It is currently 17 Nov 2017, 14:21

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In triangle ABC above, what is the length of side BC?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

6 KUDOS received
Manager
Manager
avatar
Joined: 07 Feb 2010
Posts: 155

Kudos [?]: 767 [6], given: 101

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

Show Tags

New post 21 Dec 2010, 08:17
6
This post received
KUDOS
16
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (01:08) correct 41% (01:17) wrong based on 752 sessions

HideShow timer Statistics

Image
In triangle ABC above, what is the length of side BC?

(1) Line segment AD has length 6
(2) x = 36

[Reveal] Spoiler:
Attachment:
trig2uc8.png
trig2uc8.png [ 9.64 KiB | Viewed 40792 times ]
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Oct 2017, 09:40, edited 2 times in total.
Edited the question and added the image

Kudos [?]: 767 [6], given: 101

Expert Post
13 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132509 [13], given: 12323

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

Show Tags

New post 21 Dec 2010, 08:31
13
This post received
KUDOS
Expert's post
16
This post was
BOOKMARKED
Attachment:
trig2uc8.png
trig2uc8.png [ 9.64 KiB | Viewed 41604 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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132509 [13], given: 12323

Senior Manager
Senior Manager
avatar
Joined: 28 Dec 2010
Posts: 323

Kudos [?]: 267 [0], given: 33

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

Show Tags

New post 26 Feb 2011, 22:07
the one point that puzzles me is how did you get /BAD = x ?

Kudos [?]: 267 [0], given: 33

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132509 [1], given: 12323

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

Show Tags

New post 27 Feb 2011, 00:52
1
This post received
KUDOS
Expert's post

Kudos [?]: 132509 [1], given: 12323

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 12 Oct 2011
Posts: 255

Kudos [?]: 63 [2], given: 110

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

Show Tags

New post 23 Jan 2012, 00:36
2
This post received
KUDOS
The question asks the length of side BC. From the figure, you can see that triangle BDC is an isosceles triangle with BD = BC. Thus, to know the length of BC, it is okay if we know the length of BD.

Statement 1:
To solve such problems, you have to know that in a triangle, the measure of the exterior angle is equal to the sum of the two non-adjacent angles of the triangle.

That is, in the given figure, for triangle ABD, angle BDC is the exterior angle. Thus, BDC = ABD + BAD
That is, 2x = ABD + x. Thus ABD = x.

Now, you can see that triangle ABD is an isosceles triangle in which AD = BD = 6. Thus, BD = BC = 6. SUFFICIENT

Statement 2:
x = 36 does not tell you anything about the length of any side. INSUFFICIENT

Answer: A
_________________

Consider KUDOS if you feel the effort's worth it

Kudos [?]: 63 [2], given: 110

Intern
Intern
avatar
Joined: 16 Dec 2011
Posts: 46

Kudos [?]: 7 [0], given: 12

GMAT Date: 04-23-2012
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 25 Jan 2012, 10:45
yeah its A. Bcoz B can only help us to find angle measure but no way we can fund side measrue from there .

so clearly A

Kudos [?]: 7 [0], given: 12

Senior Manager
Senior Manager
avatar
Joined: 08 Jun 2010
Posts: 387

Kudos [?]: 102 [0], given: 13

Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 20 Mar 2012, 19:09
Using Similar triangles we know that
1) BD = BC (angle BDC = angle BCD)
2) We know angle BDA = 180-2x which means angle ABD = x
3) So, from the second similar triangle we know that angle BAD = angle ABD = x
4) Using similar triangles again; AD = BD
5) Combing 1 and 4; AD = BD = BC.

So, A is sufficient.

We don't really need the angle at all.

Kudos [?]: 102 [0], given: 13

Manager
Manager
User avatar
Joined: 28 Jul 2011
Posts: 233

Kudos [?]: 161 [0], given: 16

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

Show Tags

New post 04 Apr 2012, 07:01
A

we know BD = BC

(A) AD = 6

angle ADB = 180 - 2x


triangle ADB = (180-2x) + x + angle ABD

180 = 180 - 2x + x + angle ABD
x = angle ABD

therefore AD = BD = BC = 6

(B) x = 36
using this information we can only derive that AD = BD = BC , but we dont know value of side

Kudos [?]: 161 [0], given: 16

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 740 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 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 :)

Kudos [?]: 740 [0], given: 355

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17766 [1], given: 235

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

Show Tags

New post 23 Apr 2014, 22:48
1
This post received
KUDOS
Expert's post
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
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17766 [1], given: 235

Intern
Intern
User avatar
Joined: 24 Aug 2015
Posts: 8

Kudos [?]: 2 [0], given: 0

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

Show Tags

New post 30 Sep 2015, 12:50
I'm sorry guys but the answer does not make sense at all!!

