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Math Expert V
Joined: 02 Sep 2009
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In the figure above, segments RS and TU represent two positions of the  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 56% (01:43) correct 44% (02:09) wrong based on 645 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition 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.

Data Sufficiency
Question: 91
Category: Geometry Triangles
Page: 159
Difficulty: 650

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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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1
4
MUST KNOW FOR THE GMAT:
• A right triangle where the angles are 30°, 60°, and 90°. 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°. 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: 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
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GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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1
St1: The length of TU is 10 meters. Sufficient.

Triangle TUV is a 45-45-90 triangle. The sides are in the ratio of 1:1:root 2. We can calculate the length of TV. Since the stem mentions TU and RS are the same ladder, RS = 10. Now, triangle RSV is a 30-60-90 triangle. The sides are in the ratio of 1:root 3:2. We can calculate the length of RV.

St2: The length of RV is 5 meters. Sufficient. Applying same concept as statement 1, we can find TV.

Answer (D).
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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1
Option D.Each is sufficient.
Using basic trigo:
From S1: TU=RS=10 mts.
cos 45=TV/TU (cos 45=1/sqrt2 and TU=10)
We can find TV
And cos 60=RV/RS (cos 60=1/2 and RS=10
We can find RV
The diff can be found out.Sufficient.

From S2: RV=5
We can find RS and TU by the same trigo formula-cos (angle)=Base/Hypotenuse
Then the diff between TV and RV can be found out.Sufficient.
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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MUST KNOW FOR THE GMAT:
• A right triangle where the angles are 30°, 60°, and 90°. 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°. 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: 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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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HI All,

This is a great "pattern matching" question, in that if you recognize what you're looking at, you won't need to do ANY math to get to the correct answer.

It doesn't take much to recognize the 30/60/90 and 45/45/90 right triangles in the drawing. The "key" to the shortcut is that we're told that that RS and TU are the SAME length - in math terms, this means that the hypotenuse of those two triangles is the SAME. By extension, if you know the length of ANY of the sides in EITHER of the triangles, then you can figure out EVERY side length in that drawing.

If you recognize this pattern, then dealing with the two Facts won't take much time or effort at all.

As an aside on the prior post in this thread, the GMAT will NEVER ask you a question that requires Trigonometry to solve it, so you do NOT need to know any Trig rules for this test.

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

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1
The most important point is here the word "THE SAME LADDER !!!" - missed it at the begining, but then could easily solve.. all other things in this question are just using known formulas for two particular triangles.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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I did a crucial mistake, and forgot to take into consideration that TS = RU. Clearly, D is the correct answer.
with each statement, we can find the lengths of the legs/hypotenuse, and thus find the TR...
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
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.

Data Sufficiency
Question: 91
Category: Geometry Triangles
Page: 159
Difficulty: 650

This question is one of the finest example of C trap. But remember for a 30-60-90(1:\sqrt{3}:2) and 45-45-90(1:1:\sqrt{2}) right angle triangle, knowing any side is sufficient to find other side.
And length of ladder will be same no matter what position or what angle we put it. Essentially we have 2 right triangles with equal hypotenuse.
Statement 1&2 both give us mease of one side so we can find the measure of all the sides.
Answer is D.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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1
Correct me if I am wrong.
Attachments

File comment: Solution attached. New Doc_1.jpg [ 743.46 KiB | Viewed 5789 times ]

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

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Prompt analysis
Let the length of ladder be x. SV = x sin 60.
RV = x cos 60.
TV = x cos 45
UV = x sin 45
TR = TV -RV = x cos 45 - x cos 60
SU = SV - UV = x sin 60 - x sin 45.

Super set
The answer will be positive real number

Translation
To find the value of TV-RV, we need:
1# exact value of TV and RV
2# exact value of x
3# exact value of any other length as the only variable is x

Statement analysis
St 1: x =10. TV = 10 cos 45 and RV = 10 cos 60. Tv -Rv can be found
St 2: rv = 5 = xcos 60. X = 10. Again TV -RV can be found
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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How have we determined that RS=TU? Bunuel
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Posts: 55228
Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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sadikabid27 wrote:
How have we determined that RS=TU? Bunuel

We are told that "RS and TU represent two positions of the SAME ladder", so line segments RS and TU are representing the SAME ladder just positioned in two different ways.

Hope it's clear.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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