A renovation project requires the completion of six tasks.

Question

https://gmatclub.com/forum/download/file.php?id=89680 A renovation project requires the completion of six tasks. In the diagram, the tasks are represented by circles labeled P through U, and the number above each circle represents the number of days needed to complete the task. An arrow from one task to another indicates that the first task must be completed before the second can begin. Unless prohibited by these requirements, several tasks can be worked on at the same time. The project is complete when all six tasks have been completed. Use the drop-down menus to complete each statement most accurately based on the information provided. The least number of days needed to complete the renovation project is GRAPH_1_PLACEHOLDER days. Task P could take as many as GRAPH_2_PLACEHOLDER additional days without increasing the least number of days needed to complete the project. GMAT-Club-Forum-6yjyr84x.png

officiisnobis · Answer

24 and 3

SillyTrout · Answer

22 and 2

Krangle · Answer

I also think it is 24 and 3, can you please explain why it is not correct?

impedittempore · Answer

I got it 21 and 3. what is the correct answer?

egmat · Answer

Hi Krangle,

Good news:  your answers are exactly right.  The minimum is  24 days  and Task P has  3 days of slack . You're second-guessing yourself because another reply in the thread said "22 and 2," so let me show you why  your  numbers hold and that one doesn't.

Part 1 - minimum days = the longest path

The project can't finish until the  slowest chain  of dependent tasks finishes. So list every path from  begin  to  end  and add the day-counts:

- P → R → T =  6  +  5  +  4  =  15 
- P → S → T =  6  +  8  +  4  =  18 
- P → S → U =  6  +  8  +  7  =  21 
- Q → S → T =  9  +  8  +  4  =  21 
-  Q → S → U = 9 + 8 + 7 = 24  ← longest

The longest is  24 , so the project needs  24  days. There's no valid chain that adds to  22  - that's why the other post's "22" doesn't come from any real path.

Part 2 - how much slack Task P has

Here's the key detail:  S needs  both  P and Q done before it can start.  Look at their finish times running in parallel:

- Q finishes on day  9 
- P finishes on day  6

S is already stuck waiting for Q until day  9 . So P has  9 - 6 = 3  spare days - it could finish as late as day  9  and S still starts right on time. Push P by a  4 th day and it becomes the one holding S up, adding a day to the whole project. So the max is  3 , not  2 .

Quick way to feel it:  if two runners must both finish before a relay handoff, and one takes  6  seconds while the other takes  9 , the  6 -second runner can dawdle up to  3 extra seconds  - the  9 -second runner sets the handoff either way.

So trust your work:  24 and 3.

Answer: 24

MaTaM · Answer

I got 24 and 3

24 is the sum of the longest possible chain: Q->S->U so 9+8+7=24

Now knowing that the process takes at least 24 days we can look at the longest chain involving task P (P->S->U). 
We want to find how much we can stretch task P so that this chain gets to 24 days long. 
Tasks S and U take 8 and 7 days, so in order for the chain to be 24 days long P can last 24-8-7=9 days, which is 3 more than the original 6!

A renovation project requires the completion of six tasks.

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A renovation project requires the completion of six tasks.

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