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Of the 150 houses in a certain development, 60 percent have
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14 May 2020, 09:45
14 May 2020, 09:45
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Question Stats:
51% (02:59) correct
48% (02:34) wrong based on 191 sessions
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Of the 150 houses in a certain development, 60 percent have air-conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool. If 5 of the houses have all three of these amenities and 5 have none of them, how many of the houses have exactly two of these amenities?
(A) 10
(B) 45
(C) 50
(D) 55
(E) 65
(A) 10
(B) 45
(C) 50
(D) 55
(E) 65
Re: Of the 150 houses in a certain development, 60 percent have
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19 May 2020, 05:23
19 May 2020, 05:23
7
Expert Reply
Total houses = number with air conditioning + number with sunporch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things
150 = 0.6(150) + 0.5(150) + 0.3(150) - D - 2(5) + 5
150 = 90 + 75 + 45 - D - 10 + 5
150 = 205 - D
D = 55
150 = 0.6(150) + 0.5(150) + 0.3(150) - D - 2(5) + 5
150 = 90 + 75 + 45 - D - 10 + 5
150 = 205 - D
D = 55
Re: Of the 150 houses in a certain development, 60 percent have
[#permalink]
14 May 2020, 12:59
14 May 2020, 12:59
10
Of the 150 houses,
60 percent have air-conditioning: 90 houses
50 percent have a sunporch: 75 houses
30 percent have a swimming pool: 45 houses
5 of the houses have all three of these amenities and 5 have none of them
* All details can be put in the diagram as shown
If 5 of the houses have all three of these amenities and 5 have none of them, remaining houses are 140 which either have any one of them or two of them
as per the diagram, we have 85+70+40 = 195, if all have only one out of three
No of houses have exactly two of these = 195-140 = 55
P.S. may not be an explicit explanation
60 percent have air-conditioning: 90 houses
50 percent have a sunporch: 75 houses
30 percent have a swimming pool: 45 houses
5 of the houses have all three of these amenities and 5 have none of them
* All details can be put in the diagram as shown
If 5 of the houses have all three of these amenities and 5 have none of them, remaining houses are 140 which either have any one of them or two of them
as per the diagram, we have 85+70+40 = 195, if all have only one out of three
No of houses have exactly two of these = 195-140 = 55
P.S. may not be an explicit explanation
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