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01 Apr 2022, 02:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
49% (01:43) correct
51%
(01:58)
wrong
based on 45
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Point E lies inside the rectangle ABCD. If EA = a, EB = b and EC = c then ED is equal to
A. \(\sqrt{-a^2 - 4b^2 - c^2}\)
B. \(\sqrt{a^2 - b^2 + c^2}\)
C. \(\sqrt{a^2 - 2b^2 + c^2}\)
D. \(a - b + c\)
E. \(\sqrt{2a^2 - b^2 + 2c^2}\)
2022-03-28_14-03-45.png [ 10.82 KiB | Viewed 2471 times ]
A. \(\sqrt{-a^2 - 4b^2 - c^2}\)
B. \(\sqrt{a^2 - b^2 + c^2}\)
C. \(\sqrt{a^2 - 2b^2 + c^2}\)
D. \(a - b + c\)
E. \(\sqrt{2a^2 - b^2 + 2c^2}\)
Attachment:
2022-03-28_14-03-45.png [ 10.82 KiB | Viewed 2471 times ]
01 Apr 2022, 04:25
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We aren't given any information about the lengths a, b and c, so the answer must be right for any values a, b and c can have. So we can just imagine a = 0. Then x becomes the length of the rectangle, b becomes the width, and c becomes the diagonal, and by Pythagoras, x^2 + b^2 = c^2, and x = √(c^2 - b^2). Only answer B is equal to √(c^2 - b^2) when a = 0, so it must be right.
That's how I'd do this question on a test like the GMAT. If I had to prove the answer in a math class, I'd do exactly what PyjamaScientist did above, but I've already done that in a similar question so I won't repeat the steps here. It's more work than you need to do for a real GMAT question.
That's how I'd do this question on a test like the GMAT. If I had to prove the answer in a math class, I'd do exactly what PyjamaScientist did above, but I've already done that in a similar question so I won't repeat the steps here. It's more work than you need to do for a real GMAT question.
General Discussion
PyjamaScientist
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01 Apr 2022, 03:37
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Option B.
I drew perpendiculars from E to each sides and used the pythagorus theorem to establish the relation in terms on a, b , c only.
I drew perpendiculars from E to each sides and used the pythagorus theorem to establish the relation in terms on a, b , c only.
