Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 14:45

### 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

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

# 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

Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106242 [0], given: 11618

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

### Show Tags

04 Mar 2014, 00:20
Expert's post
23
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:27) correct 46% (01:58) wrong based on 766 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:

Untitled.png [ 14.63 KiB | Viewed 7571 times ]
In 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 Project

Each 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!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106242 [1] , given: 11618

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

### Show Tags

04 Mar 2014, 00:21
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION

In 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.

_________________
Intern
Joined: 02 Oct 2013
Posts: 11
Followers: 0

Kudos [?]: 1 [0], given: 0

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

### Show Tags

05 Mar 2014, 22:39
Is there a way to tell if D is the bisector of AC?

Posted from my mobile device
Manager
Joined: 09 Nov 2013
Posts: 90
Followers: 1

Kudos [?]: 11 [1] , given: 30

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

### Show Tags

06 Mar 2014, 00:03
1
KUDOS
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
Manager
Status: Never Give up!!!
Joined: 03 Aug 2012
Posts: 51
Location: India
Concentration: Finance, General Management
Followers: 1

Kudos [?]: 41 [1] , given: 28

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

### Show Tags

06 Mar 2014, 00:49
1
KUDOS
Given data:-
In Triangle ABC:-
Angle A+ Angle ABC + Angle C = 180
Thus Angle B = 180-3x

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.

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)
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106242 [0], given: 11618

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

### Show Tags

08 Mar 2014, 14:04
SOLUTION

In 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.

_________________
Intern
Joined: 06 Jan 2014
Posts: 46
Followers: 0

Kudos [?]: 11 [0], given: 23

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

### Show Tags

08 Mar 2014, 17:48
This was a super easy question...I said D because I wasn't paying attention....PEOPLE....PAY ATTENTION!!!!
Intern
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 20
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
Followers: 0

Kudos [?]: 15 [0], given: 57

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

### Show Tags

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 )

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: 127
Followers: 0

Kudos [?]: 15 [0], given: 43

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

### Show Tags

17 May 2015, 07:56
Bunuel wrote:
SOLUTION

In 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.

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: 38908
Followers: 7739

Kudos [?]: 106242 [0], given: 11618

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

### Show Tags

18 May 2015, 04:33
erikvm wrote:
Bunuel wrote:
SOLUTION

In 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.

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 vise-versa: if two angles in a triangle are equal then it's an isosceles triangle.
_________________
Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 356 [0], given: 200

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

### Show Tags

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 ??
_________________

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

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2644
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 128

Kudos [?]: 1474 [0], given: 789

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

### Show Tags

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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Manager
Joined: 18 Aug 2006
Posts: 114
Location: United States
WE: Consulting (Telecommunications)
Followers: 1

Kudos [?]: 51 [0], given: 44

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

### Show Tags

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?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15466
Followers: 649

Kudos [?]: 209 [0], given: 0

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

### Show Tags

24 Sep 2016, 08:21
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.
_________________
Intern
Joined: 08 May 2016
Posts: 33
Location: United States
WE: Project Management (Aerospace and Defense)
Followers: 0

Kudos [?]: 7 [0], given: 24

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

### Show Tags

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.
_________________

Senior Manager
Joined: 05 Jan 2017
Posts: 436
Location: India
Followers: 14

Kudos [?]: 43 [0], given: 15

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

### Show Tags

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
Re: In triangle ABC above, what is the length of side BC?   [#permalink] 23 Feb 2017, 05:44
Similar topics Replies Last post
Similar
Topics:
1 Is BC the largest side of triangle ABC? 2 05 Sep 2016, 09:39
3 The lengths of the sides of triangle ABC are such that AB = x + 2, BC 4 02 Mar 2015, 07:24
44 In triangle ABC above, what is the length of side BC? 24 11 Apr 2017, 07:50
In the triangle above, what is the length of the side BC? 5 16 Apr 2010, 04:58
1 In triangle ABC above, what is the lenght of side BC? 1) 8 22 Nov 2010, 13:36
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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.