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The rectangular rug shown in the figure above has an accent

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Senior | Next Rank: 100 Posts
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by canbtg » Wed Jul 01, 2015 11:06 pm
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The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?

(1) The perimeter of the rug is 44 Ft

(2) The width of the border on all sides is 1 foot


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Source: — Data Sufficiency |

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by [email protected] » Thu Jul 02, 2015 10:09 am
Hi canbtg,

I'm going to offer you some *hints* about how you can go about answering this question so that you can try it again on your own...

First, we don't know ANYTHING about the dimensions or the rug nor the dimensions of the accent border. That means we can probably TEST VALUES. Based on the information in Fact 1, can you come up with some possible dimensions for the rug and the border? Do they have to be integers? With Fact 2, since you know nothing about the size of the rug, what do you think about this Fact?

[spoiler]Combined, is there more than one possibility for the overall dimensions of the rug? With differing dimensions, the 1-foot wide border would have a different impact on the area that is NOT part of the border. If you're not convinced of this, then you can come up with 2 different examples and prove it.[/spoiler]

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