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

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

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09 Feb 2006, 07:20
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Question Stats:

72% (02:04) correct 28% (00:59) wrong based on 191 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
[Reveal] Spoiler: OA

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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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09 Feb 2006, 07:36
1
KUDOS
Should be A....

Group+Group+Neither-Both=Total

x+y+(unknown)-w=z
(unknown)=z+w-x-y
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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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10 Feb 2006, 13:26
A
only french X-w
only german Y-w
French and german x-w+y-w+w ...... 1
Not studying French and Germand Z-(1)
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Re: Of the z students at a certain college, x are studying [#permalink]

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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

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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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

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.

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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))

Attachments

File comment: i personally feel, this is the best way to solve it.
grid.docx [11.88 KiB]

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

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13 Feb 2015, 10:16
Hello from the GMAT Club BumpBot!

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

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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

[Reveal] Spoiler:
A

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

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20 Oct 2016, 13:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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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

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Re: Of the z students at a certain college, x are studying   [#permalink] 22 Oct 2016, 06:39
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