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Prblem Solving

by RiyaR » Tue Sep 16, 2014 9:59 am
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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by gmatcracker0123 » Tue Sep 16, 2014 10:36 am
This question is from set theory,

The general rule states that

Total = Type A + Type B - Both Type A and B + None

Applying the same to the mentioned question

Total = Z
Type A = Students studying french = X
Type B = Students studying german = Y
Both = Students studying french and german = W
None = Students studying neither = N

Z = X + Y - W + N

Therefore N = Z + W -X -Y

Ans : A

Experts , correct me if I am wrong :)
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by Brent@GMATPrepNow » Thu Sep 18, 2014 11:08 am
RiyaR 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:
Image

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.
Image

w are studying both French and German
When we add this information to our diagram, we get the following:
Image

When we examine the TOP 2 BOXES, we see that they add to x. So, the TOP-RIGHT box must be x - w
Image

Finally, we know that the two HIGHLIGHTED boxes below must add to z - y.
Image

So, the BOTTOM-RIGHT box must equal (z - y) - (x - w)
Image

(z - y) - (x - w) = z - y - x + w

Answer: A
-------------------------------------
NOTE: This type of question is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

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by Jeff@TargetTestPrep » Mon Jan 08, 2018 11:07 am
RiyaR 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
Since we have an overlapping set problem, we can use the following formula:

number of students studying French + number of students studying German + number of students studying neither subject - number of students studying both subjects = total number of students

We are given that:

number of students studying French = x,

number of students studying German = y,

number of students studying both subjects = w, and

total number of students = z.

If we let number of students studying neither subject = n, we have:

x + y + n - w = z

n = z + w - x - y

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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