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OG quant DS geometry - ?Mistake

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OG quant DS geometry - ?Mistake [#permalink] New post 20 Aug 2006, 11:17
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Hi,

I've just been finishing the OG quant book and stumbled across this problem - would appreciate your help.

In triangle ABC below (excuse drawing), what is the length of side BC?

1) Line segment AD has length 6

2) X = 36
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 [#permalink] New post 20 Aug 2006, 14:02
1) Insuff. Gives us AD but nothing else.

2) Insuff. Gives us 2(36) = 72, BC = BD. Opposite angle of D is 108. Tells us Angle B in second triangle is 36 but tells us nothing about corresponding angle in the first triangle - do they combine to - 90? We have no way of knowing that angle value.

Combined - Insuff.

E?
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 [#permalink] New post 20 Aug 2006, 14:07
Ahh this is a weird rule....1) is suff because the remote interior angles of triangle A = the remote exterior angle 2x.

So knowing that AD = 6. and AD = DB. Also, we know DB = BC so suff.

I didnt know this.
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 [#permalink] New post 20 Aug 2006, 14:15
Well that's what I thought but here's what the solution says:

Answer = A

Solution:
The degreee measure of an exterior angle of a triangle is equal to the sum of the remote interior angles. Note that angle BDC (with an angle measure of 2x) is an exterior angle of triangle ADB and has an angle measure equal to the sum of the remote interior angles ABD and DAB. Thus, if the angle ABD has measure y degrees, then x+y = 2x, or when simplified, y = x. Since two angles of triangle ABD are equal, then the sides opposite these angles have the same length and AD=DB. For the same reason DB=BC. If AD = DB and DB = BC, then AD = BC.

1) If AD = 6, then BC must also equal 6;
SUFFICIENT

?????? Can anyone help????????

I dont understand how it gets x+y = 2x?
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 [#permalink] New post 20 Aug 2006, 14:20
I understand the whole remote interior angle rule but isn't that just saying that the sum of angles ABD + DAB = 2x. It seems that it is then assuming that angles ABD and DAB are equal!?!?

From the information we're given we dont know that AD = BD
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 [#permalink] New post 20 Aug 2006, 14:34
There's a typo in the book. I know this for a fact.
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 [#permalink] New post 20 Aug 2006, 15:41
Can anyone tell me what the OG quant book is?
Thanks
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 [#permalink] New post 20 Aug 2006, 17:14
GMAT Officiant Guide Quantitative Review
  [#permalink] 20 Aug 2006, 17:14
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