Of the 80 house in a development, 50 have a two-car garage, 40 have an

Houses which neither have 2 car garage and nor a swimming pool = 80 - houses with car garage only - houses with swimming pool only - houses with both

= 80 - (50-35) - (40-35) - 35

= 25

Option D

I also used the matrix method, but I will just show the venn diagram method now.

Please, check the image.

Answer = D = 25

Neither Car nor Garage

= Total - Garage - (Swim - Common)

= 80 - 50 - (40-35) = 80-55 = 25

MAGOOSH OFFICIAL SOLUTION:

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.

Answer = D.

simple sets problem
80-(50+40-35)=25



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We can create the equation:

Total = Garage + Pool - Both + Neither

80 = 50 + 40 - 35 + n

80 = 55 + n

25 = n

Answer: D

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