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: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.
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Will vote for C

let total be "x" projects i.e 100% projec

(A) 25% projects has number of employees >= 4

- we dont know anything about other 75% projects

(B) 35% project has number of employees <= 2


- we dont know anything about other 65% projects

(C)

for 35% --> No. of emp <= 2
for 25% --> No. of emp >= 4

based on above data we can calculate that
Remaining 40% of projects --> No. of emp = 3 (which is between 2 < no. of emp < 4)

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


Ruled out quickly A,B,D.
remained with C, E.
chose E.
then looked here:
what-is-the-median-number-of-employees-assigned-per-project-131892.html

and i still dont understand bunuel's way.
why the employees who are not in the 25% or 35% must have exactly 3 employees?
thanks
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Ans: : Median is the middle value. Statements 1 and 2 alone give us insufficient data but when we combine both of them we see that 25 % have 4 or more and 35% have 2 or less therefore 40 %have 3 employees. Therefore the median would be 3 and the answer is (C).
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35 of the projects have 2 or fewer employees.
25 of the projects have 4 or more employees.

How many employees can be assigned to the remaining 40 projects? The ranges \(\leq{2}\) and \(\geq{4}\) are covered, thus the remaining 40 projects have 3 employees assigned to them.

Hope it's clear.
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Aren't we assuming here that, statement 1 and 2 refer to highest 25 and bottom 35 percent of the employees, couldn't it be first 35 % then the next 25% and the remaining 40% with unknown number of employees per project, then the median will lie in 4 or more employees, we do not have any particular value and hence E as the correct answer.

Hi,

i understand the answers, although i must say there is no information that says that no percentage has more than for example 5 employees per project. It could be possible to have a 25% with 4 or more, and from there a group that has 5 or more. Both equalities would still be right. For example a 25% thats has 4 or more, and only 15% that has 5 or more. A group within a group. I hope i made myself clear...
In that case the answer for me would be "e"

thank you in advance,

Detailed Solution

Step-I: Given Info

The question asks us to find the median number of employees assigned per project for projects at Company Z, using the 2 statements given.

Step-II: Interpreting the Question Statement

To find the median number of employees, we need to somehow extract the central value for employees, when arranged in ascending order. Central value or median value will be the exact determination of value at the 50%th observation.

Step-III: Statement-I

Statement- I gives us the information about the 25% of projects have 4 or more employees assigned to each project.
Now let us say we have 100 projects. There could be a possibility that remaining 75 projects (>50 projects) have 3 employees. Then the central observation (50%th observation- in this case 50th project value in total 100 projects) will have a median value of 3 employees. But the remaining 75 projects can have 2 employees as well. Then the median will be 2. So we cannot determine with exact surety, the exact value of median at 50%th observation.

Hence, statement 1 is not sufficient to answer the question.

Step-IV: Statement-II

Statement- II gives us information that 35% of the projects have 2 or fewer employees assigned to each project. Now, the remaining 65 projects (>50 projects) can have 3 employees. Then the central observation (50%th observation- in this case 50th project value in total 100 projects) will have a median value of 3 employees. But the remaining 65 projects(>50 projects) can have a median value of 4 employees as well. Then the median value will be 4 employees. So we cannot determine with exact surety, the exact value of median at 50%th observation.

Hence, statement 2 is not sufficient to answer this question.

Step-V: Combining Statements I & II

When we combine both the statements we know the value of 25% of projects (4 or more employees) and 35% projects(2 or fewer employees). So the remaining 40 projects (<50 projects) will have 3 employees. When the observations are arranged in ascending order. The first 35 observations will have 2 or fewer employees and next 40 observations will have 3 employees and then next 25 observations will have 4 or more employees. Thus, the median number of employees will be 3.

Hence, the exact determination of central value or value at 50%th observation is 3.

So the correct answer is C. Both the statements together are sufficient.

Key Takeaways

Use of concept of median and evaluating all possible value of central value (median value) for observations to be able to find exact value at 50%th observation (when values arranged in ascending order).

Dear Friends,

I need your help, coz I'm having problem
I have two questions:

1) What if there is no project with THREE employees?
Why can't 40% of projects have 5 or more employees or only 1 employee for that matter

2) I couldn't understand why 40% must be between 2 (35%) and 4 (25%): please see the attachment below.
I would to know the reasoning behind why 3 employees (40%) must be between 2 and 4.
The question does not say that 25% is at the higher band or that the 35% is at the lower band. (Although we can deduce 25% band is higher than the 35% band).
Why can't the rest 100-(25+35)=40% be at an even higher band (eg 5 employees or more) ?

It hasn't been stated nowhere that 35% is the 1st and 25% is the last :


I would be so grateful, if u could explain me thoroughly.
Thank you very much!

(1) If 25 % of the projects at Company Z have 4 or more employees assigned to each project, then 75% of the projects have less than 4 employees.
The median thus would be less than 4. But don't know its exact value.

Insufficient.

BCE

(2) Therefore 65% of the projects have more than 2 employees.
But still we do not have an exact value.

Combine the two statements:

2<Median number of employees<4

Thus its 3.

C
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