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Of the z students at a certain college, x are studying

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Of the z students at a certain college, x are studying  [#permalink]

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New post Updated on: 06 Oct 2013, 09:00
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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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Originally posted by Yurik79 on 09 Feb 2006, 07:20.
Last edited by Bunuel on 06 Oct 2013, 09:00, edited 1 time in total.
Edited the question and added the OA.
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New post 09 Feb 2006, 07:36
2
Should be A....

Group+Group+Neither-Both=Total

x+y+(unknown)-w=z
(unknown)=z+w-x-y
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New post 09 Feb 2006, 07:56
Hard to answer b/c there are no parenthesis in the answer choices. Looks to as they are written, none of the answer choices are correct. I would say that the answer should be :
z-(w-(x+y))
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Re: Of the z students at a certain college, x are studying  [#permalink]

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New post 06 Oct 2013, 06:50
Yurik79 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


OA please? I got A.
Used smart numbers but not sure if it is the best approach here
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Re: Of the z students at a certain college, x are studying  [#permalink]

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New post 06 Oct 2013, 09:01
jlgdr wrote:
Yurik79 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


OA please? I got A.
Used smart numbers but not sure if it is the best approach here


{Total} = {French} + {German} - {Both} + {Neither}

z = x + y - w + {Neither}

{Neither} = z + w - x - y.

Answer: A.
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New post 07 Oct 2013, 23:41
kook44 wrote:
Hard to answer b/c there are no parenthesis in the answer choices. Looks to as they are written, none of the answer choices are correct. I would say that the answer should be :
z-(w-(x+y))

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

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New post 13 Feb 2015, 13:26
Hi All,

It looks like most of the posters in this thread recognized that this question is a variation on an Overlapping Sets question. It can be solved in a variety of ways (mostly algebraic), but there is an opportunity to TEST VALUES. You just have to be careful with your notes:

We're given 4 variables to work with:
Z = Total number of students
X = Total who study French
Y = Total who study German
W = Total who study French AND German

We're asked for the number that study NEITHER French NOR German.

Let's TEST VALUES. I'm going to keep things simple, but the note-taking here is crucial to getting the correct answer.

IF...
1 studies just French
1 studies just German
1 studies BOTH French and German

We have
X = 2 (since 1 speaks just french and another speaks both)
Y = 2 (since 1 speaks just German and another speaks both
W = 1

Now we can set the "neither" group to any positive value we want; I'm going to choose a larger number to set it apart from the others.
Neither = 5

That makes the TOTAL number of students: 1 + 1 + 1 + 5 = 8
Z = 8

So, using the values....
X = 2
Y = 2
W = 1
Z = 8

We're looking for an answer that equals 5.

Answer A: 8+1-2-2 = 5 This IS a match
Answer B: 8-1-2-2 = 3 This is NOT a match
Answer C: 8-1-2+2 = 7 This is NOT a match
Answer D: 1+2+2-5 = 0 This is NOT a match
Answer E: 1-2-2-5 = -8 This is NOT a match

Final Answer:

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

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New post 20 Nov 2015, 01:30
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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New post 20 Nov 2015, 02:49
Total = (French) + (German) - (French n German) + (Neither)
=> Neither = z + w - x - y

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

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

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

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New post 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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Re: Of the z students at a certain college, x are studying  [#permalink]

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New post 22 Oct 2016, 06:39
Yurik79 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

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

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New post 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:
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

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