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In the figure above, segments RS and TU represent two positions of the
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14 Feb 2014, 01:56
14 Feb 2014, 01:56
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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.
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Re: In the figure above, segments RS and TU represent two positions of the
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14 Feb 2014, 01:57
14 Feb 2014, 01:57
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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
• 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
General Discussion
Re: In the figure above, segments RS and TU represent two positions of the
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14 Feb 2014, 03:03
14 Feb 2014, 03:03
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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).
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).
