### Question 22

This is an interesting question. It has a hard feel to it because:

A. You are not told directly how many rooms there are; and

B. You are told the cheapest room is "d" dollars instead of a monetary amount.

The most important word is the word "remaining" at the beginning of the third line. What can we infer? We need to concern ourselves with:

A. The number of rooms; and

B. The cost of the rooms.

We are told that one-third of the rooms have a view and the "remaining" two-thirds (which = 180) do not have a view. So, 180 is two-thirds of the rooms. Therefore, on-third of the rooms = 90 and the total number of rooms is 180 + 90 = 270.

Mathematical Solution

1. As stated there are 270 rooms.

2. 180 rooms cost d\$ each and 90 rooms cost 1.2d\$ each.

3. Hence, the total cost is:

(90 times 1.2d) + 180 times d = 108d + 180 d = 288d

Multiple Choice Is Our Friend Solution

What about cost? Each of the rooms costs at least d\$. The maximum income would exist if each of the rooms was filled. So, the maximum income is at least 270d\$. Hence, (A), (B) and (C) must be eliminated.

We are left with (D) and (E). As long as even one room costs more than d\$ the maximum income must exceed 270d\$. Hence, (D) must be eliminated.