The figure above shows the dimensions of a living room floor that is

Question

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.

A: 80 
B: 156 
C: 208 
D: 216 
E: 288

The question looks overly simple, but might not be what we thinking after all.

mikemcgarry · Answer

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 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? Mike :-)

sagnik242 · Answer

what's the significance of the "overlapping part" I did not get that also I don't get why we are subtracting 16-4 for BC and adding 13 and 5 for AB.

EMPOWERgmatRichC · Answer

Hi sagnik242,

The prompt tells us that the floor has to be covered by 2 different RECTANGLE carpets that do NOT overlap. Since the room is NOT a rectangle, we have two different ways to place rectangle carpets within it.

1) 2 carpets laid down 'left-to-right'
2) 2 carpets laid down 'north-to-south'

For the first option, the dimensions of the two carpets would be 13x16 and 5x20

For the second option, the dimensions of the two carpets would be 18x12 and 5x4

GMAT assassins aren't born, they're made,
Rich

AmritaSarkar89 · Answer

The common error that usually hits us is when we look at the diagram as two halves divided at the particular segment as made evident by the image. 
Thinking like a business solver and look for other possibilities that what meets the eye.

Raffio · Answer

This problem tricked me initially. I thought the smaller segment - DEF(G)- was a square. I think the best way to solve this problem is as follows:

1. Draw an imaginary line from point D down to line AF. This creates a smaller rectangle with an area of 20 (4*5).
2. Now find the sides of the larger rectangle: 16-4 = 12, which is the length, and 13+5 = 18, which is the width. Multiply these two figures together and you get 216 (18*12), which is the answer.

sony1000 · Answer

I wish the could specify that the carpet used would miss leave out part of the geometry as the 216 area leaves out the 20 area.

solchtamas · Answer

The Question is easy, but I have a comment that is not quant related; I just like to shoot at those who claim to provide something standardized but are not consequent and consistent. Well, I know that this is an official question, but how often is that GMAC does not comply with its own rules, e.g. should not it be "larger" instead of "largest", we are talking about 2 carpets, not 3+ .... -.-

EMPOWERgmatRichC · Answer

Hi solchtamas,

There are actually 2 different ways to cover the entire floor - and each of the two options requires that 2 rectangular carpets of different sizes be used. When considering both options, there are actually 4 carpets that you have to consider (not just 2), so the usage of the word "largest" is appropriate in the context of this question.
 
GMAT assassins aren't born, they're made,
Rich

tkorzhan1995 · Answer

Bunuel ,  GMATNinja , I divided this area into two rectangles with sides 13*12 and 5*16. Then, I determined that rectangle with sides 13*12 will have a larger area, and selected incorrect answer choice B. What would be your advise on what things I need to focus in the other similar problems, so I don't repeat the same mistake as I did in this problem?

EMPOWERgmatRichC · Answer

Hi tkorzhan1995,

The 'quirk' with this PS question (re: there's more than one way to cover the floor using 2 rectangular pieces of carpet) does not appear too often in PS questions, but the issue that ultimately led you to one of the incorrect answers is about the 'thoroughness' of your thinking (which IS a big part of correctly answering many DS questions, so that issue is worth noting). When you first read this question, you saw an immediate way to create two pieces of carpet, so why didn't you see the other way? It might be because you weren't careful about reading the prompt.

GMAT questions are almost always really specifically-worded - so you should note the exact vocabulary that appears in each prompt; here, the usage of the word "largest" is interesting. If there were only two possible pieces of carpet to be used, then the word "larger" would be correct - but the wording here gives us just a little bit of a hint that there are more than 2 possible pieces that can be used to cover this floorplan. There are actually 4 pieces that you have to consider (depending on how you 'split' the space), so the usage of the word "largest" is appropriate in the context of this question (and a clue that we need to check more than just whatever option each of us notices first).

GMAT assassins aren't born, they're made,
Rich

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The figure above shows the dimensions of a living room floor that is

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