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What is the median number of employees assigned per project

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 May 2012, 02:26, edited 1 time in total.
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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: 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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raxsin12 wrote:
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.


Statement 2 and 1 must refer to the bottom and to the highest part.
"couldn't it be first 35 % then the next 25% and the remaining 40%"? NO.
The first 35% have 2 or fewer (till here correct), but then your reasoning goes against the info in statement 1.
What you are saying is that 25%+40%=65% has 4 or more employees => wrong, look at statement 1:
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.

Hope it's clear

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I've solved it this way (see attachment) -> the mid section of 40% =3 (it must be an integer, you cannot have fractions when dealing with persons ;) So Statement 1+2 are sufficient (C)
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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)
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roygush 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


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


25% of company Z projects have 4 or more that (4,5,6,....)

35% of company z projects have 2 or less (0,1,2 )...

there must b 3 employees per project of company z which consists of (25+35=60) and 100-60=40%..

0,1,2 must be first 35 projects
3 employees for next 40 project
and 4 or more than 4 employees for remaning 25 projects..
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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


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). :lol:
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rajathpanta wrote:
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.

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.



I Did not understand this. How can you deduce about the 40% of the projects based on the information given. The problem just says 25% of the projects have 4 or more. 35% of the projects have 2 or less. So it does not talk anything about 40%. 40 % can be 5,6,7 or anything right?? Could you explain it in detail.


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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1st 35% are either 1 or 2 and last 25% are 4 and above
hence 35 - 75% should be 3
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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.
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Statement (1) by itself is insufficient because we have no clue how the rest of the employees are assigned... same problem with statement (2).

When we combine the statement, we know that all the other projects have 3 employees assigned to each of them. If we were to write out the list, "3" would cover the middle terms, so it will end up being the median of the set.
Hence C.
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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).
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Thanks for the reply! Finally got this one.
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New post 30 Aug 2012, 20:42
bunuel sir great reply ...
your approach to the answers by taking apt samples scare me

i feel like i just cant do it without error
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New post 10 Dec 2012, 14:11
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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Re: What is the median number of employees assigned per project [#permalink]

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New post 27 Dec 2012, 09:24
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.

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.



I Did not understand this. How can you deduce about the 40% of the projects based on the information given. The problem just says 25% of the projects have 4 or more. 35% of the projects have 2 or less. So it does not talk anything about 40%. 40 % can be 5,6,7 or anything right?? Could you explain it in detail.
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Re: What is the median number of employees assigned per project [#permalink]

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New post 13 Apr 2013, 03:37
Thanks for the welcome and the explanation! Its clear now.....
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New post 19 Oct 2013, 11:02
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,
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Re: What is the median number of employees assigned per project [#permalink]

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New post 19 Oct 2013, 11:13
versuchmachtklug wrote:
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,



JUST GOT IT!! saying it loud helped me..thanks anyways
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Re: What is the median number of employees assigned per project   [#permalink] 16 Jun 2015, 12:13

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