Each student will visit exactly one of three cities - M, T, or V
There are two possible ways to set this up depending on your preference.
Option 1:
H: _ L: _ P: _ R: _ S: _
Option 2:
M: _ _ _ _ _ T: _ _ _ _ _ V: _ _ _ _ _
I'm going to go through the question using option 2, but it would work just as well if you prefer option 1. Now let's go through the rules.
Rule 1 - S visits a different city than P.
S --> No P P --> No S
Rule 2 - H visits the same city as R. Therefore, we have to group H and R together.
|HR|
Rule 3 - L visits M or T
L --> M or T Not M and Not T --> No L
Rule 4 - If P visits V, H visits V with him. We also know from Rule 2 that H visits the same city as R.
PV --> |HR|V Not |HR|V --> Not PV
Rule 5 - Each student visits one of the cities with at least one of the other four students. This is the most important rule because it severely restricts our possibilities.
We know that S and P cannot visit the same city. Therefore, all five students cannot visit the same city.
Rule 5 means that four students cannot visit one city and one student visit another. It also means that a distribution of two, two, and one student(s) per city is not possible.
Therefore, our only possibility is that three students will visit one city and two students will visit another.
M: _ _ _ T: _ _ _ V: _ _ _
One of the above cities will not be visited depending on the conditions imposed by the questions.
Now we can address question 1 which tells us that S visits V.
M: _ _ _ T: _ _ _ V: S _ _
Either M or T will not be visited. Rule 1 means that P must visit M or T and Rule 3 means that L must visit M or T.
This means that |HR| must visit V and that P and L must visit M or T together. |HR| cannot visit M or T because this would mean S would be visiting V alone, breaking Rule 5.
There are no conditions determining whether L and P must visit M or else T.
M: _ _ T: _ _ V: S H R
We know answer choice (A) cannot be true because H visits V.
Answer choice (E) cannot be true because only three students maximum can visit V and S, H, and R are already visiting V together.
Answer choices (B) and (C) do not have to be true because it is equally possible that L and P visit M or T.
Even though we don't know which one, we do know that L and P must visit the same city. Therefore, answer choice (D) is the correct answer.
Hope this is helpful! Please let us know if you have any further questions.
