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What is the median number of employees assigned per project

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What is the median number of employees assigned per project

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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.

OA C

Source: Official Guide

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BTGmoderatorDC 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.
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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BTGmoderatorDC 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.

OA C

Source: Official Guide
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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BTGmoderatorDC 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.

OA C

Source: Official Guide
Say there are 20 employees. I assumed 20 instead of more intuitive 10 since 25% and 35% of 10 are not integers.

We know that of a set, the median is the value of the middle-most number when the numbers in the set are arranged in an ascending or descending order.

Say the number of employees assigned per project for 20 projects arranged in an ascending order are:

a, b, c, d, e, f, g, h, i, J, K, l, m, n, o, p, q, r, s, t

Median = average of the 10th and the 11th number = (J + K)/2

Question rephrased: What's the value of J + K?

Let's take each statement one by one.

(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.

25% of 20 = 5;

=> 5 projects at Company Z have 4 or more employees assigned to each project.

Because of the phrase, "more employees," we can conclude that these 5 projects are p, q, r, s, and t. However, we can't get the value of (J + K). J and K each have values from 0 to 3. Insufficient.

(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

35% of 20 = 7;

=> 7 projects at Company Z have 2 or fewer employees assigned to each project.

Because of the phrase, "fewer employees," we can conclude that these 7 projects are a, b, c, d, e, f, and g. However, we can't get the value of (J + K). J and K each have values 3 or greater. Insufficient.

(1) and (2) together

So, of the set: a, b, c, d, e, f, g, h, i, J, K, l, m, n, o, p, q, r, s, t

a, b, c, d, e, f, and g are 2 or fewer AND p, q, r, s, and t are 4 or greater, this implies that each of h, I, J, k, l, m, n, and o is 3.

=> J + K = 3 + 3 = 6. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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