To receive a driver license, sixteen year-olds at Culliver High School have to pass both a written and a practical driving test. Everyone has to take the tests, and no one failed both tests. If 30% of the 16 year-olds who passed the written test did not pass the practical, how many sixteen year-olds at Culliver High School received their driver license?

(1) There are 188 sixteen year-olds at Culliver High School.

(2) 20% of the sixteen year-olds who passed the practical test failed the written test.

Can someone please solve this question using a method different from the double matrix method(I am not comfortable with double matrix!!). Thanks!

Try solving this problem with set theory. Let W be the set of the students who passed the written test and P be the set of those who passed the practical. The
value we need to find is (W ∩ P) i.e. those who passed both the tests

The problem statement tells us that 30% of the 16 year-olds who passed the written test did not pass the practical, so in set notation we can write

W - P = 0.3W (note that this is in set notation, not arithmetic notation)
and (W ∩ P) = 0.7W [as (W ∩ P) = W - (W - P)]

Option 1 gives us

W + P -(W ∩ P) = 188 [since the problem statement tells us that everyone took the tests and no one failed both]

By itself this is insufficient

Option 2 gives us

P - W = 0.2P , and as earlier we get

(W ∩ P) = 0.8P [(W ∩ P) = P - (P - W)]

Combining this with the info in the problem statement we have

(W ∩ P) = 0.7W and 0.7W = 0.8P or P = 7/8W

this can help us calculate the percentage of students who received their driver licence but not the actual number, hence insufficient

Combining the two we have

W + P - (W ∩ P) = 188
(W ∩ P) = 0.7W
P = 7/8W

Plugging values of P and (W ∩ P) in the main equation we get W = 160 and (W ∩ P) = 102 Hence the answer is C

It is easier to explain this kind of problem with venn diagrams rather than using the set notation (plus that is a much faster way to solve also)so I have attached a diagram image for this problem.

http://imageshack.us/photo/my-images/847/driverc.png

I’ll tell you what, the best thing I can do for you is to force you to confront your fear of the double-set matrix, because it is the single most powerful tool you will find for dealing with overlapping sets problems. So I’ll make you this deal: figure out how to use a double-set matrix on this one, convince me you understand it (or ask questions if you get stuck), and I’ll show you a different way to do the problem..

_________________
Tim Sanders
Manhattan GMAT Instructor