RiyaR wrote:Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
(A) z + w - x - y
B) z - w - x - y
(C) z - w - x + y
(D) w + x + y - z
(E) w - x - y - z

We can also use the Double Matrix Method here. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of zstudents, and the two characteristics are:
- studying French or not studying French
- studying German or not studying German

So, we can set up our diagram as follows:


Note: I placed a star in the bottom right box to remind me that this is the value we are trying to determine.

Now, if there are z students ALTOGETHER, and x of them are studying French, then the number of students NOT studying French = z - x.
Similarly, if there are z students ALTOGETHER, and y of them are studying German, then the number of students NOT studying German = z - y.
So, we can add that information to the diagram.


w are studying both French and German
When we add this information to our diagram, we get the following:


When we examine the TOP 2 BOXES, we see that they add to x. So, the TOP-RIGHT box must be x - w


Finally, we know that the two HIGHLIGHTED boxes below must add to z - y.


So, the BOTTOM-RIGHT box must equal (z - y) - (x - w)


(z - y) - (x - w) = z - y - x + w

Answer: A
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NOTE: This type of question is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

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Difficult Data Sufficiency questions
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