A hotel has two types of rooms: basic and deluxe.

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A

B

C

D

E

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A hotel has two types of rooms: basic and deluxe. On a certain night, the hotel rented 75% of its rooms, including 2/3 of its basic rooms. What percentage of the rooms that were not rented on that night was basic?

(1) 60% of all the rooms in the hotel are basic

(2) On that night, 12.5% of the deluxe rooms were not rented

The OA is the option _D_

Source: Veritas Prep
Source: — Data Sufficiency |

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by swerve » Tue Jun 25, 2019 11:26 am

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Your Answer

A

B

C

D

E

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Sets Question
\(B =\) Basic, \(D =\) Deluxe
Consider, Total Rooms \(= 100 = B + D\)
Rented Out \(= 75\)

Statement 1: 60% rooms are basic
\(\Rightarrow\) 40 rooms rented out, and 20 not rented out.
Sufficient \(\Rightarrow\,\, AD\)

Statement 2: 12.5% of deluxe rooms not rented out.
\(\Rightarrow\,\, \frac{1}{8}\) not rented out, and \(\frac{7}{8}\) rented out
\(\frac{2}{3}B + \frac{7}{8} D = 75\)
From the Question, \(B + D = 100\)

We can solve for \(B\,\, \Rightarrow\,\,\) Sufficient.

Therefore, __D__ is the correct answer.