The figure above shows the dimensions of a living room floor that is to be covered completely with two nonoverlapping rectangular pieces of carpet. What is the area, in square feet, of the largest piece of carpet that can be used?
A: 80 B: 156 C: 208 D: 216 E: 288
The question looks overly simple, but might not be what we thinking after all.
I'm happy to respond.
As in so many GMAT problems, the diagram is wildly deceiving, and is bound to lead one into all kinds of incorrect assumptions. Here's a scaled diagram:
floor with rectangular carpet.JPG [ 16.19 KiB | Viewed 605 times ]
The diagram suggest, for example, that BC and DE are about the same size, as CE and EF would seem. The scaled diagram makes clear that the dimension we aren't
given are much bigger and make the difference. Here, BC = 16 - 4 = 12, and AB = 13 + 5 = 18. The biggest piece of carpet has corners A & B & C and the point on AF below D, and it has an area of 12*18 = 216.
Does all this make sense?
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