Bunuel 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 - wFinally, 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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