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

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

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New post 03 Mar 2015, 06:05
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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.

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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 03 Mar 2015, 09:44
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1
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
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Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 03 Mar 2015, 10:49
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Using double matrix method.
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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 03 Mar 2015, 23:27
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Bunuel wrote:
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.


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
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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 04 Mar 2015, 02:37
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I also used the matrix method, but I will just show the venn diagram method now.

Please, check the image.
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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 04 Mar 2015, 21:38
Answer = D = 25

Neither Car nor Garage

= Total - Garage - (Swim - Common)

= 80 - 50 - (40-35) = 80-55 = 25
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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 08 Mar 2015, 13:36
Bunuel wrote:
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.


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:
Attachment:
set_img3.png
set_img3.png [ 15.07 KiB | Viewed 8338 times ]


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.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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simple sets problem
80-(50+40-35)=25
Bunuel wrote:
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.



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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an  [#permalink]

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New post 03 Oct 2018, 16:52
Bunuel wrote:
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


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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Re: Of the 80 house in a development, 50 have a two-car garage, 40 have an &nbs [#permalink] 03 Oct 2018, 16:52
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