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gurpreet07
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GMAT Prep Geometry 22 Sep 2009, 13:07
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Need help regarding this question..
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GMAT Prep Geometry 22 Sep 2009, 13:45
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A

Statement 1 gives you the measurement of one part. After doing some basic algebra you get the measurement of all angles:

<ADB = 180-2x
<DBC=180-4x
In triangle ABD: x+180-2x+180-4x=180
5x=180
x=36

From this you get that AD=DB and DB=BD = 6

Statement 2 may confuse you since it gives you the value of an angle, and you may subconsciously apply the value of a side from statement 1, which you shouldn't. So statement 2 is not sufficient, but statement 1 is. Answer A
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GMAT Prep Geometry 22 Sep 2009, 13:49
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gurpreet07
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i think there was another question like it?

BD=BC because they have same angles (2x)
say Y= angle ABD
you should know that angle Y+X = 2x since Y+X+180-2x = 180
since Y+X=2X Y has to be X.
Since angle ABD points to side AD and that is 6. side BD pointed by angle BAD is also 6 since it is same angle. this BC=6.
so 1
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GMAT Prep Geometry 22 Sep 2009, 21:53
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arkadiyua and shaselai, thanks to both of you....
for a nice explnation....
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GMAT Prep Geometry 23 Sep 2009, 01:45
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Trgle(BCD) is an isoceles triangle, with sides BD = BC.so statement 1 gives the measure of one of the sides.

So statement 1 alone is suff
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GMAT Prep Geometry 23 Sep 2009, 12:03
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taking diagram we have,
Angle(BDC) = Angle(DAB) + Angle(ABD) (exterior angle is equal to sum of opposite interior angles)
from this we get
2x = x + Angle(ABD)
therefore Angle(ABD) = x

Thus the two sides AD = BD. - eq(1)

Considering triangle(BDC) we have
BD = BC - eq(2)

Thus combining eq(1) and eq(2) we have
AD = BD = BC

Now considering statement 1 alone, given AD = 6, we can find BC since AD = BC
Hence statement 1 alone is sufficient

Now considering statement 2 alone, since we dont have length of any of the sides we cannot find the length of BC using statement 2 alone
Hence statement 2 alone is insufficient

Thus ans is A



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