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Of the 500 business people surveyed, 78 percent said that

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Of the 500 business people surveyed, 78 percent said that [#permalink] New post 01 Dec 2012, 01:11
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Question Stats:

96% (02:11) correct 4% (01:50) wrong based on 62 sessions
Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home, 65 percent said that they use them in hotels, and 52 percent said that they use them both at home and in hotels. How many of the business people surveyed said that they do not use their laptop computers either at home or in hotels?

A. 45
B. 55
C. 65
D. 95
E. 130


[Reveal] Spoiler:
Can somebody give the formula for this overlapping set problem?
P(AUB) = P(A)+P(B)-P(A intersection B)
I tried to use the domain matrix learnt from MGMAT. But somewhere I am going wrong, can someone help?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Oct 2013, 23:13, edited 1 time in total.
Added the OA.
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Re: Overlapping sets [#permalink] New post 01 Dec 2012, 05:05
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SreeViji wrote:
Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home, 65 percent said that they use them in hotels, and 52 percent said that they use them both at home and in hotels. How many of the business people surveyed said that they do not use their laptop computers either at home or in hotels?

A. 45
B. 55
C. 65
D. 95
E. 130

[Reveal] Spoiler:
A


Can somebody give the formula for this overlapping set problem?
P(AUB) = P(A)+P(B)-P(A intersection B)
I tried to use the domain matrix learnt from MGMAT. But somewhere I am going wrong, can someone help?

I guess you made a mathematical error. Personally, I prefer creating the matrix in percentages when the question is given in percentages. And finally multiply what I want with the total. However for illustration the matrix should be
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Re: Overlapping sets [#permalink] New post 02 Dec 2012, 12:22
No reason to use formulas or weird pictures for this problem. Just think about what each set is.

I took the totals:
390 people use their laptop at home [1]
325 people use their laptop in hotels [2]
260 people use their laptop both in hotels and at home [3]

Clearly if someone uses their laptop both in hotels and at home, they belong in both the previous two sets (1,2). By subtracting set 3 from the first two, we can determine the number of people that lie in set 1 or set 2 but not in set 3.

Gives us:
130 only use their laptop at home
65 only use their laptop in hotels
260 use their laptop in both

add them up, subtract from the total and you get 45.
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Re: Of the 500 business people surveyed, 78 percent said that [#permalink] New post 22 Oct 2013, 21:36
Refer Venn diagram below:
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Re: Of the 500 business people surveyed, 78 percent said that [#permalink] New post 23 Oct 2013, 14:40
I kept everything in percentage form since that is how the information was presented. I did not want to introduce calculations that could lead to an error.

I used the group formula:

Total = Group 1 + Group 2 - Both + Neither.

Using the formula above and the information we are given:

100% = 78% + 65% - 52% + Neither

100% = 91% + Neither or

Neither = 100% - 91% = 9%


The total here is 500 so we can multiply 9% with 500 to get the amount of business people who do no use their laptops at home or in hotels.

(9/100) * 500 = 45

All of the methods mentioned above work, but I hope someone finds this helpful too. We can never have too many ways to approach a problem.
Re: Of the 500 business people surveyed, 78 percent said that   [#permalink] 23 Oct 2013, 14:40
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