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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] New post 09 Feb 2006, 06:20
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76% (01:00) correct 24% (01:03) wrong based on 108 sessions
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, 08:00, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 09 Feb 2006, 06:36
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Should be A....

Group+Group+Neither-Both=Total

x+y+(unknown)-w=z
(unknown)=z+w-x-y
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 [#permalink] New post 09 Feb 2006, 06:56
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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 [#permalink] New post 10 Feb 2006, 12:26
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] New post 06 Oct 2013, 05:50
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] New post 06 Oct 2013, 08:01
Expert's post
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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Re: [#permalink] New post 07 Oct 2013, 22:41
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] New post 13 Feb 2015, 09:16
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Re: Of the z students at a certain college, x are studying [#permalink] New post 13 Feb 2015, 12:26
Expert's post
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:
[Reveal] Spoiler:
A


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Re: Of the z students at a certain college, x are studying   [#permalink] 13 Feb 2015, 12:26
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