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

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Senior Manager
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The area of parallelogram QRST is what percent of the area o [#permalink]  29 Oct 2012, 10:41
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Question Stats:

63% (01:55) correct 37% (01:59) wrong based on 68 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

Attachments

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Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

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Joined: 03 Sep 2006
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Kudos [?]: 471 [1] , given: 33

Re: The area of parallelogram QRST is what percent of the area o [#permalink]  29 Oct 2012, 18:33
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KUDOS
$$\frac{QR}{PU}=\frac{x}{2x}$$

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]  29 Oct 2012, 20:00
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KUDOS
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 3072 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 3075 times ]

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Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 137 [0], given: 82

Re: The area of parallelogram QRST is what percent of the area o [#permalink]  29 Oct 2012, 21:40
Thank u karishma and LM..

+1 to both of u
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Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Re: The area of parallelogram QRST is what percent of the area o   [#permalink] 29 Oct 2012, 21:40
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