Which one of the following could be the representatives who visit France and Ghana, from the first month through the ...

Irina on February 21, 2020

@masommar,

This is an advanced linear game that involves 12 visits to factory sites -3 factories each month over four months. Factory sites are in F, G and I each visited by exactly one of the four representatives - V W Y Z each representative makes 3 visits total (3 visits x 4 rep= 12 visits total), no more than one a month, meaning any one representative cannot visit more than one site in any given month.

The setup looks like a 4 x 3 grid representing visits for each of the four months. We know that every representative must appear exactly 3 times and no representative can appear twice in any single column.

F __ __ __ __ V W Y Z =3
G __ __ __ __
I __ __ __ __

The tricky part about this game is that it is tempting to spend time on setup and try to come up with various scenarios but considering the rules are fairly open, you are actually better off making fewer initial inferences and proceeding to the questions.

The following rules apply:

(1) V must visit G once and I twice, with G visited at some time between India visits.
This rule tells us that V does not visit France, so one of the remaining representatives must visit F twice or 1 of the remaining representatives must visit F three times - 3-1 or 2-1-1.. Since V must visit G between I visits, he could only visit G during the second or third month

F __ __ __ __ at least two of W Y Z
G __ /V /V __ V
I __ __ __ __ V V


(2) W must visit G at least once.

F __ __ __ __ W Y Z ?
G __ /V /V __ V W 1+
I __ __ __ __ V V

(3) Y must visit G in a month immediately preceding a month in which W visits G,

This rule tells us that Y cannot visit G in month 4 and W cannot visit G in month 1, so in combination with the previous rule, it means that Y must visit G either in month 1 or month 3 (otherwise there is no space for V)

F __ __ __ __ W Y Z ?
G /Y /V Y/V __ V YW
I __ __ __ __ V V


(4) Y cannot visit any site in the fourth month.


F __ __ __ __ W Y Z ?
G /Y/ V Y/V __ V YW
I __ __ __ __ V V
~Y

(5) Any representative who visits F cannot visit I.

This rule tells us that exactly two representatives visit F and exactly two visit I because there are 4 total and there can be no overlap between F and I. So whoever visits I along with V must make two visits, and for France, either a single representative Z could make three visits and another representative - W or Y 1 visit, or two representatives could make two visits each.

3- 1 Z Z Z W/Y
2-2 out of W/Y/Z

Now let's look at the questions:

Question 1 asks which of the following is an acceptable assignment of representatives for France and Ghana?

(A) W Y YW and Y W V Z is correct and complies with all the rules.
(B) is wrong because V must be either 2d or 3d for G
(C) is wrong because exactly two representatives must visit F
(D) is wrong because Y cannot visit any sites in month 4
(E) is wrong because W cannot visit G first.

Question 2 asks if V visits I in the second month, which of the following must be true?

If V visits I in the second month, we know that the second visit to I must be during the fourth month, and V visit to G must be in month 3 (between two I visits). Therefore, YW combination must visit G during months 1 and 2.


G: Y W V__
I: __ V __ V

(A) is correct - V must visit G in the third month.

Question 3 asks which of the following could be true.

(A) is incorrect, we know that exactly two representatives must visit France.
(B) is incorrect, we know that exactly two representatives must visit India.
(C) is incorrect because we must have either Y W V ? or ? V Y W combination in Ghana, and V can visit G only once.
(D) is correct, it is possible for Z to visit F three times.
(E) is incorrect, we know that V and another representative must visit I for two months each.

Question 4 asks if Z visits F exactly twice, which of the following must be true?

If Z visits F exactly twice, it means that he visits G exactly once, and one more representative - Y or W visits F twice.

(A) is incorrect because W or Y could visit F twice.
(B) is incorrect because W or Y could visit I twice.
(C) is incorrect because W or Y could visit I twice.
(D) is correct, if Z visits F exactly twice, he cannot visit I and must visit G once.
(E) is incorrect because no representative that visits F can visit I.

Question 5 asks which of the following could be true.

(A) is incorrect because Y must visit G before W.
(B) is incorrect because Y must visit G in the first or third month.
(C) is correct. ? V Y W is a valid order for G
(D) is incorrect because the only valid combinations for G are Y W V ? or ? V Y W , so Z could only visit in the first or fourth months
(E) is incorrect for the same reason.

Question 6 asks how many of the representatives could visit a single one of the sites three times?

We know that Y cannot visit any site in the fourth month and must visit G either 1st or 3d, meaning he cannot possible visit any site three times. V visits I and G , thus he cannot visit any site three times. W must visit G at least once, thus he cannot visit any site three times. Z is the only one that could visit F three times (and that was our inference from the initial setup) (answer choice (B).

masommar on February 21, 2020

Thank you very much for not only the setup but for the question explanations as well!