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# ABCD is a rectangle

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ABCD is a rectangle [#permalink]  19 Oct 2017, 14:45
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43% (00:36) correct 56% (00:53) wrong based on 16 sessions

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ABCD is a rectangle

R is the midpoint of AD

 Quantity A Quantity B The area of Triangle APD Twice the area of Triangle AQR

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: ABCD is a rectangle [#permalink]  19 Oct 2017, 16:11
I thank you for selecting me, you are Infinitely-so-Great to GREprep Club!
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Re: ABCD is a rectangle [#permalink]  20 Oct 2017, 06:34
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Given that R is the midpoint of AD, AR = RD. Then, the area of triangle APD is $$\frac{AD*AB}{2}$$, where AB is the height of the triangle corresponding to the shortest side of the rectangle. The double area of triangle AQR, instead, is equal to $$2*\frac{AR*AB}{2} = AR*AB$$. Then, given AR = RD and AR+RD = AD, we can rewrite AD as 2AR. Thus, the are of APD becomes $$\frac{2AR*AB}{2} = AR*AB$$.

Re: ABCD is a rectangle   [#permalink] 20 Oct 2017, 06:34
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