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Median Problem

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by ygdrasil24 » Sun Jun 30, 2013 5:13 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.
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Jun 30, 2013 7:40 am
ygdrasil24 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.

Getting lost..please post some good solution.
In ascending order of EMPLOYEES PER PROJECT, let the projects be numbered 1 through 100:
1, 2, 3.....49, 50, 51, ....98, 99, 100.
Projects 50 and 51 determine the MEDIAN number of employees:

Question rephrased: How many employees are assigned to PROJECTS 50 and 51?

Looking at the two statements, we should note that there are 3 options:
Option A: A project is assigned 2 OR FEWER employees.
Option B: A project is assigned EXACTLY 3 employees.
Option C: A project is assigned 4 OR MORE employees.

Neither statement alone is sufficient to determine the number of employees assigned to projects 50 and 51.
Statements combined:
According to statement 2, Projects 1 through 35 -- the BOTTOM 35 projects -- conform to OPTION A.
According to statement 1, Projects 76 through 100 -- the TOP 25 projects -- conform to OPTION C.
Implication:
Projects 36-75 -- the MIDDLE 40 projects -- conform to OPTION B.

Thus, Projects 50 and 51 are each assigned EXACTLY 3 employees, implying that the median number of employees per project = 3.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Wed Oct 23, 2013 7:23 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Sun Jun 30, 2013 7:49 am
ygdrasil24 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.

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 1: 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

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Brent
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by ygdrasil24 » Sun Jun 30, 2013 9:52 am
Thank you! Do you think its a 700+ question ?
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by Brent@GMATPrepNow » Sun Jun 30, 2013 10:35 pm
ygdrasil24 wrote:Thank you! Do you think its a 700+ question ?
I'd rate this as a 650 - 700 question.

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