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# What is the median number of employees assigned per project

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Joined: 23 Feb 2015
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Re: What is the median number of employees assigned per project  [#permalink]

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31 Mar 2020, 14:11
Bunuel wrote:
ITIZCODE wrote:
What is the median number of employees assigned per project for the projects at Company Z?

(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project

What is the median number of employees assigned per project for the projects at Company Z?

(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Not sufficient on its own.

(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. Not sufficient on its own.

(1)+(2) Since 35% of of the projects have 2 or fewer ($$\leq{2}$$)employees and 25% of the projects have 4 or more ($$\geq{4}$$) employees, then 100%-(25%+35%)=40% of the projects have exactly 3 employees assigned to each of them. So, the median number of employees assigned per project is 3. Sufficient.

To elaborate more: consider there are 100 projects: $$\{p_1, \ p_2, \ ... , \ p_{100}\}$$. The values of $$p_1$$ to $$p_{35}$$ will be 0, 1, or 2; the values of $$p_{36}$$ to $$p_{75}$$ will be exactly 3; the values of $$p_{76}$$ to $$p_{100}$$ will be 4 or more. $$Median=\frac{p_{50}+p_{51}}{2}=\frac{3+3}{2}=3$$.

For example list can be: $$\{2, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 4, \ ..., \ (p_{100}=4)\}$$;
OR:
$$\{0, \ 0, \ 1, \ 1, \ 1, \ 2, \ 2, \ ..., \ (p_{35}=2), \ (p_{36}=3), \ 3, \ ..., \ (p_{75}=3), \ (p_{76}=4), \ 5, \ 7, \ 27, \ ..., \ (p_{100}=10000)\}$$ (of course there are a lot of other breakdowns).

In any case median=3.

Hope it's clear.

P.S. Please post PS questions in the PS subforum: http://gmatclub.com/forum/gmat-problem-solving-ps-140/ and DS questions in the DS subforum: http://gmatclub.com/forum/gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.

Hello Bunuel
Thanks for the explanation with Kudos.
Is it the right way to keep the 0 (zero) in the list? It is all about the list of employees. Should we consider 0 (zero) for the employees in the list specially in this case?
Thanks__
Re: What is the median number of employees assigned per project   [#permalink] 31 Mar 2020, 14:11

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