What is the median duration of a client engagement, which are billed

Official Explanation

We are looking for a median here, so we are talking about a set--in this case, a bunch of client engagements, each with a length. Typically, we'd find the median by knowing how many engagements there are and how long they are, or at least which length ranks in the middle. On to the statements.

Statement (1) tells us about the longest 30 percent of engagements. We could imagine a Case I: the shorter 70 percent of engagements are all 1 week, in which case the median is 1, or a Case II: they are all 3 weeks, in which case the median is 3. So we don't have a conclusive answer. Statement (1) is insufficient.

Statement (2) tells us about the bottom 40 of engagements. Using similar logic as above, Statement (2) is insufficient.

When we combine the statements, we have 30% at 4+ weeks, 40% at 2 or fewer weeks, and that leaves a middle 30%. This middle 30% must bill at 3 weeks, since the projects are billed to the nearest week. The median falls in this middle range, so the median project duration must be 3 weeks. The statements together are sufficient.

The correct answer is (C).