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

Question

Of the 80 house 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

Kudos for a correct solution.

A. 10
B. 15
C. 20
D. 25
E. 30

Kudos for a correct  solution .

masoomdon · Answer

IMO(D)

Let 2 garage houses be set G, swimming pools be set S
n=intersection and u=union
G=50,S=40,GnS=35
houses having either one or both = G+S-GnS = 50+40-35=55
houses having none = 80-55 = 25

Aksh19 · Answer

Using double matrix method.

aj13783 · Answer

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

pacifist85 · Answer

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

Please, check the image.

PareshGmat · Answer

Answer = D = 25

Neither Car nor Garage

= Total - Garage - (Swim - Common)

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

Bunuel · Answer

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: set_img3.png 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.

Chikoo · Answer

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

Sent from my SM-A800F using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

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

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