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What is the median number of employees assigned per project [#permalink]
04 May 2012, 01:20

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00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

61% (01:59) correct
39% (01:00) wrong based on 634 sessions

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

Re: What is the median number of employees assigned per project [#permalink]
04 May 2012, 01:46

9

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Expert's post

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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).

Re: What is the median number of employees assigned per project [#permalink]
13 Apr 2013, 02:14

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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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Re: What is the median number of employees assigned per project [#permalink]
11 Dec 2012, 02:47

1

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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

Re: What is the median number of employees assigned per project [#permalink]
11 Dec 2012, 03:43

1

This post received KUDOS

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). _________________

Re: What is the median number of employees assigned per project [#permalink]
27 Dec 2012, 09:37

1

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Expert's post

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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).

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.

Re: What is the median number of employees assigned per project [#permalink]
18 May 2014, 09:57

1

This post received KUDOS

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.

What is the median number of employees assigned per project [#permalink]
10 Dec 2012, 13:11

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

Re: What is the median number of employees assigned per project [#permalink]
27 Dec 2012, 08:24

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).

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]
13 Apr 2013, 02:02

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.

Re: What is the median number of employees assigned per project [#permalink]
19 Oct 2013, 10:02

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"

Re: What is the median number of employees assigned per project [#permalink]
19 Oct 2013, 10:13

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

Re: What is the median number of employees assigned per project [#permalink]
16 Jun 2015, 11:13

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Re: What is the median number of employees assigned per project [#permalink]
20 Aug 2015, 13:36

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)

Attachments

PS 139.png [ 22.89 KiB | Viewed 913 times ]

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Re: What is the median number of employees assigned per project
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20 Aug 2015, 13:36

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