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210 college students were asked in a survey if they preferre

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210 college students were asked in a survey if they preferre [#permalink] New post 22 Sep 2011, 18:51
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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:
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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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Re: Set Theory [#permalink] New post 22 Sep 2011, 21:52
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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.
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Re: Set Theory [#permalink] New post 24 Sep 2011, 14:52
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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Re: Set Theory [#permalink] New post 24 Sep 2011, 16:26
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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
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Re: Set Theory [#permalink] New post 24 Sep 2011, 19:15
Yup, got it. Thanks.
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 12:23
Can someone show the solution by using a matrix box? Thanks in advance!
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 17:18
Improper usage of preferred makes this question confusing.. Also, don't the people who 'prefer both' technically have no preference??
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 18:33
Matrix solution
Win No Win Total
Mac 20 60 80
No Mac 40 90 130
Total 60 150 210

Thoughts?
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 18:36
Why use the formula:
total = mac only + windows only + mac & windows + neither

instead of
total = mac only + windows only - mac & windows + neither
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 21:46
Matrix is the best way to go.
Red = Given in question
Yellow = Derived
Green = Answer
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 22:36
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. :-D
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Re: 210 college students were asked in a survey if [#permalink] New post 05 Mar 2014, 23:38
Expert's post
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:
Image
"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

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Re: 210 college students were asked in a survey if   [#permalink] 05 Mar 2014, 23:38
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