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In triangle ABC above, what is the length of side BC? [#permalink]
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04 Mar 2014, 00:20
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIn triangle ABC above, what is the length of side BC? (1) Line segment AD has length 6. (2) x = 36 Data Sufficiency Question: 123 Category: Geometry Triangles Page: 162 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! Attachment:
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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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04 Mar 2014, 00:21



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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05 Mar 2014, 22:39
Is there a way to tell if D is the bisector of AC?
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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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06 Mar 2014, 00:03
angle ABD =x, so AD=DB=BC, A is Sufficient B gives only angle values and only angle values can not give length of any side
only A is suff



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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06 Mar 2014, 00:49
Given data: In Triangle ABC: Angle A+ Angle ABC + Angle C = 180 Thus Angle B = 1803x
In Triangle DBC: Angle D + Angle DBC + Angle C = 180 Thus Angle DBC = 180  4x
Thus Angle ABD = Angle ABC  Angle DBC = 180  3x  (180  4x) = x
In Triangle ABD Angle ABD = Angle A = x Thus the opposite sides are equal. i.e AD = DB ....1
From Triangle DBC Since Angle D = Angle C BD = BC .....2
From 1 and 2: AD=BD=BC Question value of BC? Thus if we find the value of either AD or BD we can get value of BC.
St1 :AD=6 There is our answer. Since BC=AD this BC = 6. Statement is sufficient.
St2 : x=36 From this angle value we cant get the value of any line segment. hence it is insufficient.
THus answer  Option (A)



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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23 Apr 2014, 06:53
I solved this question in the following way: At first sight you must see that <DBC and <CDB have the same angle. So the length of BD must be equal to BC. The rephrased question is then as followings: What is BD?First analyse the given picture as 1 triangle (ABC)The angle of B would be : 180  Angle A  Angle C = 180  3x Secondly look at the triangle (BCD).The angle of B would be now: 180  Angle C  Angle D = 180  4x To find the the Angle of B in the Triangle of ABD , subtract these two equations:180  3x  180 4x(=+)= x Since Angle <ABD = <BDA The length of AD must be equal to BD. ( Because they have the same angle ) AD=BD=BC If you know the length of AD or BD , you have sufficient information to answer the question. (1) Sufficient , you now know the length of AD. (2) You know nothing about any length , clearly insufficient.
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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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17 May 2015, 07:56
Bunuel wrote: SOLUTIONIn triangle ABC above, what is the length of side BC?Since <BDC = <BCD then the BD=BC. Also, since <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. Hey, great explaination, thanks. Question: Is it the case that whenever angles are equal, their sides must equal? Is there no exception where angle a \(=\) angle b but length a \(=/=\) length b?



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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18 May 2015, 04:33
erikvm wrote: Bunuel wrote: SOLUTIONIn triangle ABC above, what is the length of side BC?Since <BDC = <BCD then the BD=BC. Also, since <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. Hey, great explaination, thanks. Question: Is it the case that whenever angles are equal, their sides must equal? Is there no exception where angle a \(=\) angle b but length a \(=/=\) length b? Yes, the base angles of an isosceles triangle are always equal and viseversa: if two angles in a triangle are equal then it's an isosceles triangle.
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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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12 Jul 2015, 04:07
Hi All, I solved it the same way as Bunuel stated... so after some rearangements for St1 it's sufficient to know that ad=6, and St2 is not sufficient, because we have only degrees and we need length... But after solving this question I have still one question: we say that AD=BD, but how can it be that a side opposite to a smaller angle X° is equal to the side opposite to a larger angle 2X° (BCD), istn't it a bit weird ??
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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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12 Jul 2015, 04:36
BrainLab wrote: Hi All, I solved it the same way as Bunuel stated... so after some rearangements for St1 it's sufficient to know that ad=6, and St2 is not sufficient, because we have only degrees and we need length...
But after solving this question I have still one question: we say that AD=BD, but how can it be that a side opposite to a smaller angle X° is equal to the side opposite to a larger angle 2X° (BCD), istn't it a bit weird ?? IMO, your statement of side opposite x deg will be smaller than the side opposite 2x degrees is ONLY applicable for the same triangle. I can have 2 different triangles with x and 2x degrees and the corresponding 'opposite' sides still being the same (I can modify the other angles or the proportion of the other 2 sides to counter the effect of the additional 'x' degrees!) But an interesting question.



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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05 Sep 2015, 17:09
Only 55% got right ( at time of writing) and average time for solving it right is 2:20. A similar performing question else where is generally 95% hard and is 700 range question.
How is the difficulty decided?



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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18 Nov 2016, 12:13
Engr2012 wrote: BrainLab wrote: Hi All, I solved it the same way as Bunuel stated... so after some rearangements for St1 it's sufficient to know that ad=6, and St2 is not sufficient, because we have only degrees and we need length...
But after solving this question I have still one question: we say that AD=BD, but how can it be that a side opposite to a smaller angle X° is equal to the side opposite to a larger angle 2X° (BCD), istn't it a bit weird ?? IMO, your statement of side opposite x deg will be smaller than the side opposite 2x degrees is ONLY applicable for the same triangle. I can have 2 different triangles with x and 2x degrees and the corresponding 'opposite' sides still being the same (I can modify the other angles or the proportion of the other 2 sides to counter the effect of the additional 'x' degrees!) But an interesting question. Had the same question as brainlab did. That was throwing me off.
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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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23 Feb 2017, 05:44
PROMPT ANALYSIS
The figure has angle BAD =x, angle BDC =2x, angle BCD = 2x.
Super set The side length of BC could be any positive real number.
Translation Since Angle BAD + Angle ABD = Angle BDC therefore angle ABD = x. Hence triangle ABD and triangle BDC are isosceles triangles. Hence AD = BD = BC. In order to find the length of BC we need: 1# exact value of BC. 2# relation or property that will lead us to find the length of BC.
Statement analysis St 1: AD = 6. Since AD = BD = BC, therefore BC = 6 ANSWER. Option b, c and e. St 2: x =36. Since there is no idea about any side of the the figure, therefore it is insufficient.
Hence option A



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Re: In triangle ABC above, what is the length of side BC? [#permalink]
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