210 college students were asked in a survey if

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210 college students were asked in a survey if [#permalink]

22 Sep 2011, 19:51

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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

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Re: Set Theory [#permalink]

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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Re: Set Theory [#permalink]

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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Re: Set Theory [#permalink]

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:

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Re: Set Theory [#permalink]

24 Sep 2011, 20:15

Yup, got it. Thanks.
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Re: Set Theory [#permalink] 24 Sep 2011, 20:15

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210 college students were asked in a survey if

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210 college students were asked in a survey if

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