Prblem Solving

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RiyaR: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Sat May 31, 2014 8:29 pmFollowed by: 2 members; Thanked: 1 times

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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Source: Beat The GMAT — Problem Solving | Tue Sep 16, 2014 9:59 am

gmatcracker0123: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Apr 13, 2014 6:13 am

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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:

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)

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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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