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# What is the median number of employees assigned per project

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Senior Manager
Joined: 17 Jun 2015
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Re: What is the median number of employees assigned per project [#permalink]

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24 Dec 2015, 11:59
Each statement alone is insufficient

Combining the two, we understand that there are three categories of employees.

Group1: Less than 2
Group 2: Between 2 and 4 i.e. 3
Group 3: Greater than or equal to 4.

The media falls in the mid - the 50th percent, which is group 2

Hence C, Both statements together are sufficient.
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What is the median number of employees assigned per project [#permalink]

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13 Feb 2016, 04:39
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 :
rohantiwari wrote:
1st 35% are either 1 or 2 and last 25% are 4 and above hence 35 - 75% should be 3

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

Bunuel 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. 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.

BrainLab wrote:
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)

hdwnkr wrote:
Each statement alone is insufficient
Combining the two, we understand that there are three categories of employees.
Group1: Less than 2
Group 2: Between 2 and 4 i.e. 3
Group 3: Greater than or equal to 4.
The media falls in the mid - the 50th percent, which is group 2
Hence C, Both statements together are sufficient.

Zarrolou wrote:
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.

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

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22 Feb 2016, 22:00
studentsensual wrote:
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 :
rohantiwari wrote:
1st 35% are either 1 or 2 and last 25% are 4 and above hence 35 - 75% should be 3

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

Because "5 or more" is already a part of "4 or more" set.

Look, the number of employees assigned to a project could be any of the following:
0 (debatable but ok), 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... and so on

When you say 35% project have 2 or fewer employees assigned, it means that 25% projects have either 0 or 1 or 2 employees assigned. All projects that have 1 employee assigned to them are a part of this 25%. Say, this is the first group.

When you say 25% projects have 4 or MORE employees assigned, it includes all projects with 4 or 5 or 6 or 7 or 8 etc employees assigned to them. Any project that has 5 or more employees is already a part of this 25%. This is the second group.

So what about the rest of the 40% projects? Can they have 1 employee assigned? No. All those projects are accounted for in first group. Can they have 6 employees assigned? No. All those projects are accounted for in second group. The only number left that is not accounted for in wither group is 3.
So 40% projects must have exactly 3 employees assigned.

Makes sense, now?
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Re: What is the median number of employees assigned per project [#permalink]

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03 Feb 2017, 08:32
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.

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

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02 Apr 2017, 06:59
(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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Re: What is the median number of employees assigned per project [#permalink]

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01 Sep 2017, 15:00
Top Contributor
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

Target question: What is the median number of employees assigned per project?

Statement 1: 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
Let's pretend that there are 4 projects altogether.
There are several sets of values that meet this condition. Here are two:
Case a: the set of numbers representing employees per project are {1, 1, 1, 4} in which case the median is 1
Case b: the set of numbers representing employees per project are {2, 2, 2, 4} in which case the median is 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.
Using logic similar to the above, we can show that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
35% projects have 2 employees OR FEWER, and 25% of the projects have 4 employees OR MORE. So, 40% projects have EXACTLY 3 employees.

To find the median, we must find the middlemost value when all of the values are listed in ASCENDING order.
So, the first 35% of the numbers will be 1's and 2's.
Then next 40% of the numbers will be 3's
And the last 25% of the numbers will be 4, 5's, etc

As you can see, the MIDDLEMOST value will be 3. In other words, the median must be 3.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

[Reveal] Spoiler:
C

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Re: What is the median number of employees assigned per project   [#permalink] 01 Sep 2017, 15:00

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