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

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.
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Solution:
Look at the diagram:

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.
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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
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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
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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

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