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14 Sep 2018, 01:52
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (02:23) correct
32%
(02:16)
wrong
based on 35
sessions
History
Date
Time
Result
Not Attempted Yet
In square ABCD above, if DE = 2EB, then the area of the shaded region is what fraction of the area of the square region ABCD?
A. 1/9
B. 2/9
C. 1/6
D. 1/3
E. 2/3
Attachment:
image029.gif [ 1.85 KiB | Viewed 2041 times ]
Updated on: 14 Sep 2018, 02:33
Originally posted by GMATinsight on 14 Sep 2018, 02:06.
Last edited by GMATinsight on 14 Sep 2018, 02:33, edited 1 time in total.
Last edited by GMATinsight on 14 Sep 2018, 02:33, edited 1 time in total.
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Bunuel
Diagonal Divides the square into two equal halfs
DE = 2EB means that bases of similar triangles DBC and DEF are in the ratio 2/3 (Ratio of corresponding sides in similar triangles are equal)
hence ratio of areas of DEF to DBC = (2/3)^2 = 4/9
i.e. DEF = 4/9 of triangle DBC
i.e. Shaded region = (1/2)*(4/9)* Area of square
i.e. Shaded region = (2/9)* Area of square
Answer: Option B
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14 Sep 2018, 02:29
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Bunuel
When two Triangles are Similar. their Area is in the Ratio of the squares of their side.
Hence, \(\frac{Area of Tr. DEF}{Area of Tr. BCD} = \frac{4}{9}\) or
\(\frac{Area of Tr. DEF}{2*Area of Tr. BCD} = \frac{2}{9}\)
Hence, B.
