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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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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 [ 18.43 KiB | Viewed 3834 times ]
[Reveal] Spoiler: OA

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

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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.

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

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29 Oct 2012, 21:00
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Expert's post
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 [ 6.14 KiB | Viewed 3735 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 [ 9.84 KiB | Viewed 3737 times ]

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

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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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26 Aug 2016, 08:13
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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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