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# Rectangular region QRST is divided into four smaller rectang

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Rectangular region QRST is divided into four smaller rectang [#permalink]  24 Mar 2017, 14:44
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Question Stats:

37% (04:19) correct 62% (01:08) wrong based on 16 sessions
Rectangular region QRST is divided into four smaller rectangular regions, each with length l and width w.

 Quantity A Quantity B $$\frac{QR}{QS}$$ $$\frac{3}{4}$$

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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Bildschirmfoto 2017-03-24 um 23.43.08.png [ 26.44 KiB | Viewed 1353 times ]

Last edited by mpmbtr on 23 Aug 2017, 07:24, edited 3 times in total.
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Re: Rectangular region QRST is divided into four smaller rectang [#permalink]  25 Mar 2017, 08:23
Expert's post
Please post the question in the right format. Thnk you for your collaboration.

Regards
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Re: Rectangular region QRST is divided into four smaller rectang [#permalink]  01 Apr 2017, 04:31
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I think the question should have the Quantity 'A' asking for the ratio between QR/RS or QR/QT

In this case the Each rectangle inside the bigger rectangle has a width 'x'( Assume)

Now QR is nothing but the combination of 3 horizontally placed rectangles whose side length is the addition of the widths of those rectangles

QR = x+x+x = 3x ( From this ,the length of each of the rectangle is 3x - we can Conclude this by carefully noticing the 3 Horizontal rectangular widths = one vertically lying rectangular length)

Now coming to the denominator : If we need to Find out RS or QT we can notice the side is the combination of two rectangles which is Length of one Horizontal rect + width of vertical rect

So RS = x + 3x = 4x

Finally we get the ration as 3x/4x and we can cancel 'x' in numerator and denominator which is left with a ration of 3/4 and it is equal to quantity B

Thank you

Correct me in case of any mistakes
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Re: Rectangular region QRST is divided into four smaller rectang [#permalink]  03 Apr 2017, 22:01
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prasanna kumar wrote:
I think the question should have the Quantity 'A' asking for the ratio between QR/RS or QR/QT

In this case the Each rectangle inside the bigger rectangle has a width 'x'( Assume)

Now QR is nothing but the combination of 3 horizontally placed rectangles whose side length is the addition of the widths of those rectangles

QR = x+x+x = 3x ( From this ,the length of each of the rectangle is 3x - we can Conclude this by carefully noticing the 3 Horizontal rectangular widths = one vertically lying rectangular length)

Now coming to the denominator : If we need to Find out RS or QT we can notice the side is the combination of two rectangles which is Length of one Horizontal rect + width of vertical rect

So RS = x + 3x = 4x

Finally we get the ration as 3x/4x and we can cancel 'x' in numerator and denominator which is left with a ration of 3/4 and it is equal to quantity B

Thank you

Correct me in case of any mistakes
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Re: Rectangular region QRST is divided into four smaller rectang [#permalink]  06 Apr 2017, 07:38
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Expert's post
HarveyKlaus wrote:
Rectangular region QRST is divided into four smaller rectangular regions, each with length l and width w.

 Quantity A Quantity B $$\frac{QR}{QS}$$ $$\frac{3}{4}$$

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.

Now we can see from the figure that $$QR = 3 \times w$$ and RS is $$RS= l+w$$

Now $$QS =\sqrt{QR^2 + RS^2}=\sqrt{(l+w)^2 + (3w)^2}$$

So ratio $$QR:QS=3w:\sqrt{(l+w)^2 + (3w)^2}=3w:\sqrt{(4w)^2 + (3w)^2}= \frac{3}{5}$$.

Hence option B is correct.
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Re: Rectangular region QRST is divided into four smaller rectang [#permalink]  25 Apr 2017, 12:10
We can see from the figure that QR =3w . Also, it is clear that L=3w since ST = L = QR .

Now, QS = Sq.root(QR^2 + RS^2) = Sq.root[(L+w)^2 + (3w)^2] = Sq.root[(3w+w)^2 + (3w)^2] = Sq.root(25w^2) = 5w.

Therefore , QR/QS = 3w/5w = 3/5 . Given option B i.e. 3/4 is greater than 3/5. Answer is B.
Re: Rectangular region QRST is divided into four smaller rectang   [#permalink] 25 Apr 2017, 12:10
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