Which of the following is a town that CANNOT be ranked fifth on any one of the three criteria?

Irina August 14, 2019

@Lauren-Sapienza,

Great question. There are two most obvious ways to set up this game, one is the way you set it up and another is to put 1 2 3 4 5 on x-axis and C L F on Y-axis and fill the resulting 3 x 5 table. I would personally use the latter because this game uses the ranking as a point of reference, and it is more visually intuitive to see the towns matched by rank. That being said, if the other option works better for you, it is perfectly fine to stick with that.

Let's look at the alternative set up

Five towns - P Q R S T are ranked 1 to 5 based on three criteria: C L F.

C
___ ___ ___ ___ ___
L
___ ___ ___ ___ ___
F
___ ___ ___ ___ ___
1 2 3 4 5


Let's look at the rules:

(1) For each of the three criteria, none of the five towns receives the same ranking as any other town does.

This rule simply says that it is impossible for any town to be ranked the same as any other town for a given criterion, i.e. P and Q cannot both be #1 in C. It means that we have to assign a town to every one of these 15 squares.

(2) In climate, T is ranked 3, and S - 4.
(3) In location, Q is ranked 2, R- 3, and P- 4.
(4) In friendliness, T is ranked better than P, Q is ranked 4, and S -5
T>P


C ___ ___ T S ___

L ___ Q R P ___

/T /T/P /P
F ___ ___ ___ Q S
1 2 3 4 5


Since T > P, we can also conclude that T cannot be #3 in F, and P cannot be #1 in F, so T has to be 1 or 2, and P has to be 2 or 3.

(5) R receives a better ranking in climate than in friendliness.

R (c) >R (f)

This rule tells us that R must be #1 or #2 in climate, it cannot be #5 because the lowest possible ranking in friendliness R could get is #3 since #4 &5 are already occupied by other towns. It also tells us that R must be #2 or #3 in climate because then it would be impossible for R to get a better ranking in climate. Finally, we can conclude that since P must be 2 or 3 in F per rule (4) and R must be 2 or 3 in F, T must be #1 in F.

/R /R ~R
C ___ ___ T S ___

L ___ Q R P ___

/P/R /P/R
F T ___ ___ Q S
1 2 3 4 5

(6) Q three rankings are all different from each other.

Since Q is #2 in L and #4 in F, Q must be #1 or #5 in C.

Let's put all the rules together to complete the diagram:

P/R/Q /R/P /Q/P
C ___ ___ T S ___

/T/S /T/S
L ___ Q R P ___

/P/R /P/R
F T ___ ___ Q S
1 2 3 4 5


Now, the question asks us which of the following CANNOT be ranked 5th?

Let's compare our diagram to each of the answer choices:

(A) P

We can see that P could be ranked #5 for C, thus this answer choice is incorrect.

(B) Q

We can see that Q could be ranked #5 for C, thus this answer choice is also incorrect.

(C) R

R must be #1 or #2 for C, is ranked #3 for L, and must be #2 or #3 for F, thus it CANNOT be #5 and this is the correct answer choice.

(D) S

S is ranked #5 for F, we can right away eliminate this answer choice.

(E) T
T is ranked #3 for C, and #1 for F, but could be either #1 or #5 for L, thus this answer choice is incorrect.

Does this setup make sense?

Feel free to try both versions and see which one is more intuitive for you and helps you go through the questions faster.

Let me know if you have any further questions.