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

Question

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

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

pushpitkc · Accepted Answer

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)

ydmuley · Answer

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

Posted from my mobile device

Shiv2016 · Answer

Total= 200
Aluminium= 25
Remaining= 175

175= 40+ B +B/4
b= 108

chetan2u · Answer

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
Our ANSWER
C

Shanks1 · Answer

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?

Vep22 · Answer

Need calrity . why r we adding both

KarishmaB · Answer

Vep22 :

These are two different formulas. The first two terms in them are different. Observe:

Total = n(A) + n(B) - n(Both) + n(Neither)

Total = n(Only A) + n(Only B) + n(Both) + n(Neither)

You subtract 'Both' in the first case because it is included twice - once in A and then in B. 
A = 'Only A + Both' 
B = 'Only B + Both'

You add 'Both' in second case because it is not included in either of the first two terms. The first term is 'Only A' and the second term is 'Only B'.

Rebaz · Answer

The trick with question is to know that  faced entirely with brick.   means brick ONLY.

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

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