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In a sample of the front facing of 200 houses in a suburban neighborho

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In a sample of the front facing of 200 houses in a suburban neighborho  [#permalink]

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New post 28 Aug 2017, 23:41
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In a sample of the front facing of 200 houses in a suburban neighborhood, 25 of them were faced completely in aluminum siding. The remaining homes used either stucco, brick, or a brick/stucco combination. 40 of them used only stucco, but for every 4 households that was faced entirely with brick, 1 households used a combination of brick/stucco. How many homes had only brick facings?

A. 27
B. 45
C. 108
D. 128
E. 135

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Re: In a sample of the front facing of 200 houses in a suburban neighborho  [#permalink]

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New post 29 Aug 2017, 00:40
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We have a total of 200 homes, of which 25 were faced completely in aluminium
We have 175 homes which use Stucco, Brick or a combination or both!

P(Total) = P(Only Stucco) + P(Only Brick) + P(Both)

We know that P(Total) = 175
Also, given in the question stem, P(Only Stucco) = 40
We know that ratio of Only Brick to both is 4:1.
So for every 4x homes that use only Brick, x homes will use both

Substituting these values,
175 = 40 + 4x + x
5x = 135 or x = 27

Theefore, the number of home using only Brick is 4x = 108(Option C)
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Re: In a sample of the front facing of 200 houses in a suburban neighborho  [#permalink]

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New post 29 Aug 2017, 01:14
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Ratio of B : B-S = 4:1 Let B-S = x

25 + 40 + 4x + x = 200

65 + 5x = 200

5x = 135

x = 27

B = 4 x 27

B = 108

Hence, C

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Re: In a sample of the front facing of 200 houses in a suburban neighborho  [#permalink]

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New post 04 Sep 2017, 09:56
Total= 200
Aluminium= 25
Remaining= 175

175= 40+ B +B/4
b= 108
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Re: In a sample of the front facing of 200 houses in a suburban neighborho  [#permalink]

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New post 04 Sep 2017, 10:30
Bunuel wrote:
In a sample of the front facing of 200 houses in a suburban neighborhood, 25 of them were faced completely in aluminum siding. The remaining homes used either stucco, brick, or a brick/stucco combination. 40 of them used only stucco, but for every 4 households that was faced entirely with brick, 1 households used a combination of brick/stucco. How many homes had only brick facings?

A. 27
B. 45
C. 108
D. 128
E. 135



Hi..

Ofcourse the method is as mentioned in above posts.

But a small observation can get you close to answer in no time.
The number is 4*something, so a MULTIPLE of 4..
Only C and D are left.
Ratio is 4:1, so if 4 parts are 108,.... (4+1) parts will be 108*5/4=135..
Total 135+25+40=200.... Fits in
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Re: In a sample of the front facing of 200 houses in a suburban neighborho  [#permalink]

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New post 14 Dec 2019, 11:17
Hi Bunuel,
Small clarification needed please. Are we ignoring the subtraction for "Both" part per the Venn formula because the count of houses to be built would obviously add?
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Re: In a sample of the front facing of 200 houses in a suburban neighborho   [#permalink] 14 Dec 2019, 11:17
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