Author 
Message 
TAGS:

Hide Tags

Director
Joined: 25 Oct 2008
Posts: 543
Location: Kolkata,India

If CD = 6, what is the length of BC?
[#permalink]
Show Tags
06 Nov 2009, 05:58
Question Stats:
46% (01:24) correct 54% (01:21) wrong based on 544 sessions
HideShow timer Statistics
Attachment:
g2.JPG [ 4.99 KiB  Viewed 7563 times ]
If CD = 6, what is the length of BC? (1) \(BD=6\sqrt{3}\) (2) x = 60
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902




Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 20:26
yangsta8 wrote: So just for my knowledge, if we know 2 sides of a triangle, and the angle in between we can safely determine that the information is sufficient? This is a very good question. Well, I think everybody agrees that knowing such tips is very important for GMAT. Especially in DS as it helps to avoid time wasting by not calculating an exact numerical values. When can we say that information given is sufficient to calculate some unknown value in triangle? Think it's the same as determining congruency. If we are given some data and we can conclude that ONLY one triangle with given measurements exists, it should mean also that with given data we can calculate anything regarding this triangle. Determining congruency: 1. SAS (SideAngleSide): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. 2. SSS (SideSideSide): If three pairs of sides of two triangles are equal in length, then the triangles are congruent. 3. ASA (AngleSideAngle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. So, knowing SAS or ASA is sufficient to determine unknown angles or sides.NOTE IMPORTANT EXCEPTION:
The SSA condition (SideSideAngle) which specifies two sides and a nonincluded angle (also known as ASS, or AngleSideSide) does not always prove congruence, even when the equal angles are opposite equal sides. Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter than the known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In all other cases with corresponding equalities, SSA proves congruence. The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known as the HL (HypotenuseLeg) condition or the RHS (RightangleHypotenuseSide) condition), we can calculate the third side and fall back on SSS. To establish congruence, it is also necessary to check that the equal angles are opposite equal sides. So, knowing two sides and nonincluded angle is NOT sufficient to calculate unknown side and angles. AngleAngleAngle
AAA (AngleAngleAngle) says nothing about the size of the two triangles and hence proves only similarity and not congruence. So, knowing three angles is NOT sufficient to determine lengths of the sides.In our original question we had had SAS situation with (1), and ASA situation in (2) so each alone was indeed sufficient to calculate any other unknown value in this 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



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: If CD = 6, what is the length of BC?
[#permalink]
Show Tags
20 Jun 2013, 06:23




Director
Joined: 01 Apr 2008
Posts: 814
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 10:55
Draw BE perpendicular to AD, let \(CE = y\).
stmt1: \(sin30 = BE/BD\), BD is known, so BE can be found as sin30 =1/2. \(cos30 = DE/BD\), \(\sqrt{3}/2 = (6+y)/BD\) , so y can be found. Now we know BE and CE, apply pythagoras and find BC.
stmt2: \(sin30 = BE/BD\), BD is known, so BE can be found as sin30 =1/2. Now apply \(sin60 = BE/BC\), so BC can be found.
D




Senior Manager
Joined: 31 Aug 2009
Posts: 400
Location: Sydney, Australia

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 06:27
1) Is insufficient  This length doesn't help us except to tell us that BCD is not a right isosceles triangle. 2) x = 60. This means that Angle BCD = 18060 =120. The remaining angle CBD = 18012030 = 30. This tells us that the triangle is isosceles. BC = CD = 6.
ANS = B



Director
Joined: 25 Oct 2008
Posts: 543
Location: Kolkata,India

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 06:33
Nope..that's what I thought too!!please try again..
_________________
http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 07:03
tejal777 wrote: Nope..that's what I thought too!!please try again.. If CD = 6, what is the length of BC?As it's a DS question no need to actually find the value of BC, rather than to determine that it's possible to find it with either of statements: (1) \(BD=6\sqrt{3}\). We know CD, BD and the angle between them. The opposite side BC is fixed and has single value, meaning that you cannot draw two or more triangles with given two sides and the angle between them. Sufficient. (2) \(x=60\). Again we know x, hence we know all the angles in triangle BCD, plus we know one of the sides CD=6, again only one such triangle exists, hence the length of BC can be determined. Sufficient. Answer: D.
_________________
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



Senior Manager
Joined: 31 Aug 2009
Posts: 400
Location: Sydney, Australia

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 15:06
Kudos to both of you. Had not thought about that.
So just for my knowledge, if we know 2 sides of a triangle, and the angle in between we can safely determine that the information is sufficient?
When answering I did think about what you guys said, but thought that we a) couldn't assume that if we have 2 fixed sides and an angle we can derive the 3rd (althgouh I know we don't need to actaully derive it) and b) that trigonometry wasn't really required knowledge for the GMAT?



Director
Joined: 25 Oct 2008
Posts: 543
Location: Kolkata,India

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 17:44
Bunuel's way is absolutly correct!! And no trig is not reqd:)
_________________
http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902



Director
Joined: 01 Apr 2008
Posts: 814
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: geometry triangles
[#permalink]
Show Tags
06 Nov 2009, 20:47
Yup. Bunuel is bang on...And yes, trig knowledge is NOT required for GMAT, but if you have a basic understanding, it helps.



