median question..

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Dec 03, 2013 5:08 am

I) 25% of the project at company Z have 4 or more employees assigned to each project.
INSUFFICIENT as we don't know the distribution of 1, 2 or 3 employees in the other 75%.

II) 35% of the project at company z have 2 or fewer employee assigned to each project.
INSUFFICIENT as we don't know the distribution of employees.

I & II Combined:
Look at bands of quantities of employees and the corresponding percentage scales below:
[________<=2)________][_______3_______][_____>=4_______]
[_________________75%________________][______25%______]
[________35%_________][_____________65%_______________]

The median is located at 50.5% which is between 35% and 75%.
3 is the only quantity between 35% and 75%.
Therefore the median is 3.
SUFFICIENT.

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sahilbilga: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sat Apr 20, 2013 9:34 pm

by sahilbilga » Fri Jan 10, 2014 12:52 am

I think, answer should be C. Because 35% projects have 2 or less than 2 employees and 25% of projects have 4 or more employees. This means remaining 40% has 3 employees(By Combing both statements)

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Jan 10, 2014 7:14 am

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.

Getting lost..please post some good solution.

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.

This tells us that the median must be 3.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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