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A building has 48 one- and two-bedroom apartments to rent,

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A building has 48 one- and two-bedroom apartments to rent,

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A building has 48 one- and two-bedroom apartments to rent, some with balconies and others without. If one of these apartments is to be selected at random, is the probability greater than 1/2 that the apartment has two bedrooms and a balcony?

(1) Of the apartments, 40 have two bedrooms.
(2) Of the apartments, 30 have a balcony.

OA E

Source: EMPOWERgmat

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BTGmoderatorDC wrote:
A building has 48 one- and two-bedroom apartments to rent, some with balconies and others without. If one of these apartments is to be selected at random, is the probability greater than 1/2 that the apartment has two bedrooms and a balcony?

(1) Of the apartments, 40 have two bedrooms.
(2) Of the apartments, 30 have a balcony.

OA E

Source: EMPOWERgmat
Given: A building has 48 one- and two-bedroom apartments to rent, some with balconies and others without.

Question: If one of these apartments is to be selected at random, is the probability greater than 1/2 that the apartment has two bedrooms and a balcony?

Let's take each statement one by one.

(1) Of the apartments, 40 have two bedrooms.

Case 1: Say all the 40 two-bedroom apartments have a balcony, then the probability that the apartment has two bedrooms and a balcony = 40/48 = 5/6 > 1/2 (greater than 1/2 ). The answer is Yes.

Case 2: Say none of the 40 two-bedroom apartments have a balcony, then the probability that the apartment has two bedrooms and a balcony = 0/48 = 0 < 1/2 (less than 1/2 ). The answer is No.

Insufficient.

(2) Of the apartments, 30 have a balcony.

Case 1: Say there are 30 two-bedroom apartments and each has a balcony, then the probability that the apartment has two bedrooms and a balcony = 30/48 = 5/8 > 1/2 (greater than 1/2 ). The answer is Yes.

Case 2: Say there are 30 one-bedroom apartments and each has a balcony, then the probability that the apartment has two bedrooms and a balcony = 0/48 = 0 < 1/2 (less than 1/2 ). The answer is No.

Insufficient.

(1) and (2) together

Case 1: Say 30 of the 40 two-bedroom apartments have a balcony, then the probability that the apartment has two bedrooms and a balcony = 30/48 = 5/8 > 1/2 (greater than 1/2 ). The answer is Yes.

Case 2: Since there are 40 two-bedroom apartments, thus, there are 48 - 40 = 8 one-bedroom apartments.
Say all the 8 one-bedroom apartments have a balcony, thus, only 30 - 8 = 22 two-bedroom apartments have a balcony.
Thus, the probability that the apartment has two bedrooms and a balcony = 22/48 = 11/24 < 1/2 (less than 1/2 ). The answer is No.

Insufficient.

The correct answer: E

Hope this helps!

-Jay
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