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Triangles- Geometry- GMATPrep 1 question

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Source: — Data Sufficiency |
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by niketdoshi123 » Thu Jul 12, 2012 9:11 am
Mjkourtis wrote:See attachment for the figure.

What is BC?
(i) AD= 6
(ii) x=36
Consider triangle ABC
angle(B) = 180 - angle(A) - angle(C)
=> angle(B) = 180 - x - 2x = 180 - 3x
and angle(B) = angle(b1) + angle(b2)

Now, consider triangle DBC

angle(b1) = 180 - angle(d) - angle(C)
angle(b1) = 180 -2x -2x = 180 - 4x

angle(B) = angle(b1) + angle(b2)
180 - 3x = 180 - 4x + angle(b2)
=>angle(b2) = x

So, angle(A) = angle(b2) = x
Hence, ABD is an isosceles triangle with sides AD = BD

and we know that BD = BC
so AD = BD = BC

Statement 1 SUFFICIENT
As AD = 6 = BC

Statement 2 INSUFFICIENT

No information about the length of BC is provided.

Hence the answer is A
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by Brent@GMATPrepNow » Sat Jul 14, 2012 6:14 am
I should point out that, in the original question, we are not told that x=36. This is given in statement 2.
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by Brent@GMATPrepNow » Sat Jul 14, 2012 6:17 am
Here's a free video that features tips for handling Data Sufficiency questions involving Geometry:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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