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Of the z students at a certain college, x are studying
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Updated on: 06 Oct 2013, 09:00

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Question Stats:

78% (01:25) correct 22% (01:29) wrong based on 238 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

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))

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

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

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

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

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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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
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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

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

Answer: A
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Of the z students at a certain college, x are studying French and y
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08 Jan 2018, 15:35

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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:

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)