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# In the figure above, segments RS and TU represent two positions of the

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

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23 Jan 2012, 02:11
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Question Stats:

64% (01:09) correct 36% (01:31) wrong based on 453 sessions

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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 Length of RV?

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

I went with C, because these two figures form two right triangles i.e. 30-60-90 and 45-45-90 and if we know one side of the triangle we can calculate other sides.But the OA says D(In the explanation it says both triangles have same hypotenuse....But how is this true because we never about the sides SU and TR..right??

Can anyone please justify this???

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

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23 Jan 2012, 03:22
8
7
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:
Attachment:

untitled_141.jpg [ 7.66 KiB | Viewed 13049 times ]

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 10m. Sufficient.
(2) The length of RV is 5m. Sufficient.

Hope it helps.
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Senior Manager
Joined: 28 Jul 2011
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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23 Jan 2012, 06:06
Bunuel wrote:
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:
Attachment:
untitled_141.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 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 10m. Sufficient.
(2) The length of RV is 5m. Sufficient.

Hope it helps.

I misread the question Question such that RS Not equal TU.

Thanks a lot Bunnel........
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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23 Jan 2012, 11:08
1
what an explanation wow!!
Manager
Joined: 24 Mar 2013
Posts: 59
Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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06 Mar 2014, 02:09
mydreammba wrote:

I misread the question Question such that RS Not equal TU.

Thanks a lot Bunnel........

I made a similar mistake and picked C, as got distracted in the question and forgot about the hypotenuse being the same length. Really need to outline 'what I know' at the beginning of questions like this.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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27 Apr 2014, 15:44
Yeah, 90% of the problem is complete once you know that because the ladder is the same, RS=TU. I for one hate questions like this.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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12 Aug 2016, 20:38
Bunuel wrote:
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:
Attachment:
untitled_141.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 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 10m. Sufficient.
(2) The length of RV is 5m. Sufficient.

Hope it helps.

I still dont see where it is written RS=TU in the question...??
I mean it says there are two positions of the same ladder ...It could still be S and U are different points on the wall ??

Can you please clarify ..
I marked C bcoz I see Point S and U are different ...and I still feel it is that way ..
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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17 Aug 2016, 22:40
mihir0710 wrote:
Bunuel wrote:
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:
Attachment:
untitled_141.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 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 10m. Sufficient.
(2) The length of RV is 5m. Sufficient.

Hope it helps.

I still dont see where it is written RS=TU in the question...??
I mean it says there are two positions of the same ladder ...It could still be S and U are different points on the wall ??

Can you please clarify ..
I marked C bcoz I see Point S and U are different ...and I still feel it is that way ..

Agreed. I have the same issue with this question. How is RS=TU? I don't see it at all.
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Joined: 17 Jun 2016
Posts: 525
Location: India
GMAT 1: 720 Q49 V39
GMAT 2: 710 Q50 V37
GPA: 3.65
WE: Engineering (Energy and Utilities)
Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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17 Aug 2016, 23:34
butch3r wrote:
mihir0710 wrote:
Bunuel wrote:
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:
Attachment:
untitled_141.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 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 10m. Sufficient.
(2) The length of RV is 5m. Sufficient.

Hope it helps.

I still dont see where it is written RS=TU in the question...??
I mean it says there are two positions of the same ladder ...It could still be S and U are different points on the wall ??

Can you please clarify ..
I marked C bcoz I see Point S and U are different ...and I still feel it is that way ..

Agreed. I have the same issue with this question. How is RS=TU? I don't see it at all.

I dont knw whats wrong but neither bb nor Bunuel replies to my queries....Not even on personal message ...
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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18 Aug 2016, 06:59
2
mihir0710 wrote:

I dont knw whats wrong but neither bb nor Bunuel replies to my queries....Not even on personal message ...

The question clearly says that "segments RS and TU represent two positions of the same ladder", so RS = TU.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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18 Aug 2016, 08:25
Quote:
I still dont see where it is written RS=TU in the question...??
I mean it says there are two positions of the same ladder ...It could still be S and U are different points on the wall ??

Can you please clarify ..
I marked C bcoz I see Point S and U are different ...and I still feel it is that way ..

Hi!

RS=TU because it is the same ladder: "RS and TU represent two positions of the same ladder" It is gonna be 10 meters in any position
Hope it helps
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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18 Aug 2016, 08:51
1
Bunuel wrote:
mihir0710 wrote:

I dont knw whats wrong but neither bb nor Bunuel replies to my queries....Not even on personal message ...

The question clearly says that "segments RS and TU represent two positions of the same ladder", so RS = TU.

Since the image isn't drawn to scale, and theoretically, we can shrink the isosceles hypotnuse, I guess I don't see how the "segments ... represent two positions of the same ladder" translates into the two hypotnuse being equal. Maybe, the wording doesn't make sense...
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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22 Sep 2016, 00:30
soln:statement i) TV=10
COS45=TV/TU=TV/10
1/√2=TV/10 which gives us TV=10/√2
COS60=RV/10
1/2=RV/10 which gives us RV so i) is sufficient

ii) RV=5
COS60=RV/(SR=TU)
1/2=RV/TU =5/TU which gives us TU=10=SR
COS45=TV/TU = TV/10
1/√2 =TV/10 which gives us TV so ii) sufficient

finally either i)or ii) is sufficient so D) is the answer
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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24 Feb 2017, 04:23
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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31 May 2017, 18:48
mydreammba wrote:

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?

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

I went with C, because these two figures form two right triangles i.e. 30-60-90 and 45-45-90 and if we know one side of the triangle we can calculate other sides.But the OA says D(In the explanation it says both triangles have same hypotenuse....But how is this true because we never about the sides SU and TR..right??

Can anyone please justify this???

This problem hinges on reading the stimulus correctly. If you look closely, you'll note that it says the same ladder is re-positioned. So that means that the lengths RS and TU are equivalent. If you miss that detail, the one word in the passage, you will get this problem incorrect.

The goal is to find the difference between TV and RV.

Statement 1) TU is 10 meters.

TU = RS = 10

Since we have a 45-45-90 triangle, we can solve for the length of each leg once we have the hypotenuse. Similarly, we have a 30-60-90 triangle, so we can solve for each of the sides once we have the hypotenuse. Sufficient.

Statement 2) RV = 5.

We know that triangle RSV is a 30-60-90 triangle, so its sides are in proportion 1:sqrt(3):2. The base, RV, is 5, so the hypotenuse is 10. Hence, RS = 10 = TU. Once we have one side for TU, we can solve for all the others. Sufficient.
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Re: In the figure above, segments RS and TU represent two positions of the  [#permalink]

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