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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] New post 29 Oct 2012, 10:41
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61% (01:51) correct 39% (01:52) wrong based on 57 sessions
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: OA

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343 (1).png [ 18.43 KiB | Viewed 1813 times ]


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Re: The area of parallelogram QRST is what percent of the area o [#permalink] New post 29 Oct 2012, 18:33
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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] New post 29 Oct 2012, 20:00
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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 1781 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 1784 times ]


Answer (A)
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Re: The area of parallelogram QRST is what percent of the area o [#permalink] New post 29 Oct 2012, 21:40
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] 29 Oct 2012, 21:40
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