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DS - Geometry.

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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Sep 07, 2011 2:11 pm
Image
Statement 1: BD = 6√3.
Draw a 30-60-90 triangle:
Image

∆EBD is a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are proportioned x : x√3 : 2x.
In ∆EBD, 2x = 6√3.
Thus, EB = 3√3 and and ED = 3√3 * √3 = 9.

Since ED = 9, EC = 9-6 = 3.
In ∆EBC the legs are 3 and 3√3, indicating that ∆EBC also is a 30-60-90 triangle with a hypotenuse of 6.
Thus, BC = 6.
Sufficient.

Statement 2: x=60.
x=60 will yield the same drawing shown in statement 1.
Thus, the same reasoning can be used to determine that BC = 6.
Sufficient.

The correct answer is D.
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by pm » Thu Sep 08, 2011 3:16 am
Mitch,

Does every isosceles 30-30-120 triangle follows 1-1-2Root3 property?
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by GMATGuruNY » Thu Sep 08, 2011 3:38 am
pm wrote:Mitch,

Does every isosceles 30-30-120 triangle follows 1-1-2Root3 property?
The sides of a 30-30-120 triangle are proportioned x : x : x√3.

Image

In my solution to the problem posted above, the 30-30-120 triangle has sides 6, 6 and 6√3.
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by pm » Thu Sep 08, 2011 3:42 am
Thank you Mitch.
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by prateek_guy2004 » Thu Sep 08, 2011 9:06 am
We have one side of a triangle .

What do we need another side to answer the ques.

Statement 1----Clearly mentions thats.

Suff

statement 2-----Tells us x= 60 now its in a straight line so 60 -x= 180

Suff

Hence IMOD
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