169. 30% o the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

(a) 60
(b) 80
(c) 100
(d) 120
(e) 140

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I had serious difficulty answering this question because I did not make the assumption that every member of the club had taken the test. In fact, there is no information suggesting otherwise.

Because of this, I had identified six distinct groups:
a: taken the test AND passed AND NOT taken the prep course
b: taken the test AND NOT passed AND NOT taken the prep course
c: taken the test AND passed AND taken the prep course
d: taken the test AND NOT passed AND taken the prep course
e: NOT taken the test AND taken the prep course
f: NOT taken the test AND NOT taken the prep course

The answer for this question assumes that everyone has taken the test, which provides simply four variables to work with. I burned several minutes trying to solve this by creating quadratic equations so that I could generate enough equations to solve the problem, but it was clear there was not enough information.

How does MGMAT suggest I approach these dilemmas should they arise on test day?

Joseph, In this problem it matters not whether all members of the club have taken the test. If 30% of the members have passed the test, the remaining members (70%) have not passed the test, whether they have taken it or not. In other words, passed/not passed is an either/or characteristic; there is no other possibility. The problem would have had to explicitly break this "not passed" into subcategories for you to derive a more detailed interpretation.

The same is true of taken/not taken the course: it too is an either/or characteristic. Thus, the 12 + 30 = 70%(Total). Total = 60 members.

-dan

ps - remember, ALL problems on the GMAT must be solvable within approximately 2 minutes. If you are on a path that will take significantly more than two minutes, reevaluate your understanding of the problem and/or your strategic approach.

Hope that helps!

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