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Of the 150 houses in a certain development, 60 percent have

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Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

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New post 03 Oct 2018, 09:20
ScottTargetTestPrep wrote:
ganand wrote:
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


We can create the following equation:

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

Answer: D


Dear Scott

Thanks for a detailed response, I always like your responses.

I need your help though, if you could please advice, why are we using 2(5) in the equation. I understand 5 is for people who are doing all three activities but multiplication by 2?

Frankly, I have made similar error in other question as well, not having understood the secret of multiplication by 2?

Thank You
Abhinav
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Re: Of the 150 houses in a certain development, 60 percent have  [#permalink]

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New post 04 Oct 2018, 18:27
1
proabhinav wrote:
ScottTargetTestPrep wrote:
ganand wrote:
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


We can create the following equation:

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

Answer: D


Dear Scott

Thanks for a detailed response, I always like your responses.

I need your help though, if you could please advice, why are we using 2(5) in the equation. I understand 5 is for people who are doing all three activities but multiplication by 2?

Frankly, I have made similar error in other question as well, not having understood the secret of multiplication by 2?

Thank You
Abhinav



Notice that in a 3-circle Venn diagram, when we add each individual circle, we include the “triple overlap” three times since each circle has the “triple overlap.” However, we only can count it once, so we have to subtract 2 times whatever number in the “triple overlap.”
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Re: Of the 150 houses in a certain development, 60 percent have &nbs [#permalink] 04 Oct 2018, 18:27

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