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In triangle ABC above, what is the length of side BC?
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04 Mar 2014, 00:20
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In triangle ABC above, what is the length of side BC? (1) Line segment AD has length 6. (2) x = 36 The Official Guide For GMAT® Quantitative Review, 2ND EditionAttachment:
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Re: In triangle ABC above, what is the length of side BC?
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04 Mar 2014, 00:21
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.
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Re: In triangle ABC above, what is the length of side BC?
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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?
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23 Apr 2014, 14:31
Why is AD=BD=BC? If AD is opposite to X, BD opposite to X as well and BC opposite to 2x? Shouldn't BC be larger than both or equal to both TOGETHER? Thanks for clarifying Cheers! J



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Re: In triangle ABC above, what is the length of side BC?
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23 Apr 2014, 22:48
jlgdr wrote: Why is AD=BD=BC? If AD is opposite to X, BD opposite to X as well and BC opposite to 2x? Shouldn't BC be larger than both or equal to both TOGETHER? Thanks for clarifying Cheers! J Yes but they are sides of different triangles. Note that by the same logic, BD is opposite to 2x as well. The point is that it is opposite to x in one triangle (ABD) and opposite to 2x in another triangle (BDC). BC will be equal to BD because they are both opposite 2x in triangle BDC. AD will be equal to BD because they are both opposite angle x in triangle ABD. So AD = BD = BC
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Re: In triangle ABC above, what is the length of side BC?
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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?
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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?
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29 Jan 2016, 11:07
Bunuel wrote: Attachment: trig2uc8.png In triangle ABC above, what is the length of side BC? As <BDC=<BCD then the BD=BC. Also as <ADB=1802x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(1802x)+<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. Why did you assume that ADC is a straight line. Because if it isint given specifically in the question then the entire logic fails. then angle BDA and BDC are not supplementary.



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Re: In triangle ABC above, what is the length of side BC?
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30 Jan 2016, 02:41
kritika90 wrote: Bunuel wrote: Attachment: trig2uc8.png In triangle ABC above, what is the length of side BC? As <BDC=<BCD then the BD=BC. Also as <ADB=1802x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(1802x)+<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. Why did you assume that ADC is a straight line. Because if it isint given specifically in the question then the entire logic fails. then angle BDA and BDC are not supplementary. OFFICIAL GUIDE:Problem SolvingFigures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. Data Sufficiency:Figures:• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). • Lines shown as straight are straight, and lines that appear jagged are also straight.• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. • All figures lie in a plane unless otherwise indicated.
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Re: In triangle ABC above, what is the length of side BC?
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01 Feb 2016, 00:56
kritika90 wrote: Bunuel wrote: Attachment: trig2uc8.png In triangle ABC above, what is the length of side BC? As <BDC=<BCD then the BD=BC. Also as <ADB=1802x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(1802x)+<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. Why did you assume that ADC is a straight line. Because if it isint given specifically in the question then the entire logic fails. then angle BDA and BDC are not supplementary. The lines that appear straight are straight. Also ABC is a triangle (given). So AC is a straight line. D is a point on AC and we have been given the measure of angle BDC as 2x. Hence there is no ambiguity here.
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Re: In triangle ABC above, what is the length of side BC?
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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?
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11 Mar 2018, 03:37
I'm not getting the concept underlying this problem. Could anyone please clarify me that and refer to a particular topic from any book/blog/website to learn this. Thanks . Bunuel mikemcgarry VeritasPrepKarishma



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Re: In triangle ABC above, what is the length of side BC?
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11 Mar 2018, 03:50
sadikabid27 wrote: I'm not getting the concept underlying this problem. Could anyone please clarify me that and refer to a particular topic from any book/blog/website to learn this. Thanks . Hey sadikabid27 , Let me explain you. We need to find out the length of BC. We already know that BD = BC because triangle BDC is isosceles. (1) Also, angle ABD + angle BAD = angle BDC ( Sum of interior opposite angles = Exterior angle.) => angle ABD = 2x  x = x. => Triangle BDA is also isosceles. => AD= BD (2) from (1) and (2), we can say AD = BC. Now option A is giving us AD, Hence the value will be same for BC. Hence, sufficient. Option B isn't giving us any length. Hence, insufficient. Does that make sense?
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Re: In triangle ABC above, what is the length of side BC?
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11 Mar 2018, 04:00
Thanks for your fast response abhimahna. Maybe, it's very silly of me but I'm not getting these steps "Also, angle ABD + angle BAD = angle BDC ( Sum of interior opposite angles = Exterior angle.) => angle ABD = 2x  x = x. => Triangle BDA is also isosceles"



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Re: In triangle ABC above, what is the length of side BC?
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11 Mar 2018, 04:07
sadikabid27 wrote: Thanks for your fast response abhimahna. Maybe, it's very silly of me but I'm not getting these steps "Also, angle ABD + angle BAD = angle BDC ( Sum of interior opposite angles = Exterior angle.) => angle ABD = 2x  x = x. => Triangle BDA is also isosceles" Hey sadikabid27 , You need to learn the properties of the triangles. One of the properties says : The exterior angle of a triangle is always equal to the sum of the two opposite interior angles. Check this image: Attachment:
Untitled.gif [ 2.64 KiB  Viewed 5128 times ]
Does that make sense?
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Re: In triangle ABC above, what is the length of side BC?
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11 Mar 2018, 23:53
sadikabid27 wrote: I'm not getting the concept underlying this problem. Could anyone please clarify me that and refer to a particular topic from any book/blog/website to learn this. Thanks . Bunuel mikemcgarry VeritasPrepKarishmaThere are two Geometry concepts being tested here: 1. If two angles of a triangle are equal, sides opposite to them are equal too (isosceles triangle). 2. Measure of the exterior angle is the sum of interior opposite angles. Check this: https://mathbitsnotebook.com/Geometry/S ... Angle.htmlEven if you don't know the theorem (point 2), you can easily derive it. The exterior angle BDC makes a straight angle with BDA so their sum will be 180. BDC + BDA = 180 Also, DAB + ABD + BDA = 180 ( sum of angles of a triangle) BDC + BDA = DAB + ABD + BDA BDC = DAB + ABD
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Re: In triangle ABC above, what is the length of side BC?
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11 Feb 2019, 10:29
Bunuel wrote: 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 Target question: What is the length of side BC? Statement 1: Line segment AD has length 6. BEFORE we deal with statement 1, let's see what information we can add to the diagram. For example, since ∆BDC has 2 equal angles (of 2x°), we know that side BD = side BC: Next, since angles on a line add to 180°, and since ∠BDC = 2x°, we know that ∠ADB = (180  2x)° Now focus on ∆BAD Since angles in a triangle add to 180°, we know that ∠ABD = x° ASIDE: Notice that x° + x° + (180  2x)° = 180° Now that we know ∆BAD has two equal angles (x° and x°), we know that side AD = side BD This means AD = BD = BCStatement 1 tells us that AD = 6, which means BC = 6The answer to the target question is side BC has length 6Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: x = 36Notice that our diagram doesn't any lengths. We can SHRINK or ENLARGE the diagram and the angles remain the same. However the length of side BC changes. Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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