Coworkers Fang, Gan, Hua, Di, and Kun must complete three new projects

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=73540 Coworkers Fang, Gan, Hua, Ji, and Kun must complete three new projects: a brochure, a report, and a spreadsheet. Each worker will work on exactly one of these projects. Exactly one worker—but not Hua—will work on the spreadsheet. The coworkers' manager will not assign any workers who are close friends to work together on a project. Lines in the graph connect two names if and only if the two Individuals are close friends. Select from each drop-down menu the option that creates the most accurate statement, assuming the constraints described in the passage are adhered to. GRAPH_1_PLACEHOLDER could be assigned to work on the brochure, but only if Gan is assigned to work on the GRAPH_2_PLACEHOLDER . ID: 700178 1st.PNG

chetan2u · Accepted Answer

Great question but a very convoluted Official explanation, if it is from the official book. In that case, same can be said about these explanations as has been said many times about Verbal explanations, that they have been written very poorly.

If we go by the explanation, only possibility is having Hua and Kun as partners and Gan & Ji. So, surely as said by  AnkurGMAT20 ,  ishar25 , and  Palakg17 , Kun would do Brochure only if Gan does report because both have to be doing opposite things.

So, My solution would be.

The biggest FLAW everyone including the official explanation is doing is to take the groups as 1-2-2.
 Why cant it be 1-1-3? : It is nowhere mentioned that the remaining work in pairs.

Let us first touch upon  Spreadsheet , which is surely done by just one person.
1) We know Fang has all others as close friends so has to work alone.  So, one project - Fang alone 
2) Hua can work alone or be in a pair with Kun.
3) Ji cannot work alone as then Gan and Hua, who are close friends will have to work together.
4) Gan cannot work alone as then Ji and Hua, who are close friends will have to work together.
5) Kun cannot work alone as then Gan, Ji and Hua, who are close friends will have to work together.
Apart from Fang, only Hua can work alone, but it is given that Hua does not work on spreadsheet.
  Spreadsheet - Fang

Now we are left with two projects and 4 person.
Hua works alone or works with Kun.
1) Hua alone, then Gan-Ji-Kun together
2) Hua-Kun, then Gan-Ji

With this info let us get back to the blanks.
Kun/Ji/Fang could be assigned to work on the brochure, but only if Gan is assigned to work on the Spreadsheet/Brochure/Report.

Fang has already been tasked for Spreadsheet, so the blanks become
Kun/Ji could be assigned to work on the brochure, but only if Gan is assigned to work on the Brochure/Report.

Now Kun could do exactly the same thing as Gan, if Gan-Ji-Kun are working on the same project or Kun could do opposite if Kun-Hua are together.
We can say two things when we are speaking in relation to Gan
 1) Hua will always do the opposite thing , but Hua is not there in the first blank.
 2) Ji will always do the same thing  as Ji always partners with Gan.
Thus,  Ji   goes into the first blank, and Gan also has to do the same project, so  brochure   goes to second blank.

Ji   could be assigned to work on the brochure, but only if Gan is assigned to work on the   Brochure  .

https://www.youtube.com/watch?v=5s79GU3-R1E

egmat · Answer

Here is a  detailed video solution  for this interesting question.  See how this question can be solved in the test environment using " Owning the Dataset " approach.

https://www.youtube.com/watch?v=a6eHD_0N2QA

Let us know if you have any questions.

BottomJee · Answer

OFFICIAL EXPLANATION

In what follows, the letters B, R, and S denote, respectively, brochure, report, and spreadsheet. Also, individual assignments will be denoted as Fang-R, Ji-S, etc. where, for example, Kun-B means Kun is assigned to work on the brochure. The discussion below will be easier to follow by drawing one or more diagrams labeled with the 5 names and then writing B, R, or S by the appropriate names as the assignments are determined or considered.

The first selection amounts to making one of the following three possible assignments—Fang-B, Ji-B, or Kun-B. If the assignment Fang-B is made, then Hua cannot be assigned the spreadsheet (violates Hua constraint) or the brochure (violates close friends constraint with Fang), and thus we must have Hua-R. At this point, no matter which of Gan, Ji, or Kun is assigned the spreadsheet, at least one of Gan and Ji will not be assigned the spreadsheet, and thus at least one of Gan and Ji must be assigned either a brochure or a report. However, each of these possibilities violates the close friends constraint—brochure violates the close mends constraint with Fang, and report violates the close friends constraint With Hua. Therefore, the assignment Fang-a is not even possible.