VP
Joined: 05 Mar 2008
Posts: 1422

Re: geometry triangles
[#permalink]
Show Tags
15 Nov 2009, 19:44
Economist wrote: Yup. Bunuel is bang on...And yes, trig knowledge is NOT required for GMAT, but if you have a basic understanding, it helps. wow..very good tip..never knew that... would a question like this actually appear on an exam? if so, I got some studying to do



Intern
Joined: 02 Sep 2010
Posts: 43
WE 1: Business Development Manger
WE 2: Assistant ManagerCarbon Trading
WE 3: ManagerCarbon Trading

Re: geometry triangles
[#permalink]
Show Tags
18 Nov 2010, 09:43
From statement 1 we can know that the triangle BDC is 306090 degree because cd=6 and bd =6root3 so for a 306090 triangle xxroot32x=66root312 so the length of BC =12 From Statement 2 I dont have asolution yet



Verbal Forum Moderator
Joined: 31 Jan 2010
Posts: 423
WE 1: 4 years Tech

Re: geometry triangles
[#permalink]
Show Tags
20 Nov 2010, 06:21
tejal777 wrote: :cry: Using Premise 1) when BD is given,BC is given ,use cosine formula BC ^ 2 = BD ^ 2 + + CB ^ 2  2 CB.BC Cos 30 2) When x = 60, BCD=120 , Triangle is isoceles , CB=6 therefore D, either premise satisfies
_________________
My Post Invites Discussions not answers Try to give back something to the Forum.I want your explanations, right now ! Please let me know your opinion about the Chandigarh Gmat Centrehttp://gmatclub.com/forum/gmatexperienceatchandigarhindiacentre111830.html



Manager
Joined: 05 Nov 2012
Posts: 65
Concentration: International Business, Operations
GPA: 3.65

Re: If CD = 6, what is the length of BC?
[#permalink]
Show Tags
21 Jun 2013, 11:23
tejal777 wrote: Attachment: The attachment g2.JPG is no longer available If CD = 6, what is the length of BC? (1) \(BD=6\sqrt{3}\) (2) x = 60 One way to solve this would be to draw a perpendicular line from B to A to make a 90 deg triangle and then solve. Statement 1: \(BD=6\sqrt{3}\)  SufficientFor Triangle BAD we know <C = 30, <A = 90, so <B = 60. We now have a 30:60:90 triangle with sides in the ratio x:x\(\sqrt{3}\):2x. Knowing BD allows us to calculate the value of x = 3\(\sqrt{3}\). So AD = 9 and hence AC = 3 and BA = 3\(\sqrt{3}\). Now for triangle BAC we know the 2 sides we can calculate BC the 3rd side. Sufficient. Statement 2: x = 60  SufficientIf x = 60 then <C = 120 and <B = 30. We now have an isosceles triangle with two equal sides making BC and CD equal (corresponding angles being equal) so BC = 6. Sufficient.
Attachments
triangle.jpg [ 11.95 KiB  Viewed 7095 times ]
_________________
___________________________________________ Consider +1 Kudos if my post helped



Senior Manager
Joined: 13 May 2013
Posts: 430

Re: If CD = 6, what is the length of BC?
[#permalink]
Show Tags
10 Dec 2013, 13:46
If CD = 6, what is the length of BC?
(1) BD=6\sqrt{3}
We know the length of BD and CD. We also know the angle that lies between them. BC is fixed. We don't have to find the solution, just confirm that there is only one possible solution. The only way that BC's angle or length could change is if line DC were extended to the left but as the diagram states, that isn't possible because we are given it's length. Sufficient.
(2) x = 60
If x = 60 then the interior angle c = 120. Seeing as angle d = 30, angle b also = 60. The shape and side lengths of this triangle are fixed into position and cannot be changed. Given side length CD = 6 then there is only one possible answer for BC. Sufficient.



Board of Directors
Joined: 17 Jul 2014
Posts: 2692
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

If CD = 6, what is the length of BC?
[#permalink]
Show Tags
03 Mar 2015, 08:17
(1) we know that CD = 6, and angle CDB = 30 we can draw a perpendicular line, and get 2 right triangles (306090), since the new angle CFD must be 90 degrees, we can conclude that angle C must be 60 degrees. Thus, we have CD = 6, CF = 3, and FD = 3 sqrt 3. Hm, this is interesting, 3 sqrt 3 is half of BD. That means that CF is the median of BD. Knowing FD & BF, we can calculate for BC. but that is not needed. Statement 1 Sufficient (2) x = 60, thus we can conclude that we have an isosceles triangle, and BC = CD.
Attachments
Untitled.jpg [ 16.5 KiB  Viewed 5280 times ]



Manager
Status: single
Joined: 19 Jan 2015
Posts: 90
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)

Re: If CD = 6, what is the length of BC?
[#permalink]
Show Tags
03 Mar 2015, 09:27
Hi bunnel pls correct me if my approach is wrong. Here angle D is 30
In statement 1 BD 6root3
Draw a perpendicular from Cto BD at O then angle at O 90 angle D 30 angle C 60. If CD =6 then side opposite to D 30 degree is half then CO is 3 then OD is 3root3 then OB= 3root3. Trianlge OCD are congruent OCB then BC =CD. Value of BC=6



NonHuman User
Joined: 09 Sep 2013
Posts: 8091

Re: If CD = 6, what is the length of BC?
[#permalink]
Show Tags
04 Jul 2018, 09:00
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: If CD = 6, what is the length of BC? &nbs
[#permalink]
04 Jul 2018, 09:00






