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Of the z students at a certain college, x are studying French and y ar
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06 May 2021, 05:14
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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 ar
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06 May 2021, 05:47
1
Carcass 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)