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# 210 college students were asked in a survey if they preferred windows

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Intern
Joined: 29 Dec 2010
Posts: 32
210 college students were asked in a survey if they preferred windows [#permalink]

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13 Mar 2011, 18:41
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:16) correct 43% (01:17) wrong based on 110 sessions

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210 college students were asked in a survey if they preferred windows or mac brand computers. 60 students claimed that they preferred mac to windows brand computers. One third as many of the students who preferred mac to windows, equally preferred both brands. 90 of the studenys had no preference. how many of the students in the survey preferred windows to mac brand computers?

A. 25
B. 40
C. 50
D. 60
E. 75

[Reveal] Spoiler:
this is what I did.. I simple used the group formula

210=60+x-20+90
60= number of students who preferred windows
-20= both...
90= neither...

with that formula I get 80 students that does not appear in the answers...

regards
[Reveal] Spoiler: OA
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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Joined: 03 Feb 2011
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Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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13 Mar 2011, 20:30
Only Mac + Only Windows + Both + Neither = 210

Both = 1/3 * Only Mac = 1/3 * 60 = 20
60 + x + 20 + 90 = 210
x = 40
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1935
Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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14 Mar 2011, 00:34
1
KUDOS
gmat1220's solution would be correct if you read the question like this;

210 college students were asked in a survey if they preferred windows or mac brand computers. 60 students claimed that they preferred ONLY mac to windows brand computers. One thierd as many of the students who preferred mac to windows, equally preferred both brands. 90 of the studenys had no preference. how many of the students in the survey preferred ONLY windows to mac brand computers?

60+20+x+90=210
x=40
***********************

I believe there is some ambiguity in the question.
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Intern
Joined: 06 Feb 2011
Posts: 7
Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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14 Mar 2011, 18:56
fluke wrote:
gmat1220's solution would be correct if you read the question like this;

210 college students were asked in a survey if they preferred windows or mac brand computers. 60 students claimed that they preferred ONLY mac to windows brand computers. One thierd as many of the students who preferred mac to windows, equally preferred both brands. 90 of the studenys had no preference. how many of the students in the survey preferred ONLY windows to mac brand computers?

60+20+x+90=210
x=40
***********************

I believe there is some ambiguity in the question.

If you prefer one to the other, you can't also prefer both equally, so they are mutually exclusive. The answer of 40 should be correct.
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Joined: 16 Nov 2010
Posts: 1508
Location: United States (IN)
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Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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14 Mar 2011, 20:01
Students with at least 1 preference = 120

M-W -> 60 and common preference = 20

So Win to Mac = 120 - 60 - 20 = 40

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Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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14 Mar 2011, 21:29
3
KUDOS

So this is a Venn Diagram Question.

But first, I should say that this question is poorly worded. And even if the wording were a little better, you would never see a question like this on the actual GMAT.

Why? Because of politics!

OK, you're probably wondering what politics has to do with the GMAT.

Well, just think about it. By throwing a question like this, the GMAC guys presented an example of people slightly favoring Macs over PCs--and they did this in front of hundreds of thousands of GMAT test takers. That's good marketing for Macs--but not so good for PCs.

Do you think the PC guys would be happy about this? Can you imagine the letters of lawsuits or cease and desist letters that GMAC would receive if they made a question like this go live?

So you'd never see this specific type of example on the GMAT exam. It's fine to use sources outside of the OG and GMATPrep--but just keep in mind you probably won't see them on the actual exam.

Additionally, as a few of you have noted, the word "only" needs to be included where appropriate to make the distinction between the categories clearer.

Having said all of the above, the mental diagram you should be picturing inside of your head looks like the above picture.
The overlapped area in the middle is the 20 mentioned in the question.
The 60 presents ONLY Macs.
And the question is asking you how many are on the ONLY PC side.
You are given 210 students surveyed--of them 90 don't really have an opinion.

60 + 20 + 90 + x = 210
170 + x = 210
x=40

Make sure this diagram makes sense so you can apply it to future questions. Hope that helps!
Director
Joined: 01 Feb 2011
Posts: 696
Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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18 Mar 2011, 19:46
Agreed. Point made. no one can prefer two or more things equally.

khaynes3 wrote:
fluke wrote:
gmat1220's solution would be correct if you read the question like this;

210 college students were asked in a survey if they preferred windows or mac brand computers. 60 students claimed that they preferred ONLY mac to windows brand computers. One thierd as many of the students who preferred mac to windows, equally preferred both brands. 90 of the studenys had no preference. how many of the students in the survey preferred ONLY windows to mac brand computers?

60+20+x+90=210
x=40
***********************

I believe there is some ambiguity in the question.

If you prefer one to the other, you can't also prefer both equally, so they are mutually exclusive. The answer of 40 should be correct.
Manager
Joined: 11 Dec 2010
Posts: 115
WE: Consulting (Consulting)
Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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03 Apr 2011, 22:21
A good strategy for solving venn diagram questions is to name each different area with an alphabet (more useful in 3 set problems). No need to remember any venn diagram formula if you can use this technique.

60 prefer mac
20 prefer both (1/3*60)
Therefore 120-60-20 = 40 prefer Windows over mac... So option B - 40
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Re: 210 college students were asked in a survey if they preferred windows [#permalink]

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24 Oct 2017, 10:25
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Re: 210 college students were asked in a survey if they preferred windows   [#permalink] 24 Oct 2017, 10:25
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