Which one of the following could be an accurate ranking of all the crews, in order from first to sixth, for a given w...

Irina on December 24, 2019

@BB427,

The game requires us to rank the productivity of six crews - F G H R S T from 1st to 6th. Two of the crews are night shift crews - either G & T or S & H - and the remaining 4 are day shift crews. In other words, there are two possible scenarios:

G T - night, F H R S - day
S H - night, F G R T - day

__ __ __ __ __ __
1 2 3 4 5 6

The following rules apply:

(1) F > G
(2) R > S
(3) R > T

R > S
> T

(4) S > H
R > S > H
> T

(5) G > T
F > G > T

So overall, we have the following two chains:

R > S > H
>T

F > G > T

Question 1 asks us which of the following could be an accurate ranking of all the crews for a given week?

(A) is incorrect because R >T
(B) is incorrect because S > H
(C) is incorrect because F > G > T
(D) is correct and complies with all the rules
(E) is incorrect because G > T

Question 2 asks if F is ranked third, then which of the following could be true?

Well if F is ranked third, and G & T have to come after it they must be ranked either 4th and 5th or 5th and 6th

R S F ___ ___ __
/G G/T /T
/H /H
R and S must be # 1nad #2, and H is a free variable that could be either fourth or sixth.

The only answer that could be true is (B) - H is ranked fourth, or alternatively it could be ranked sixth.

Question 3 asks which of the following CANNOT be the crew ranked fifth for any given week of the study?

Considering we have these two chains

R> S >H
> T

F > G >T

we can tell that R or F can never be ranked fifth because at least two crews must come after them (answer choice (C)

Question 4 asks for any given week of the study, the ranking of all crews is completely determined if one of the following is true.

Since H must be preceded by R &S , we know that if H is ranked third, R & S must be ranked first and second, and F G T must be 4th, 5th and 6th respectively (C).

Question 5 asks if the night crew rank fifth and sixth for a week, then which of the following could be true.

So in other words if G &T or S & H rank last, which of the following could be true.

Let's consider both scenarios:

__ __ __ __ G T
R > S> H
F

__ __ __ __ S H
F > G> T
R

We can see that (A), (B), (D) , and (E) are impossible in both scenarios. Only (C) - R could rank third could be true:

F G R T S H .

Question 6 asks which of the following crews cannot rank third?

We know that R could be third from the previous question, so we can right away eliminate (B). We can also see that H could be third from our scenario above, thus we can eliminate (A). We can also see that G could be ranked third - R F G T S H, thus we can eliminate (D) and finally, we can eliminate (C) - R S F H G T could be true per our scenario above. Hence, the only one that could not be third is T (E).

bb427 on December 24, 2019

Thank you. Keeping the chains separate in this game, at least to me, made it clearer as to questions 2, 3, and 4. By trying to create a longer chain, thereby bring the crossover of T into the visual for me, created too many complications for the HGT relationships. In your answer to 3 above, you have G/T as possible for 4. But isn't H also a possibility for 4 since, as you say, H is a free variable? Thanks again.

Irina on December 25, 2019

@bb427,

I am assuming you are asking if H could be #5. Yes, H could also be 5th, or 4th or 6th. Good catch!

Anna20 on June 9, 2020

Hi @Irina - many thanks for the above, that's helpful. Please could you explain further how to deal with the crews that are night shift crews - (G & T or S & H ) - how do you approach this in terms of the number line? I see that you broke this out into two separate chains, but grateful if you could please explain further. Many thanks!