Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We want to know the median number of employees assigned per project for the
projects at Company Z. Recall that the median is the middle number of a data set if
the numbers of the data set are listed in ascending (or descending) order.
Furthermore, the median is also the 50 th percentile of a data set. That is, the
median is the number that splits a data set between its top 50 percent and bottom
50 percent.
Statement One Alone:
25 percent of the projects at Company Z have 4 or more employees assigned to
each project.
This means each of the top 25 percent of the projects has 4 or more employees
assigned to it. In other words, the 75 th percentile is the number 4 and any
percentile less than 75 will be a number less than 4. However, without further
information, we don’t know what the median (i.e., the 50 th percentile) is, since it
can be 3, 2 or 1.
Statement one alone is not sufficient to answer the question. We can eliminate answer
choices A and D.
Statement Two Alone:
35 percent of the projects at Company Z have 2 or fewer employees assigned to
each project.
This means each of the bottom 35 percent of the projects has 2 or fewer employees
assigned to it. In other words, the 35 th percentile is the number 2 and any
percentile higher than 35 will be a number more than 2. However, without further
information, we don’t know what the median (i.e., the 50 th percentile) is, since it
can be 3, 4, 5, etc. Statement two alone is not sufficient to answer the question.
We can eliminate answer choice B.
Statements One and Two Together:
From statements one and two, we know the 75 th percentile is 4 and the 35 th
percentile is 2. Therefore, any percentile between 35 and 75 must be a whole
number between 2 and 4. The median (i.e., the 50 th percentile) is between the 35 th
and the 75 th percentile and the only whole number between 2 and 4 is 3. Therefore,
the median is 3. The two statements together are sufficient to answer the question.
Answer: C
