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.

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.

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.

Attachments

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