Problem Solving

Q30:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
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I would say the answer is C. Of course this is not "official", but I'm pretty sure I'm correct.

If you order all the projects by number of employees assigned, the "median" means you want to know the number of employees assigned for the project at the 50th percentile. Makes sense?

With statement (1), you have the top 25% covered, but you don't know anything about the other 75%. For example, 75% of the projects could have 1 employee assigned, or 2, or 3, or a mixture, so you don't know about the project at 50%.

Similarly, with statement (2), you have the bottom 35% covered, but you don't know about the other 65%. All other projects might have 3 employees assigned, or 5, or 30... so at 50%, it could be any number greater than 2.

Two statements taken together, you have both the top 25% and bottom 35% covered. From this, the following statement is necessarily true:

40% of the projects have more than 2 but less than 4 number of employees assigned to each project.

The median falls within this middle 40% (ie, above 35% but below the top 25%). Notice that only one integer falls between 4 and 2, and that is 3. So, 40% of the projects have 3 people assigned to each project, and 3 is the median you're looking for.