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In the figure above, segments RS and TU represent two

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In the figure above, segments RS and TU represent two [#permalink]

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In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than the length of RV?

(1) The length of TU is 10 meters.
(2) The length of RV is 5 meters.

OPEN DISCUSSION OF THIS TOPIC IS HERE: in-the-figure-above-segments-rs-and-tu-represent-two-positi-167496.html
[Reveal] Spoiler: OA

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Re: In the figure above, segments RS and TU represent two [#permalink]

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New post 22 Feb 2011, 10:59
\(\triangle{TVU}\) is a right-angled triangle with angles 45-90-45.
Ratio of its sides
\(Base:Altitude:Hypotenuse::\bar{TV}:\bar{UV}:\bar{TU}::1:1:\sqrt{2}\)

\(\triangle{RVS}\) is a right-angled triangle with angles 30-90-60.
Ratio of its sides
\(Base:Altitude:Hypotenuse::\bar{RV}:\bar{VS}:\bar{SR}::1:\sqrt{3}:2\)


(1)
TU=RS=10
\(\bar{TV}=\frac{10}{\sqrt{2}}\)
\(\bar{RV}=\frac{10}{2}\)

Find TV-RV
Sufficient.

(2)
RV=10
\(\bar{RS}=5*2=\bar{TU}\)
\(\bar{TV}=\frac{10}{\sqrt{2}}\)
Find TV-RV
Sufficient.

Ans: "D"
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Re: In the figure above, segments RS and TU represent two [#permalink]

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New post 03 Mar 2011, 07:44
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Same ladder = same length. TU=RS

In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than the length of RV?
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Re: In the figure above, segments RS and TU represent two [#permalink]

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New post 03 Mar 2011, 09:51
You can also use basic trigonometry to get this information. Let's see how:

Statement 1 says TU = 10 metres which would be same as RS as its the same ladder.

Now TV = TU*Cos45 and
and RV = RS*Cos60

So both TV and RV can be calculated by using given information, so sufficient

Statement 2 gives RV = 5, but we know that RV = RS*Cos60 so, RS = TS = RV/Cos60 and hence TV can also be determined. Thus we again know TV and RV, so sufficient.

Answer D
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Re: In the figure above, segments RS and TU represent two [#permalink]

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Re: In the figure above, segments RS and TU represent two [#permalink]

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New post 26 Aug 2016, 00:40
Baten80 wrote:
Attachment:
QR DS 91.jpg

In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than the length of RV?

(1) The length of TU is 10 meters.
(2) The length of RV is 5 meters.


MUST KNOW FOR THE GMAT:
• A right triangle where the angles are 30°, 60°, and 90°.
Image
This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio \(1 : \sqrt{3}: 2\).
Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

• A right triangle where the angles are 45°, 45°, and 90°.
Image
This is one of the 'standard' triangles you should be able recognize on sight. A fact you should also commit to memory is: The sides are always in the ratio \(1 : 1 : \sqrt{2}\). With the \(\sqrt{2}\) being the hypotenuse (longest side). This can be derived from Pythagoras' Theorem. Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles.

BACK TO THE ORIGINAL QUESTION:
Image
In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than Length of RV?

Given: RS=TU. Question: TV-RV=?

Now, according to the properties above if we knew RS (or which is the same TU), then we would be able to find ANY line segment in the given figure: RS would give us RV and SV, while TU would give us TV and UV. Thus knowing RS/TU would be sufficient to get the value of TV-RV.

If we knew RV: we could get RS (or which is the same TU) and would have the same exact case as above.

(1) The length of TU is 10 meters. Sufficient.
(2) The length of RV is 5 meters. Sufficient.

Answer: D.

Similar questions to practice:
a-ladder-25-feet-long-is-leaning-against-a-wall-that-is-130364.html
in-the-figure-above-segments-rs-and-tu-represent-two-140752.html

OPEN DISCUSSION OF THIS TOPIC IS HERE: in-the-figure-above-segments-rs-and-tu-represent-two-positi-167496.html
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Re: In the figure above, segments RS and TU represent two   [#permalink] 26 Aug 2016, 00:40
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