If the assignment Ji-B is made, then Hua cannot be assigned the spreadsheet (violates Hua constraint) or the brochure (violates dose friends constraint With Di), and thus we must have Hua-R. Given these two assignments, Gan-R is not possible (violates dose friends constraint with Hua) and Gan-S is not possible (otherwise we would have Fang-a or Fang-R, each of which violates the close friends constraint with Ji-a and Hua-R). Therefore, we must have Gan-B. Summarizing, Ji can be assigned to work on the brochure only if Gan is to work on the brochure. Although it is not necessary to continue analyzing the worker assignment possibilities, we mention that since neither Fang-B nor Fang-R is possible (each violates the close friends constraint with Ji-B and Hua-R), it follows that we must have Fang-S, after which either Kun-B or Kun-R is possible. The diagram below shows the two possible worker assignments that include Ji-B.

The argument above shows the correct choice of the avo selections. However, for completeness, the diagram below shows two possible worker assignments if the assignment Kun-B is made, one of which includes the assignment Gan-B (use first coordinates of the project assignment pairs shown) and the other of which includes the assignment Gan-R (use second coordinates of the project assignment pairs shown). Therefore, if Kun is assigned to work on the brochure, then there is no single project that must be assigned to Gan.

Blank 1: The correct answer is Ji.
Blank 2: The correct answer is brochure.

Show Spoiler

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AnkurGMAT20 · Answer

BottomJee   GMATCoachBen   KarishmaB  I didn't understand why we can't have two possibilities here, though I got the question right, what I fail to understand is why the second option is not possible. We have two constraints here, Hua can't be assigned to spreadsheets and no two friends can be in the same project. Now, we have two options here:

1. Assign J and G to Brochure, Assign H and K to Report and Assign F to Spreadsheets. That's the official answer as well.

However, I see there is second possibility as well:

If we assign H and K to Brochure, G and J to reports and F can be assigned to spreadsheets, we are meeting the requirements i.e.   Each worker will work on exactly one
of these projects. Exactly one worker—but not Hua—will work on the spreadsheet. The coworkers' manager will not assign any workers who are close
friends to work together on a project.

What I am missing here, could you please help?

KarishmaB · Answer

Sure you are meeting the requirements but tell me how will you fill the blanks? __________ could be assigned to work on the brochure, but only if Gan is assigned to work on the ___________ You need a necessary condition - Is it necessary that Gan is assigned to work on brochure/reports if Kun is assigned to work on brochures? Since Kun is not close friends with any of the other 3 - Gan, Hua, Ji - we don't have any necessary condition related to Kun and Gan. Hence we must be talking about the first case you mentioned! See, it isn't just about solving for possible cases. It is about filling up the blanks appropriately. Here is a video explanation of this complex problem: https://youtu.be/Jw2nLj00Nus

AnkurGMAT20 · Answer

Thanks KarishmaB, however, I still didn't get this completely. If both conditions are right, we can assign Gan to report and Kun to Brochure. This option will also not violate any condition. Not sure where I am going wrong here.

KarishmaB · Answer

I am guessing you have understood this now. There is certainly no assumption made that the groups must be 1-2-2. Certainly 1-1-3 is a possibility.

The problem lies here: We can assign Gan to reports and Kun to Brochure but this doesn't give us a NECESSARY condition. The blanks are looking for a necessary condition.

_____Kun_____ could be assigned to work on the brochure, but only if Gan is assigned to work on the ____reports_______

is not a correct statement to make. Is it true that Kun can be assigned to brochure ONLY IF Gan is assigned to reports? No. Kun could be assigned to brochures even if Gan is assigned to brochures, not reports. You have to find a NECESSARY condition to fill in the blanks (notice the use of 'ONLY IF')
We don't have a necessary condition if we select 'Kun' for blank 1. So we must select 'Ji' for blank 1.

GMATinsight · Answer

Please check the video explanation here

https://www.youtube.com/watch?v=IcF_qMkm3eI

StorkStark · Answer

I think fastest way to solve this is negate given graph , that clearly shows F can work alone , H can only work with K. combine with question stem you can figure out _ - B , only if G- _ relation ?

answer is unique !!
I have attached photo of above approach.

kanwar08 · Answer

Ans. Ji and Brochure.

Since, Fang is co-worker with every other worker, he can ONLY be assigned Spreadsheet.

Rest Pairs possible are:
(Ji, Kun) , (Hua, Kun), (Gan, ji) and (Gan, Kun)

Possibility 1:
I assign any of the remaining to (Ji, Kun)
The other pair will be (Gan, Hua). But this isn't possible.
So, this possibility doesn't exist.

Possibility 2:
Assign any of the remaining to (Hua, Kun)
Then, the other Paid can only be (Gan, ji)
Possible. So, if Ji is a Brochure, then Gan needs to be working only on the Brochure

Possibility 3:
Assign any of the remaining to (Gan, Kun)
But, the other possibility can't exist (Hua, Ji)

Coworkers Fang, Gan, Hua, Di, and Kun must complete three new projects

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Coworkers Fang, Gan, Hua, Di, and Kun must complete three new projects

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