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What is the median number of employees assigned per project

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

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New post 01 Sep 2017, 15:00
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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


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

Answer:
[Reveal] Spoiler:
C


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

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New post 24 Nov 2017, 09:07
Okay, I know this question has been asked before, but people's answers to it aren't helping me, so if anyone can re-phrase then that would be hugely appreciated.

I do not understand how the statements do not allow there to be projects that have 5, 10, 15, 20, 1000 etc people working on them. Let's say that there are 100 projects at Company Z.

(1) 25 projects have 4 or more employees.
This could be laid out like this:
Project number 75 has 4 employees.
Project number 76 has 5 employees.
Project number 77 has 6 employees.
...
Project number 100 - 29 employees.

Then once we know that there are projects with 0, 1, 2, and 3 employees (and this information is gleaned from statement (2) as discussed earlier in the thread), we have a collection of 100 projects, with 1, 2, 2, 2, 2 (x 35 projects), 3 (x 40 projects), 4, 5, 6, 7 ... 29 employees. In this case the median has to be 15, not 3.

Does my analysis make sense?
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Re: What is the median number of employees assigned per project [#permalink]

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New post 17 Jan 2018, 15:17
priyamne 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


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:


I understand that we're looking for the median and that each statement alone only tell us PART of what we want to know...further, I understand adding up both %s [25 & 35] and deducing that 40% have 3 employees.
- HOWEVER, how do we know that 40% contains the median? What if we changed the numbers in Statement 1 & 2 both to 35? In this case, 30% would be left for 3 employees...how would this affect the answer?
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Re: What is the median number of employees assigned per project [#permalink]

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New post 18 Jan 2018, 08:16
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LakerFan24 wrote:
priyamne 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


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:


I understand that we're looking for the median and that each statement alone only tell us PART of what we want to know...further, I understand adding up both %s [25 & 35] and deducing that 40% have 3 employees.
- HOWEVER, how do we know that 40% contains the median? What if we changed the numbers in Statement 1 & 2 both to 35? In this case, 30% would be left for 3 employees...how would this affect the answer?


It won't change the answer. Say there are 20 projects.
If 35% have 4 or more employees, it means 7 projects have 4 or more employees.
If 35% have 2 or fewer employees, it means 7 projects have 2 or fewer employees.
The leftover 30% i.e. 6 projects have 3 employees.

To find the median, you will need to arrange the number of employees in increasing order

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7

The one in the middle will be 3.
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Re: What is the median number of employees assigned per project   [#permalink] 18 Jan 2018, 08:16
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