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Of the 80 houses in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?
  • a)
    10
  • b)
    15
  • c)
    20
  • d)
    25
  • e)
    30
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Of the 80 houses in a development, 50 have a two-car garage, 40 have a...
Here, we have two categories: (a) with or without two-car garage, and (b) with or without an in-the-ground pool.  Houses can be members of either, both, or neither category.  We will use a two circle Venn diagram:

We know the total of the group is 80 —– A + B + C + D = 80.  We know the green circle, two-car garages, has 50 members, so A + B = 50.  We know the blue circle, in-the-ground pool, has 40 members, so B + C = 40.  We also know the crucial overlap region, B = 35.  If B = 35, in the green circle, we can deduce that A = 15, and in the blue circle, we can deduce that C = 5.  Then
A + B + C + D = 15 + 35 + 5 + D = 80
D = 25
Thus, 25 houses in this development have neither a two-car garage nor an in-the-ground swimming pool. 
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