A Hotel has Two Types of Rooms: Basic and Deluxe. On a Certain Night GMAT Data Sufficiency

Question: 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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: (D)

Approach Solution 1:

S1: 60% of all rooms are basic, therefore 40% of the basic rooms are rented and 20% are not rented. Since 25% of all rooms were not rented, that means that 80% of all rooms not rented were basic (20/25 = 4/5)

Sufficient

S2: 12.5% or 1/8 of the deluxe rooms was not rented. This means that 7/8 of the deluxe rooms were rented. Let basic rooms = B and deluxe rooms = D. we know that B + D = 1, and that 2B/3 + 7D/8 = 0.75
Solving for these two equations, we get B = 3/5 or 60%
Sufficient

Approach Solution 2:

Sets Question D = Deluxe, B = Basic
Think of the formula: Total Rooms = 100 + B + D
70 days rented out
S1: 60% rooms are basic
=> 40 are rented out and 20 are not.

This is sufficient -> AD
S2 :12.5% of deluxe rooms not rented out

The number for not rented out is 1/8; The number for rented out is 7/8

\(\frac{2}{3}B + \frac{7}{8}D\)  = 75

B + D equals 100 in the question.
B is solvable

Therefore this is sufficient

“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?”- is a topic of the GMATQuantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review".GMAT Quantsection consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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