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09 Dec 2014, 15:39
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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:
45%
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64% (01:41) correct
36%
(01:38)
wrong
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In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC
Attachment:
triang ABCD.JPG [ 3.38 KiB | Viewed 24973 times ]
ENGRTOMBA2018
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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25 Jul 2015, 05:00
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Bunuel
Tough and Tricky questions: Geometry.
In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC
Kudos for a correct solution.
Attachment:
The attachment triang ABCD.JPG is no longer available
Per statement 1, Area Triangle (BAD} = Area Triangle {BDC}
---> 0.5*BE*AD = 0.5*BE*CD ---> AD = CD . But no information about AB and BC. Thus this triangle may or may not be isosceles. Thus this statement is not sufficient.
Per statement 2, BD┴AC and AD = DC ---> Triangles BDA and BDC are congruent. ---> AB = BC ---> Triangle ABC is isosceles. Thus this statement is sufficient.
B is the correct answer.
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2015-07-25_7-55-54.jpg [ 20.54 KiB | Viewed 22242 times ]
09 Dec 2014, 20:53
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Statement 1: The area of triangular region ABD is equal to the area of triangular region DBC.
This means that the point D is mid-point of AC. But, we can't still say whether the triangle ABC is isosceles or not. Insufficient.
Statement 2: BD┴AC and AD = DC. Signifies that the median drawn from the vertex B is a perpendicular bisector. This can only happen if the triangle is isosceles triangle with AB = BC. Sufficient
The answer should be B
This means that the point D is mid-point of AC. But, we can't still say whether the triangle ABC is isosceles or not. Insufficient.
Statement 2: BD┴AC and AD = DC. Signifies that the median drawn from the vertex B is a perpendicular bisector. This can only happen if the triangle is isosceles triangle with AB = BC. Sufficient
The answer should be B
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