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

RELATED VIDEO