Data Sufficiency

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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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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