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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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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:

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

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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).

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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18 Jan 2018, 08:16
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).

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

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15 Aug 2018, 21:29
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: http://gmatclub.com/forum/gmat-problem-solving-ps-140/ and DS questions in the DS subforum: http://gmatclub.com/forum/gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.

this is how I thought about it...

first 35 projects have 2 or fewer assigned to each so that can be 0,1 or 2

next 25 that is from 36 - 61 have 4 or more....so that can be anything from 4,5,6...

so the last 39 ie from 62- 100 must be more than 4?

so the median can be either 4 or above 4

please correct my line of thinking I'm lost...
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