The figure above shows the plan for the ground floor of a house. The thickness of the walls should be ignored in answering the questions. The dimensions are in feet, and each region is rectangular.




If the kitchen is square, what is the ratio of the area of the kitchen to the area of the dining room?


A. \(\frac{16}{37}\)

B. \(\frac{3}{7}\)

C. \(\frac{4}{7}\)

D. \(\frac{8}{11}\)

E. \(\frac{16}{21}\)
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Dear msk0657,

first of all the graph is clear, I do not know why you say it is neat. Of course, it is not in high resolution or 4k but consider it comes from the old paper OG 10th edition. We can not do more. However, I do think the following:

• the figure is clear enough to permit you to answer the question;
• it is an amazing querstion to stretch your mental muscles;
• this is the proper case in which you in difficult condition (if we wanna to put it this way), you are still able to find a solution. This is indeed what this test is all about: find a solution no matter what.

Back to the question: notice that I do not have a solution to this question, I have only the OA. As such, I came to the solution just like you, via reasoning.

Now, notice that the stem says the figure drawn the scale and this is in your favour: you do not have to be suspicious, just enough.
Moreover, the stem also adds that the rooms are rectangular but in this case to consider the kitchen as a square.



One side of the kitchen itself is 8. so, if it is a square the area is \(s^2 = 64\)

Now think about the denominator of the ratio. See this figure



If you see, point one = 14

point two = 4,5

These two points added make the entire side of the house: \(14 + 4,5 = 18,5\).

Now, this side is also the entire upper side of the house. Notice also that we said one side of the square is 8, which means all the side length 18,5 minus 8 = \(10,5\)

This is the upper side of the dining room. The other side is also 8, because the dining room and the kitchen room share the same wall-side, which is \(8\).

The area of the rectangular dining room is \(b * h = 10,5 * 8 = 84\)

Our ratio kitchen room / dining room = \(\frac{64}{84} = \frac{32}{42} = \frac{16}{21}\)

The answer is E
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