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14 May 2017, 11:57
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:20) correct
30%
(01:40)
wrong
based on 123
sessions
History
Date
Time
Result
Not Attempted Yet
The triangle above has side DC of the square as its base. What is the area of the shaded region?
(1) DM = 5
(2) M is the midpoint of side AB
Attachment:
2017-05-14_2254.png [ 7.06 KiB | Viewed 6232 times ]
15 May 2017, 00:04
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St1: DM = 5 --> Clearly insufficient as we do not know any other information about the triangle.
St2: M is the midpoint --> Drop a perpendicular from M to DC. We can get to know that the 4 resulting triangles are congruent.
Area of shaded region = Area of MCD
We do not have any data on the sides of the square or triangle.
Not Sufficient.
Combing St1 and St2; MD^2 = a^2 + a^2/4
25 = 5a^2/4 --> a^2 = 20
Area of shaded region = a^2/2 = 10
Answer: C
St2: M is the midpoint --> Drop a perpendicular from M to DC. We can get to know that the 4 resulting triangles are congruent.
Area of shaded region = Area of MCD
We do not have any data on the sides of the square or triangle.
Not Sufficient.
Combing St1 and St2; MD^2 = a^2 + a^2/4
25 = 5a^2/4 --> a^2 = 20
Area of shaded region = a^2/2 = 10
Answer: C
Attachments
IMG_20170515_123125.jpg [ 1.17 MiB | Viewed 5823 times ]
15 May 2017, 05:35
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Bunuel
The shaded region = Area of square - Area of Triangle CDM = ?
Statement 1: DM = 5
This statement doesn't help us find the area of triangle or area of the square hence
NOT SUFFICIENT
Statement 2: M is the midpoint of side AB
This statement doesn't help us find the area of triangle or area of the square hence
NOT SUFFICIENT
Combining the two statements
Since M is the midpoint so triangle DMC becomes an isosceles triangle with height equal to the base
Now using pythagorus theorem both base and height which inturn are equal to the side of the square can be calculated leading to area of both square and triangle hence
SUFFICIENT
Answer: option C
