January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431

In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
03 Mar 2014, 23:20
Question Stats:
58% (01:54) correct 42% (02:21) wrong based on 903 sessions
HideShow timer Statistics
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:
Untitled.png [ 14.63 KiB  Viewed 12179 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
03 Mar 2014, 23:21




Intern
Joined: 02 Oct 2013
Posts: 10

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
05 Mar 2014, 21:39
Is there a way to tell if D is the bisector of AC?
Posted from my mobile device



Manager
Joined: 09 Nov 2013
Posts: 71

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
05 Mar 2014, 23:03
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



Intern
Status: Never Give up!!!
Joined: 02 Aug 2012
Posts: 47
Location: India
Concentration: Finance, General Management

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
05 Mar 2014, 23:49
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)



Intern
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 16
Location: Netherlands
Concentration: Strategy, International Business
GMAT 1: 470 Q37 V18 GMAT 2: 570 Q36 V32 GMAT 3: 560 Q37 V30 GMAT 4: 610 Q41 V34

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
23 Apr 2014, 05:53
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.
_________________
Structural persistence is the key to succes . Party hard, study harder.
Still bashing, will continue to do so , although it's important to chill aswell ; ) STUDY+CHILL=VICTORY



Manager
Joined: 26 Feb 2015
Posts: 115

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
17 May 2015, 06:56
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?



Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
18 May 2015, 03:33
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 10 Mar 2013
Posts: 503
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
12 Jul 2015, 03:07
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 ??
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



CEO
Joined: 20 Mar 2014
Posts: 2636
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
12 Jul 2015, 03:36
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.



Manager
Joined: 18 Aug 2006
Posts: 87
Location: United States
WE: Consulting (Telecommunications)

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
05 Sep 2015, 16:09
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?



Intern
Joined: 08 May 2016
Posts: 28
Location: United States
WE: Project Management (Aerospace and Defense)

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
18 Nov 2016, 11:13
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.
_________________
What's your totem?



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 535
Location: India

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
23 Feb 2017, 04:44
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
_________________
GMAT Mentors



NonHuman User
Joined: 09 Sep 2013
Posts: 9463

Re: In triangle ABC above, what is the length of side BC?
[#permalink]
Show Tags
23 Feb 2018, 14:15
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In triangle ABC above, what is the length of side BC? &nbs
[#permalink]
23 Feb 2018, 14:15






