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I'm stuck on one step of the explanation offered by GMAT and

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Manager
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I'm stuck on one step of the explanation offered by GMAT and [#permalink] New post 02 May 2007, 19:13
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I'm stuck on one step of the explanation offered by GMAT and hoped someone could help. Please see the attached file for pic of triangle.

In triangle ABC above, what is the length of side BC?
(1) Line segment AD has length of 6.
(2) x = 36

The explanation goes like this:

Angle BDC (2x) is an exterior angle of triangle ADB and therefore is equal to the sum of the two remote interior angles of triangle ADB (i.e. angles ABD and DAB). I follow that...

Quote:
"Thus if angle ABD has measure of y degrees, then x+y=2x, or when simplified, y=x."


WHOA! That's where they lost me...

How can we arbitrarily assign 'x' to one of those remote interior angles? My thinking is that by doing that, we are saying that angle is 1/2 of the measure of the angle we are given. But how do we know that?

I guess what I'm saying is, how do we know that one of the remote interior angles isn't 1.5x and the other angle isn't 0.5x?

Sorry to take so long to get to the point...BTW, the OA is "A".
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Director
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 [#permalink] New post 03 May 2007, 05:30
You are missing something in the file you attached

I have the GMAT quant review and it also says that the measure of angle BAD = x. it's not simply assigned in the solution, it is given in the problem.
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 [#permalink] New post 03 May 2007, 05:37
Here is how I'd approach this problem:

(1) AD = 6
-------------
very obvous, since angles BDC = BCD, then BC = BD
Now,

ABD = z
DBC = y

z+y+3x = 180
x + z + 180 - 2x = 180
-x + z = 0 --> z = x

since BAD = ABD = x = z
then AD = BD = BC = 6

Statement 1 is sufficient


The key is the concept : the sum of the interior angles in a triangle always = 180 degrees.

The sum of angles layed in a stright line = 180 degrees.
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 [#permalink] New post 03 May 2007, 07:24
I'm grateful to Mishari for explaining the answer so clearly. This problem as bothered me as well.

Thanks!
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 [#permalink] New post 03 May 2007, 16:50
Quote:
You are missing something in the file you attached

I have the GMAT quant review and it also says that the measure of angle BAD = x. it's not simply assigned in the solution, it is given in the problem.


Wow, that explains a lot. I went back and checked again. There is no 'x' in the problem or the picture for BAC. I must have gotten a bad copy. Thank you Mishari.
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 [#permalink] New post 18 Jul 2007, 01:05
Wow
I got a bad copy also mavery
This exact same question was baffling me also
So I came online and it's nice to see I have company
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 [#permalink] New post 18 Jul 2007, 07:54
...How can we arbitrarily assign 'x' to one of those remote interior angles? My thinking is that by doing that, we are saying that angle is 1/2 of the measure of the angle we are given. But how do we know that?


Dude, I had the similar issue few days ago. The green book that I have does not mention that in the question but when I saw a similar question on GMatPrep test, I realize that 'x is missing' in the question.
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 [#permalink] New post 12 Aug 2007, 18:20
This explains a lot. I am one of those unfortunate folks too. The angle BAD part was never mentioned in my copy of the book.

I was sure that someone might have discussed the same doubt in the forums. And this forum never disappoints me. Thanks again.
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 [#permalink] New post 24 Aug 2007, 07:51
I've said it before, and I'll say it again... This is a great place to be... I was searching for the exact same problem, as in the OG Green Quant Book (#117 D/S), Angle BAD is blank in the book, but came across the same problem in the GMATPrep software, and Angle BAD is labeled as x. Go figure :-D Cheers all, GMAT in 7 days...
  [#permalink] 24 Aug 2007, 07:51
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