<BDC = <BCD ( I got this)
<ADB = 180 - 2x (I got this)
The sum of this triangle is 180

180 = x + (180-2x) + <ABD

now I'm confused. How did you come up with <ABD is equal to x??????? Even if we substitute <ABD with x, thus would be:

180 = x + 180-2x + x
180 = 2x -2x +180
180 = 180

Kudos [?]: 2 [0], given: 0

Manager
Manager
avatar
Joined: 01 Jan 2015
Posts: 63

Kudos [?]: 93 [0], given: 14

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

Show Tags

New post 30 Sep 2015, 13:10
blendercroix wrote:
I'm sorry guys but the answer does not make sense at all!!

<BDC = <BCD ( I got this)
<ADB = 180 - 2x (I got this)
The sum of this triangle is 180

180 = x + (180-2x) + <ABD

now I'm confused. How did you come up with <ABD is equal to x??????? Even if we substitute <ABD with x, thus would be:

180 = x + 180-2x + x
180 = 2x -2x +180
180 = 180


The sum of two non-adjacent interior angles of a triangle is always equal to the measure of an exterior angle of a triangle. Even if you didn't know this property, say <ABD is y, so now we have <BAD is x, <ABD is y and <BDA is 180-2x. The sum of the interior angles of a triangle must sum to 180 degrees. So we have x+y+180-2x=180-->y=x

Kudos [?]: 93 [0], given: 14

1 KUDOS received
Intern
Intern
User avatar
Joined: 09 Apr 2015
Posts: 15

Kudos [?]: 20 [1], given: 26

Location: United States
Concentration: Marketing, International Business
GMAT 1: 740 Q49 V42
WE: Sales (Consulting)
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 08 Oct 2015, 11:26
1
This post received
KUDOS
Just another take on the question. Experts can correct me.

< BAD is x and < BDC is 2x. It means triangle ABC can be considered as a triangle circumscribed in a circle with D as its center.
Hence, AD = DC = DB, the radius of the circle. Also, BD = BC (opposite to equal angles.)

Hence the length of AD is enough to answer the question. Choice A
_________________

Kudos Please
if you find my question / solution helpful.

Kudos [?]: 20 [1], given: 26

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 591

Kudos [?]: 476 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 11 Jan 2016, 13:50
anilnandyala wrote:
Attachment:
trig2uc8.png
In triangle ABC above, what is the length of side BC?

(1) Line segment AD has length 6
(2) x = 36


<BDC=2x and is the exterior angle for the triangle ABD, hence <ABD=x. AD=BD=BC

let's start with statement 2, as it's easier to evaluate.

(2) x=36, clearly not sufficient.
(1) <BDC=2x and is the exterior angle for the triangle ABD, hence <ABD=x. AD=BD=BC=6. Sufficient

Answer A
_________________

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

Kudos [?]: 476 [0], given: 200

Intern
Intern
avatar
Joined: 05 Feb 2014
Posts: 3

Kudos [?]: 5 [0], given: 27

Location: United States
Concentration: Finance, Other
WE: Law (Law)
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 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=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.


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.

Kudos [?]: 5 [0], given: 27

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132509 [0], given: 12323

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

Show Tags

New post 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=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.


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 Solving
Figures: 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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132509 [0], given: 12323

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17766 [1], given: 235

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

Show Tags

New post 01 Feb 2016, 00:56
1
This post received
KUDOS
Expert's post
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=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.


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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17766 [1], given: 235

Intern
Intern
User avatar
Joined: 18 Jul 2015
Posts: 43

Kudos [?]: 13 [0], given: 33

Location: Brazil
Concentration: General Management, Strategy
GMAT 1: 640 Q39 V38
GMAT 2: 700 Q47 V38
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 04 Mar 2016, 11:01
Took me some time to see that this question is simple:

Concept: In a triangle, the the sum of two angles = the measure of the outside angle from the last angle. To be clear: 2x = x + (the other angle), which can only be x.

(1) We have that AD = 6. Using the concept, we can see that the triangle is isosceles and share one side with another isosceles triangle. So AD=BD=BC SUFFICIENT.

(2) INSUFFICIENT: we have no values to find any measure.

ANSWER A.

Kudos [?]: 13 [0], given: 33

Manager
Manager
avatar
S
Status: active
Joined: 25 Jan 2016
Posts: 166

Kudos [?]: 34 [0], given: 10

Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Web Development (Computer Software)
Re: In triangle ABC above, what is the length of side BC? [#permalink]

Show Tags

New post 11 Apr 2017, 07:50
In triangle ABC above, what is the length of side BC?

(1) Line segment AD has length 6
(2) x = 36


A is answer
USING THE PROPERTY TWO SIDES WITH ANGLES THEIR LENGTHS ARE ALSO EQUAL

B
no info abt the sides of the triangle.Not suff

Kudos [?]: 34 [0], given: 10

Re: In triangle ABC above, what is the length of side BC?   [#permalink] 11 Apr 2017, 07:50
Display posts from previous: Sort by

In triangle ABC above, what is the length of side BC?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.