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14 Jan 2015, 02:21
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Difficulty:
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50% (01:48) correct
50%
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wrong
based on 123
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In the figure below, segments AB and CD represent two different ways the same steel girder can support wall EC. The length of AE is how much greater than the length of DE?
(1) The length of AB is 20 meters.
(2) The length of DE is 8 meters.
Kudos for a correct solution.
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2015-01-14_1320.png [ 8.3 KiB | Viewed 3815 times ]
14 Jan 2015, 12:05
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The figure gives us two triangles with two angles each. As both are known triangles, we know the ratio of the sides of each, but we don't have any information on the ratio between the two. Since the question is asking us about exactly that, we need information on both, or on their ratio.
(1): The statement gives us one length of the left triangle, so we can calculate all other lengths of the left triangle, but not the right. Not sufficient.
(2): This is exactly the = information we need to calculate the lengths of the right triangle, however, given this statement alone is also insufficient.
Both taken together allow us to calculate all lengths in the figure and therefore enough information to answer the question.
Answer C.
(1): The statement gives us one length of the left triangle, so we can calculate all other lengths of the left triangle, but not the right. Not sufficient.
(2): This is exactly the = information we need to calculate the lengths of the right triangle, however, given this statement alone is also insufficient.
Both taken together allow us to calculate all lengths in the figure and therefore enough information to answer the question.
Answer C.
14 Jan 2015, 22:40
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The Question states segments AB and CD represent two different ways the same steel girder can support wall. That implies that the length of AB & CD are the same.
We also have the angle with with AB , CD forms a right triangle against the wall.
Statement 1: It gives the the value of AB, which is equal to CD
now for AE = ABcos45
similarly ED = CDcos60 = ABcos60
AE - ED = AB(Cos45 - Cos60)
Hence sufficient
Statement 2: It gives us the value DE
We Know DE = CDcos60 = ABcos60
so CD = AB = [DE][/Cos60] (= DEsec60)
Now AE = ABcos45 = DEcos45/cos60
now AE - DE = DE( cos45/cos60 - 1)
Hence sufficient.
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We also have the angle with with AB , CD forms a right triangle against the wall.
Statement 1: It gives the the value of AB, which is equal to CD
now for AE = ABcos45
similarly ED = CDcos60 = ABcos60
AE - ED = AB(Cos45 - Cos60)
Hence sufficient
Statement 2: It gives us the value DE
We Know DE = CDcos60 = ABcos60
so CD = AB = [DE][/Cos60] (= DEsec60)
Now AE = ABcos45 = DEcos45/cos60
now AE - DE = DE( cos45/cos60 - 1)
Hence sufficient.
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