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# 210 college students were asked in a survey if they preferre

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Manager
Joined: 10 Jan 2010
Posts: 117
GPA: 4
WE: Programming (Computer Software)
210 college students were asked in a survey if they preferre [#permalink]

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22 Sep 2011, 19:51
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Question Stats:

61% (02:18) correct 39% (01:15) wrong based on 114 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 students 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:
Attachment:

1.jpg [ 70.42 KiB | Viewed 2748 times ]

OPEN DISCUSSION OF THIS QUESTION IS HERE: 210-college-students-were-asked-in-a-survey-if-they-127387.html
[Reveal] Spoiler: OA

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Manager
Joined: 20 Aug 2011
Posts: 146
Re: Set Theory [#permalink]

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22 Sep 2011, 22:52
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According to the question out of 210 students, 90 don't have a preference.
Hence, out of these 210 students 120 students have a preference.
Out of these 120 students 60 prefer Mac to Windows.
1/3 of 60 i.e. 20 students equally prefer both
So, the remaining students must prefer Windows to Mac
120-(60+20)
i.e. 40 students prefer Windows to Mac.
Manager
Joined: 10 Jan 2010
Posts: 117
GPA: 4
WE: Programming (Computer Software)
Re: Set Theory [#permalink]

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24 Sep 2011, 15:52
Thanks for the reply.
I was bit confused with this question during the exam. Does the "60" refer Only Mac or both Windows and Mac?.
I messed it up during the exam as given below:
Can you please help me in pointing out what went wrong?
210=x+60-20 +90
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Director
Joined: 01 Feb 2011
Posts: 755
Re: Set Theory [#permalink]

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24 Sep 2011, 17:26
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60 there refers to only mac, so you shouldn't be subtracting 20 there.

number of people who preferred mac to windows ( in other words they only prefer mac ) = mac only = 60

1/3 as many who preferred mac to windows , preferred both equally = mac & windows = (1/3)*60 = 20

let number of people who prefer windows to mac = windows only = x

also given number of people who prefer nothing = 90

=> total = mac only + windows only + mac & windows + neither

210 = 60 + x + 20 + 90

=> x = 40

Answer is B.

maheshsrini wrote:
Thanks for the reply.
I was bit confused with this question during the exam. Does the "60" refer Only Mac or both Windows and Mac?.
I messed it up during the exam as given below:
Can you please help me in pointing out what went wrong?
210=x+60-20 +90
Manager
Joined: 10 Jan 2010
Posts: 117
GPA: 4
WE: Programming (Computer Software)
Re: Set Theory [#permalink]

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24 Sep 2011, 20:15
Yup, got it. Thanks.
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Intern
Joined: 30 Jan 2014
Posts: 4
Re: 210 college students were asked in a survey if [#permalink]

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05 Mar 2014, 13:23
Can someone show the solution by using a matrix box? Thanks in advance!
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Joined: 20 Dec 2013
Posts: 189
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Re: 210 college students were asked in a survey if [#permalink]

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05 Mar 2014, 18:18
Improper usage of preferred makes this question confusing.. Also, don't the people who 'prefer both' technically have no preference??
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Intern
Joined: 30 Jul 2013
Posts: 3
Re: 210 college students were asked in a survey if [#permalink]

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05 Mar 2014, 19:33
Matrix solution
Win No Win Total
Mac 20 60 80
No Mac 40 90 130
Total 60 150 210

Thoughts?
Intern
Joined: 30 Jul 2013
Posts: 3
Re: 210 college students were asked in a survey if [#permalink]

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05 Mar 2014, 19:36
Why use the formula:
total = mac only + windows only + mac & windows + neither

instead of
total = mac only + windows only - mac & windows + neither
Moderator
Joined: 02 Jul 2012
Posts: 1223
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: 210 college students were asked in a survey if [#permalink]

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05 Mar 2014, 22:46
Matrix is the best way to go.
Red = Given in question
Yellow = Derived
Green = Answer
Attachments

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Intern
Joined: 03 Aug 2012
Posts: 20
Location: United States (OR)
Concentration: Finance, International Business
GPA: 3.53
WE: Analyst (Entertainment and Sports)
Re: 210 college students were asked in a survey if [#permalink]

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05 Mar 2014, 23:36
How my brain processed this one...

Step 1 --> Identify preferences.

Of 210 students, 60 prefer Mac, (1/3) of those 60 prefer both, 90 prefer neither, an unknown amount prefer Windows.

Step 2 --> Convert to equation.

210 = 60 + ((1/3)*60) + 90 + X

Step 3 --> Isolate X.

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

Answer is B.
Math Expert
Joined: 02 Sep 2009
Posts: 39575
Re: 210 college students were asked in a survey if [#permalink]

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06 Mar 2014, 00:38
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 students 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

Refer to the diagram below:

"One third as many of the students who preferred Mac to Windows, equally preferred both brands" means that 1/3*60=20 equally preferred both brands;

So, we have that 60+20+x+90=210 --> x=40.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: 210-college-students-were-asked-in-a-survey-if-they-127387.html

Theory on Overlapping Sets:
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DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

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Re: 210 college students were asked in a survey if   [#permalink] 06 Mar 2014, 00:38
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# 210 college students were asked in a survey if they preferre

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