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What is the area of the shaded region in the figure shown?

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by M7MBA » Mon Apr 22, 2019 5:57 am

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Answers

A

B

C

D

E

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What is the area of the shaded region in the figure shown?

(1) The area of the rectangle ABCD is 54.
(2) AE = 2ED

[spoiler]OA=A[/spoiler]

Source: Official Guide
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Source: — Data Sufficiency |

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by Ian Stewart » Mon Apr 22, 2019 8:01 am
Draw a vertical line starting from point E, up to the line BC. That line will divide the large rectangle (ABCD) into two smaller rectangles. Line BE cuts one of those smaller rectangles in half along the diagonal, while line EC cuts the other one in half along the diagonal. So half of each smaller rectangle is shaded, and half is not, and therefore half of the entire large rectangle is shaded. So with Statement 1, we know the shaded area is 27, while Statement 2 isn't helpful at all.
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