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The rectangular rug shown in the figure above has an accent

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The rectangular rug shown in the figure above has an accent

by Gmat_mission » Sun Jun 30, 2019 9:03 am

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

[spoiler]OA=E[/spoiler]

Source: Official Guide
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Source: — Data Sufficiency |
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by deloitte247 » Sat Jul 13, 2019 5:25 am

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Question=> what is the area of rug that excludes the border.
Statement 1 => The perimeter is 44ft
2l + 2w = 44 [ length & width of rug and border]
2 [ l + w ] = 44
l + w = 44/2 = 22
There are so many variation of 2 integers that sum up to 22, information given is not enough to arrive at a definite answer. Statement 1 is NOT SUFFICIENT.

Statement 2 => The width of the border on all sides is 1 foot but no information was provided regarding the length and width of the rug, hence statement 2 is INSUFFICIENT.

Combine both statement together,
Since the width of the border on all sides is 1ft
Length of rug = l - ( 1+1 ) => l - 2
Width of rug = w - ( 1+1 ) =>w - 2
Area of rug = ( l -2 ) * (w - 2)
Value of l and w is unknown hence both statement together are NOT SUFFICIENT
Answer = option E
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