cars on each floor must have the same characteristics, so we don't have to worry about individual cars. Try to think of it this way: each of the three floors comes with three characteristics.

F/S N/U P/R

Each floor will have some combination of these three choices.

F/S N/U P/R
3: _ _ _
2: _ _ _
1: _ _ _

Rule 1: If both sports and family cars are included, then all sports cars must be higher up than all family cars. In other words, we cannot have F above S.

Rule 2: These sufficient and necessary rules are interesting, and very helpful, because there are only two options for each category. For example, (not F) and (S) mean the exact same thing!

(U ------> not R) is the same as saying (U -----> P)
and the contrapositive
(R -----> not U) is the same as saying (R ------> N)

Rule 3: Very similar to rule 2.
(R -----> not S) or (R -----> F)
and the contrapositive
(S ----> not R) or (S -----> P)

Combining these, we can see that if a floor has research models, then they must be new and family cars. R -----> N and F

I will write the last two rules into the diagram.

F/S N/U P/R
3: _ U P
2: _ _ _
1: _ N _

Why did I add P to the third floor? Because of rule 2! If the car is used, then it cannot be a research model. It can only be a production model.

Let's take a look at the question here. We are given a new condition. All new cars in the exhibition are research models.
N ---> R

What comes with R? F, according to Rule 3.

F/S N/U P/R
3: _ U P
2: _ _ _
1: F N R

What must be true?

A. Do you see any rule that would prevent a used family car on floors 2 or 3? I don't. A does not have to be true.

B. Would something stop us from putting family cars on floor 3? As long as there are no sports models below it (rule 1), then there is no problem here. B does not have to be true.

C. We know that this cannot be true, because we have completed floor 1.

D. Remember how I completed that 1st floor? We were told N ---> R. What does R lead to? R ----> F (rule 3). We have N ----> R ----> F. Answer choice D must be true, making it the correct answer.

E. Is there anything to prevent floor 3 from containing production sports cars? No. This does not have to be true.