An engineering firm is organized so that each of its T team leaders ma

Question

An engineering firm is organized so that each of its T team leaders manages exactly P project managers, and each project manager manages exactly D designers. If P = 4, which of the following represents a possible combination of the number of team leaders and designers at the firm?

abhimahna · Accepted Answer

I will go with 4 Team players and 112 designers.

Explanation : Let we have 4 team players. Each Manage 4 PM. => Total PM = 4*4 = 16 .

Now, since each PM manages exactly D designers, therefore total designers must be a multiple of 16 which is 112 here. Hence the answer.

Please post the OA and suggest if I am missing anything.

Cellchat · Answer

We know the number of designers is going to be a multiple of 4.

We also can quickly deduce that the number of team leaders is either 3 or 4 as all other values will give too many developers for even the greatest answer choice.
Example, If T = 18 --> no. P managers = 4x18 = 72 --> min no. developers = 144 (as stem mentions developer s  in plural).

If we pick T = 3, then D will be a multiple of 12. Scan through RH column and you will find there to be no such multiple.

We then pick T = 4, no. managers = 4x4 = 16, scanning through RH column for any multiple of 16 we find 112.

T = 4 
 D = 112

Apt0810 · Answer

Team player number should be divisible by 4 (P) so number of team players = 4 so total number of PMs = 4*4= 16, now the number divisible by 16 is 112 so number of designers = 112

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sssaniaa · Answer

Cellchat

Thanks for posting a clear response! I work in Business myself & my mind went automatically to one of my managers that manages 4 employees.

In this case, in order for this problem to work properly in my head, I imagined that since there are 4 Project Manager's, there must be a minimum of 4 Team leaderS because it's plural in the problem & not singular.

My question is, how can I steer away from thinking of a conventional business model where a manager can manage 4 individuals at once or 2 managers can manage 4 individuals (each two)?

Westfolia007 · Answer

sssaniaa  
Even I made the same mistake but the point to be noted is that EACH OF the team leader is managing P project managers and each of P project managers are managing D designers. 
My approach :
It is quite clear that D has to be a multiple of 4, so with that we can eliminate a few numbers. Now let us assign a number for the Team Leaders. Starting with 3, if there 3 TL, then we would have 3*4 PM which is 12PM. If the number of Pm is 12, the the number of D will have to be a multiple of 12 and we clearly do not have a multiple of 12 in the options
Moving onto 4TL, we will have 16 PM and that means the number of D has to be a multiple of 16. 112 is the only multiple of 16, so the answer is 4 and 112 respectively
Hope this helps

Kmohan1 · Answer

Total number of team leaders= T
Total number of project managers= T*P (since each team leader manager P project managers)
Total number of designers= T*P*D (since each project manager manages D designers)
P=4
Q: T*P*D? and T?
T*P*D will be some multiple of 4. Total number of designers can be 4, 52 or 112. 
So T*D can be 1, 13, or 28. Values of T can be 1,13,28,4,7,2,14. From the options we can see only 4 is present. So T=4, then T*P*D=112

rajatyadav1994 · Answer

Important distinction to make here is that the variables given are Number of Project Managers per Team Lead, Number of Designers per Project Manager, etc, and the answer requires you to give the TOTAL NUMBER of team leads/ designers.

> So Total Number of Team Leads = T (
> Total Number of Designers = T*P*D
>> = T*4*D
Therefore, the number of designers is a multiple of 4

We can now look at suitable options for the number of designers: 4,52,112

a) T*4*D = 4: This does not work as we do not have 1 as an option for either T or D
b) T*4*D = 52 : Factors Pairs (  ,  ,   ) - Holding either of these in place of T to get 52 as the product does not work, given P=4
c) T*4*D = 112: Factors Pairs (  ,  ,  ,  ....we see that T=8 will help yield 112 as Number of Designers

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An engineering firm is organized so that each of its T team leaders ma

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