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Of the apartments in a certain building, 75 have a balcony, 80 have

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Bunuel
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Of the apartments in a certain building, 75 have a balcony, 80 have [#permalink] New post   09 Aug 2023, 10:00
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Of the apartments in a certain building, 75 have a balcony, 80 have a fireplace, and 30 have neither a balcony nor a fireplace. How many of the apartments in the building that have a balcony do not have a fireplace?

(1) There is a total of 150 apartments in the building.
(2) 35 of the apartments in the building that have a balcony also have a fireplace.
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Re: Of the apartments in a certain building, 75 have a balcony, 80 have [#permalink] New post   09 Aug 2023, 21:23
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Bunuel wrote:
Of the apartments in a certain building, 75 have a balcony, 80 have a fireplace, and 30 have neither a balcony nor a fireplace. How many of the apartments in the building that have a balcony do not have a fireplace?

(1) There is a total of 150 apartments in the building.
(2) 35 of the apartments in the building that have a balcony also have a fireplace.


We can plot the information over a 2*2 matrix as shown below.

Each of the statements provides us with sufficient information to obtain the required information.

Option D
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Re: Of the apartments in a certain building, 75 have a balcony, 80 have [#permalink] New post   31 Aug 2023, 07:37
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Bunuel wrote:
Of the apartments in a certain building, 75 have a balcony, 80 have a fireplace, and 30 have neither a balcony nor a fireplace. How many of the apartments in the building that have a balcony do not have a fireplace?

(1) There is a total of 150 apartments in the building.
(2) 35 of the apartments in the building that have a balcony also have a fireplace.


#Balcony = 75
#Fireplace = 80
#Neither = 30

We need to answer the question:

#Balcony & No-fireplace = ?

Statement One Alone:

=> There is a total of 150 apartments in the building.

Total = 150
#No-fireplace = Total - #Fireplace = 150 – 80 = 70
#Balcony & No-fireplace = #No-fireplace - #Neither = 70 – 30 = 40

Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> 35 of the apartments in the building that have a balcony also have a fireplace.

#Both = 35
#Balcony & No-fireplace = #Balcony - #Both = 75 – 35 = 40

Statement two is sufficient.

Answer: D
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Re: Of the apartments in a certain building, 75 have a balcony, 80 have [#permalink] New post   08 Apr 2024, 23:01
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Bunuel wrote:
Of the apartments in a certain building, 75 have a balcony, 80 have a fireplace, and 30 have neither a balcony nor a fireplace. How many of the apartments in the building that have a balcony do not have a fireplace?

(1) There is a total of 150 apartments in the building.
(2) 35 of the apartments in the building that have a balcony also have a fireplace.

­This is the data given in the question:

Attachment:
Screenshot 2024-04-09 at 11.27.12 AM.png
Screenshot 2024-04-09 at 11.27.12 AM.png [ 64.36 KiB | Viewed 443 times ]

Question: How many of the apartments in the building that have a balcony do not have a fireplace?
We need the number in the blue region alone.

(1) There is a total of 150 apartments in the building.
Total = 150.
Then we can use the formula Total = A + B - Both + Neither to get 'Both'
Number in Blue region will be 75 - Both. Sufficient.

We don't need to calculate anything here. But if you wanted to, 150 = 75 + 80 - Both + 30, gives Both = 35.
Number in Blue region will be 75 - 35 = 40.

(2) 35 of the apartments in the building that have a balcony also have a fireplace.
We directly have Both here. Sufficient alone.

Number in Blue region will be 75 - 35 = 40.

Answer (D)­
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Re: Of the apartments in a certain building, 75 have a balcony, 80 have [#permalink]
08 Apr 2024, 23:01
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