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.

Answer: C.

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.

this is how I thought about it...

next 25 that is from 36 - 61 have 4 or more....so that can be anything from 4,5,6...