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The area of parallelogram QRST is what percent of the area o

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The area of parallelogram QRST is what percent of the area o [#permalink]

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New post 29 Oct 2012, 11:41
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The area of parallelogram QRST is what percent of the area of rectangle PUST?

(1) The ratio of QR to PU is 1:2

(2) The area of the rectangle is 30.

[Reveal] Spoiler:
Attachment:
343 (1).png
343 (1).png [ 18.43 KiB | Viewed 3440 times ]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Aug 2016, 01:49, edited 1 time in total.
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Re: The area of parallelogram QRST is what percent of the area o [#permalink]

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New post 29 Oct 2012, 19:33
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\(\frac{QR}{PU}=\frac{x}{2x}\)

ratio of areas =\(\frac{1*(x+2x)*Length}{2*2x*Length}\)=\(\frac{3}{4}\)

From (A) it is sufficient.

From B, we can't know or judge about the length of QR.

So answer should be A.
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Re: The area of parallelogram QRST is what percent of the area o [#permalink]

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New post 29 Oct 2012, 21:00
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sanjoo wrote:
The area of parallelogram QRST is what percent of the area of rectangle PUST?

(1) The ratio of QR to PU is 1:2

(2) The area of the rectangle is 30.


Notice that QRST is a trapezoid, not a parallelogram.

Area of trapezoid = (1/2)*Altitude*(Sum of parallel sides)

Statement 1:

Attachment:
Ques4.jpg
Ques4.jpg [ 6.14 KiB | Viewed 3404 times ]


AREA of QRST = (1/2)*b*(a/2 + a) (Since QR is half of PU)
Area of rectangle PUST = a*b

Ratio = Area of QRST/Area of PUST = [(1/2)*b*(3a/2)]/a*b = 3/4
Sufficient

Statement 2: The area of the rectangle is 30
The position of Q and R will decide the area of QRST. In the two cases given below, the areas will be different. Area of the rectangle is not enough to know the ratio of area of trapezoid and rectangle.

Attachment:
Ques3.jpg
Ques3.jpg [ 9.84 KiB | Viewed 3406 times ]


Answer (A)
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New post 29 Oct 2012, 22:40
Thank u karishma and LM..

+1 to both of u :)
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Re: The area of parallelogram QRST is what percent of the area o [#permalink]

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New post 26 Aug 2016, 08:13
Hello from the GMAT Club BumpBot!

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Re: The area of parallelogram QRST is what percent of the area o   [#permalink] 26 Aug 2016, 08:13
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