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

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In triangle ABC above, what is the length of side BC? [#permalink] New post 03 Mar 2014, 23:20
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

57% (02:13) correct 43% (02:03) wrong based on 176 sessions
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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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

Data Sufficiency
Question: 123
Category: Geometry Triangles
Page: 162
Difficulty: 650


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

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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.

Answer: A.
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Re: In triangle ABC above, what is the length of side BC? [#permalink] New post 05 Mar 2014, 21:39
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] New post 05 Mar 2014, 23:03
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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] New post 05 Mar 2014, 23:49
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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.

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] New post 08 Mar 2014, 13:04
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SOLUTION

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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.

Answer: A.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: In triangle ABC above, what is the length of side BC? [#permalink] New post 08 Mar 2014, 16:48
This was a super easy question...I said D because I wasn't paying attention....PEOPLE....PAY ATTENTION!!!!
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Re: In triangle ABC above, what is the length of side BC? [#permalink] New post 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.
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Re: In triangle ABC above, what is the length of side BC?   [#permalink] 23 Apr 2014, 05:53
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