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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]

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22 Sep 2011, 19:51
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Question Stats:

62% (02:21) correct 38% (01:20) wrong based on 107 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:
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1.jpg [ 70.42 KiB | Viewed 2437 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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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.
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24 Sep 2011, 15:52
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:
210=x+60-20 +90
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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

maheshsrini wrote:
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:
210=x+60-20 +90
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24 Sep 2011, 20:15
Yup, got it. Thanks.
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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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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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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?
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05 Mar 2014, 19:36
Why use the formula:
total = mac only + windows only + mac & windows + neither

total = mac only + windows only - mac & windows + neither
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05 Mar 2014, 22:46
Matrix is the best way to go.
Red = Given in question
Yellow = Derived
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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

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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.

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

Theory on Overlapping Sets:
how-to-draw-a-venn-diagram-for-problems-98036.html

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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