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# Of the z students at a certain college, x are studying French and y

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Math Expert
Joined: 02 Sep 2009
Posts: 46305
Of the z students at a certain college, x are studying French and y [#permalink]

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20 Nov 2015, 01:30
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:57) correct 13% (01:32) wrong based on 98 sessions

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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

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

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20 Nov 2015, 02:49
Total = (French) + (German) - (French n German) + (Neither)
=> Neither = z + w - x - y

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

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20 Nov 2015, 03:16
total students =z
studying french =x
Studying german=y
both=w
z=x+y-w+neither
neither=z-x-y+w
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Re: Of the z students at a certain college, x are studying French and y [#permalink]

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20 Nov 2015, 12:04
Z(total) = X(french)+Y(German)-W(Both)+N(Neither)
N = z+w-x-y

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

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22 Nov 2015, 03:00
Total Students = French Students + German Students - (French and German) students + Neither
Z = X +Y -W + Neither
Neither = z + w - x - y

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

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08 Jan 2018, 15:35
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Top Contributor
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 - 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

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Of the z students at a certain college, x are studying French and y   [#permalink] 08 Jan 2018, 15:35
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