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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

Re: Of the z students at a certain college, x are studying French and y [#permalink]

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20 Nov 2015, 01:49

Total = (French) + (German) - (French n German) + (Neither) => Neither = z + w - x - y

Answer A
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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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Re: Of the z students at a certain college, x are studying French and y
[#permalink]
08 Jan 2018, 14:35