IMAT 2014 Q15 [Hotel Paint]

The owner of a hotel needs to decorate 20 rooms. He has found prices for four different types of interior wood paint and calculated the volume of paint he needs for each room. He will use the same type of paint for all the rooms.


What is the least amount he needs to spend on paint?

A. €116
B. €120
C. €126
D. €112
E. €108


Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve

Right away we can eliminate Quick Dry Gloss because it is more expensive than Once Gloss in every category and it also takes more per room. That leaves us we three options so far. Next, we can eliminate Satinwood because it requires more litres per room than Once Gloss and it is more expensive until buying 1.25L but we can easily see that this will not be what we are buying the most of because it is more expensive, we will only buy$1$ can of it max at the end, so the bulk of the money spent will be on the 2.5L cans. Therefore we can eliminate Satinwood as well. That leaves us we only two options, Non-Drip Gloss or Once Gloss. Here, you should start with Once Gloss because off face value it looks like it will be the cheapest.

First, find out how much paint is needed and then find the cost.

Non-Drip Gloss

(1.4L)(20 rooms) = 28L

(2.5L)(11 cans) = 27.5 L
We can stop our calculation here because we can easily see that (11 cans)(€16) = €176, which is more than any of our answer choices.

Once Gloss
(0.8L)(20 rooms) = 16L

(2.5L)(6 cans) = 15L

(1.25L)(1 cans) = 1.25L

15L + 1.25L = 16.25L, so we have enough. Now to find the cost.

(€18)(6 2.5L cans) = 108€
(€12)(1 1.25L cans) = 12€

Total cost of Once Gloss: €108 + €12 = €120

Now we know that all the other paints are more expensive or will be more expensive because they require more volume per room, so we can conclude that Once Gloss is the cheapest.

\fcolorbox{red}{grey!30}{Therefore the answer is B, $€120$}
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