What is the median number of employees assigned per project

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BTGmoderatorLU: Moderator; Posts: 2585; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu Oct 03, 2019 7:42 am

Source: Official Guide

What is the median number of employees assigned per project for the projects at Company Z?

1) 25 percent of the employees at Company Z have 4 or more employees assigned to each project.
2) 35 percent of the employees at Company Z have 2 or fewer employees assigned to each project.

The OA is C

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Source: Beat The GMAT — Data Sufficiency | Thu Oct 03, 2019 7:42 am

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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 » Thu Oct 03, 2019 7:51 am

BTGmoderatorLU wrote:Source: Official Guide

What is the median number of employees assigned per project for the projects at Company Z?

1) 25 percent of the employees at Company Z have 4 or more employees assigned to each project.
2) 35 percent of the employees at Company Z have 2 or fewer employees assigned to each project.

The OA is C

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: C

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Oct 03, 2019 8:32 am

BTGmoderatorLU wrote:Source: Official Guide

What is the median number of employees assigned per project for the projects at Company Z?

1) 25 percent of the employees at Company Z have 4 or more employees assigned to each project.
2) 35 percent of the employees at Company Z have 2 or fewer employees assigned to each project.

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.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8183; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: What is the median number of employees assigned per project

by Scott@TargetTestPrep » Thu May 20, 2021 9:12 am

BTGmoderatorLU wrote: ↑
Thu Oct 03, 2019 7:42 am
Source: Official Guide

What is the median number of employees assigned per project for the projects at Company Z?

1) 25 percent of the employees at Company Z have 4 or more employees assigned to each project.
2) 35 percent of the employees at Company Z have 2 or fewer employees assigned to each project.

The OA is C

Solution:

Question Stem Analysis:

We need to determine the median number of employees assigned per project for the projects at Company Z.

Statement One Alone:

We know the upper 25 percent of the projects at Company Z have 4 or more employees assigned to each project. However, we can’t determine the median number of employees assigned per project because it could be 3, 2, or even 1 person.

Statement Two Alone:

We know the lower 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project. However, we can’t determine the median number of employees assigned per project because it could be 3, 4, or even more people.

Statements One and Two Together:

We know the upper 25 percent of the projects at Company Z have 4 or more employees assigned to each project and the lower 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project, which means the middle 40 percent of the projects at Company Z must have exactly 3 employees assigned to each project. Since the middle 40 percent of the projects contains the median number, the median number of employees assigned per project must be 3.

Answer: C

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