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GMATPrep Test 1 #2_DS Triangles #7

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Source: — Data Sufficiency |
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by Anurag@Gurome » Sun Mar 11, 2012 9:00 pm
kwah wrote:What is the most efficient way to achieve the result for question attached?

Answer: A

Thanks,
K
Angle BDC = Angle BCD implies BD = BC ( equal angles have equal sides opposite to them)
Also, exterior angle ADB = 180 - 2x
Sum of the angles of a triangle = 180 degrees
So, in triangle ADB, x + (180 - 2x) + angle ABD = 180 implies angle ABD = x
Angle ABD = x, which is equal to angle DAB
So, AD = BD implies AD = BD = BC
We have to find BC.

Statement 1: AD = 6 implies AD = BD = BC = 6; SUFFICIENT.

Statement 2: x = 36 implies we know the angles but this does not help to find the length of BC; NOT sufficient.

The correct answer is A.
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by GMATGuruNY » Mon Mar 12, 2012 4:18 am
Image

PLUG IN FOR THE ANGLES to see how they affect each other.
Just be sure to:

-- Satisfy the conditions in the problem.
-- Satisfy the rules of geometry (the sum of angles that form a straight line must be 180, etc.).

Image

The drawings above show two combinations of angles that satisfy the rules of geometry and all of the conditions in the problem.
In each case, angle BAD = angle ABD and angle BDC = angle BCD.
Thus, AD = BD = BC.
Thus, to determine the length of BC, we need to know the length of AD or BD.

Question rephrased: What is the length of AD or BD?

Statement 1: AD = 6.
Sufficient.

Statement 2: x=36.
No information about the any of the lengths.
Insufficient.

The correct answer is A.
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by [email protected] » Sun Mar 18, 2012 5:56 am
By using the exterior angle property, we get the answer as A.

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