Q#20: The carshare dilemma

Suppose we have selected a group of people to take a survey. 35% of the group like Uber, 20% like both Lyft and Uber, and 25% like neither Lyft nor Uber. Given this information, what percentage of the sample likes Lyft?
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ANSWER

This question tests your understanding of basic statistics and can be reasoned out relatively easily, though it maybe difficult under pressure as there are a few traps

The total percent has to equal 100 and the only caveat is that we have to be careful in the amount of overlap between surveyors who like both and those that like just 1. The first step is rather simple we can freely subtract the 25% from the total percent and we are left with 75% in the remaining three options. Here it’s easiest to use a venn diagram to solve (see below). Logically, it stands to reason that if 20% like both than only 15% like exclusively Uber, therefore 40% of the surveyors like Lyft exclusively. Another more clever way to solve, is to realize that the information on who likes both is extraneous in this case and simply summing the other three conditions to 100 provides an answer of 40% as well.