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This one is driving me nuts. It's from the OG Quantitative [#permalink]
 08 Mar 2006, 20:25
Question Stats:
30% (02:23) correct
70% (03:10) wrong based on 10 sessions
This one is driving me nuts. It's from the OG Quantitative review and the explanation is very vague.
(note that the measure of angles BDC and BCD is 2x degrees)
In triangle ABC above, what is the length of side BC
(1) Line segment AD has length 6.
(2) x =36
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kook44 wrote: This one is driving me nuts. It's from the OG Quantitative review and the explanation is very vague. (note that the measure of angles BDC and BCD is 2x degrees) In triangle ABC above, what is the length of side BC (1) Line segment AD has length 6. (2) x =36 The answer should be "A".
angle DAB = angle DBA = x
this means, ABD is an isosceles triangle
=> AD = BD
but it's given in the figure that, BD = BC (BDC is also an isosceles triangle)
=> AD=BD=BC=6
Is it clear?
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vivek123 wrote: kook44 wrote: This one is driving me nuts. It's from the OG Quantitative review and the explanation is very vague. (note that the measure of angles BDC and BCD is 2x degrees) In triangle ABC above, what is the length of side BC (1) Line segment AD has length 6. (2) x =36 The answer should be "A". angle DAB = angle DBA = x this means, ABD is an isosceles triangle => AD = BD but it's given in the figure that, BD = BC (BDC is also an isosceles triangle) => AD=BD=BC=6 Is it clear? For me it is not clear how do you assume that DAB = DBA.... It is actually the essiantial info in answering this question. I tried to prove it but didn't find the way.
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I think, I made a mistake.
We can't say "angle DAB = angle DBA = x"
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One of the properties on the exterior angle of any triangle is:
in this case Angle BDC (exterior angle of triangle ADB) = Angle DAB +Angle DBA. Which translates to 2x = x+x. Hence Angle, DAB=Angle DBA. This is not an assumption. Since both the angles are x degrees, they are equal. Hence, AD=DB and we already know that BD =DC.
I hope this is more clear Kook.
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Gordon & Vivek, you are both right, the OA is A. However, you are both assuming the one part of the explanation that I dont understand. I understand the property that an exterior angle of a triangle is equal to the sum od the two remote interior angles so angle BDC = 2x, therefore, 2x = DAB + DBA. But how do we know they are both equal????
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Gordon wrote: One of the properties on the exterior angle of any triangle is:
in this case Angle BDC (exterior angle of triangle ADB) = Angle DAB +Angle DBA. Which translates to 2x = x+x. Hence Angle, DAB=Angle DBA. This is not an assumption. Since both the angles are x degrees, they are equal. Hence, AD=DB and we already know that BD =DC.
I hope this is more clear Kook.
Gordon, this can't be assumed unless it is given. What if 2x = 0.5x+1.5x?
kook44,
Are we missing anything in the question itself?
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vivek123 wrote:
Gordon, this can't be assumed unless it is given. What if 2x = 0.5x+1.5x?
kook44,
Are we missing anything in the question itself?
I agree with you - that's why I can't see the solution. And no - the is nothing missing from the question (maybe there is a typo in the guide???). Its #117 in the OG Quantitative Review.
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I think based on this answer should be E.
What you guys think?????
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I am stuck at: 2x = angle BAD + angle DBA
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2x is the exterior angle for the triangle BAD.
From the property of triangles,
Exterior angle = Sum of the opposite interior angles.
Hence, 2x = angle DBA + angle BAD
But, 2x = x + x or 1.9x+0.1x or 1.2x+0.8x , etc....
Hence, we can't say that AD = BD
So, 1st statement AD=6 is not of help.
2nd statement gives the angles of triangle BDC but unless we have atleast one side length, we can't calculate the length of BC.
Combining them also does not give the length BC as side AD does not
belong to triangle BDC.
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SAILAJA KATTUBADI
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I really think there is a typo in the guide, and one of the angles BAD or ABD was intended to have been labeled explicitly as "x". Then it would all make sense.
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That makes sense..I must check. agree with sailaja and the rest on E though.
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I had this problem in the first GMATprep practice test and they labelled angle DAB as 'x'.
From there you can solve triangle DAB is isoceles.
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Pennyarcade wrote: I had this problem in the first GMATprep practice test and they labelled angle DAB as 'x'.
From there you can solve triangle DAB is isoceles.
Thanks pennyarcade, that makes me feel good and bad. Good because now I know that the problem was not above my ability, and bad because, from GMAC's website:
"There is no overlap between questions found in the Official Guide for GMAT® Review, 11th Edition, the Official Guide for GMAT® Quantitative Review, the Official Guide for GMAT® Verbal Review, and GMAT® Prep."
http://www.mba.com/mba/Store/products/PreparefortheGMAT/officialguidequantitativereview.htm
also - who knows how many other typos are in the guide...
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I can't find value of BC applying any theorems my ancestors had invented!!
I will go for E.
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Answer should be E. I saw this one in the OG and had a problem with it as well. I believe the OA given is not correct, typo.
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the answer will be A ,, I got this prob on gmatprep test today .i marked E . post reading this post its clear to me that it is A :
now Angl A = X
Angl BDC =2X
Angl DCB =2X
NOW WE KNOW 2X=X + Angl ABD
=> Angl ABD = 2X-X = X
SO AD=BD
STMT1 GVN AD=6 THEN BD=6
GVN BD=BC
HENSE AD=BD=BC=6
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The answer has to be E from my perspective  Posted from GMAT ToolKit
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Fairness wrote: The answer has to be E from my perspective Posted from GMAT ToolKitBelow is correct form of this question. Note that angle BAC equals to x degrees. Attachment: 
trig2uc8.png [ 9.64 KiB | Viewed 819 times ]
In triangle ABC above, what is the length of side BC? As <BDC=<BCD then the BD=BC. Also as <ADB=180-2x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(180-2x)+<ABD=180 --> <ABD=x. Now, we have that <ABD=x=<DAB so AD=BD --> AD=BD=BC. Question: BC=? (1) Line segment AD has length 6 --> AD=BD=BC=6. Sufficient. (2) x = 36 --> we know only angles which is insufficient to get the length of any line segment. Answer: A.
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