Last year, 36 houses in a certain development had roof repairs and 48

Question

Last year, 36 houses in a certain development had roof repairs and 48 houses were repainted. If 20 houses in the development had roof repairs but were not repainted last year, how many houses were repainted but did not have roof repairs?

(A) 12
(B) 16
(C) 20
(D) 28
(E) 32

(A) 12
(B) 16
(C) 20
(D) 28
(E) 32

IanStewart · Answer

I'd draw a Venn diagram here, but in words: if 20 had roof repairs but were not repainted, then the rest with roof repairs, 16 houses, both had roof repairs and were repainted. Taking those 16 away from the 48 that were repainted, we find that 32 houses were repainted but did not have roof repairs.

GMATWhizTeam · Answer

Solution:
Look at the diagram:
 https://www.dropbox.com/s/84dc9v9cdi7ja1z/new%20drop%20box%20pics.jpg?dl=1 
Here a is the number of houses which only had their roof repaired, b is the number of houses which were only repainted, and c is the number of houses which had their roof repaired as well as repainted.
We need to find the value of b.
 • a = 20
• a + c = 36
 o c = 36 – 20 = 16 
• b + c = 48
 o b + 16 = 48 
o b = 48 – 16 = 32  
Hence the correct answer is Option E.

sujoykrdatta · Answer

Number of houses that had roof repairs = 36
Some of these could have been repainted as well (while the others only had roof repairs)

Number of houses that had roof repairs but were not repainted (i.e. only had roof repairs) = 20

Thus, number of houses that had roof repairs and were also repainted 
= (Number of houses that had roof repairs) - (Number of houses that had roof repairs but were not repainted)
= 36 - 20 = 16

Number of houses that were repainted = 48
Some of these could have had roof repairs as well (while the others had only been repainted)

Thus, number of houses that were repainted but did not have roof repairs
= (Number of houses that were repainted) - (Number of houses that had roof repairs and were also repainted)
= 48 - 16
 = 32

Answer E

ScottTargetTestPrep · Answer

We can create the equation:

36 - both = 20

both = 16

Thus, the number of houses that were repainted only was 48 - 16 = 32.

Answer: E

Nipungupta9081 · Answer

Answer E

I solved this using a double matrix method.
 
 Might help anyone who's trying to solve it by the same approach.

Here's how i did it. Hope this helps

bumpbot · Answer

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Last year, 36 houses in a certain development had roof repairs and 48

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Last year, 36 houses in a certain development had roof repairs and 48

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