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Prblem Solving

This topic has 2 expert replies and 1 member reply
RiyaR Senior | Next Rank: 100 Posts Default Avatar
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Prblem Solving

Post 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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Post 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

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Jeffrey Miller Head of GMAT Instruction

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GMAT/MBA Expert

Post 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:


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
-------------------------------------
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: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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

Easy Problem Solving questions
- http://www.beatthegmat.com/the-aam-aadmi-party-t272242.html
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- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
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Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3[img]

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gmatcracker0123 Junior | Next Rank: 30 Posts Default Avatar
Joined
13 Apr 2014
Posted:
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Post 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 Smile

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