February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
Author 
Message 
Math Expert
Joined: 02 Sep 2009
Posts: 52910

In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
17 Jan 2019, 23:13
Question Stats:
59% (01:44) correct 41% (01:40) wrong based on 56 sessions
HideShow timer Statistics



Intern
Joined: 17 Jan 2019
Posts: 5

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 12:06
could anybody explain it pls?
Posted from my mobile device



Intern
Joined: 20 Mar 2018
Posts: 48
Location: Ghana
Concentration: Finance, Real Estate

In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
Updated on: 19 Jan 2019, 12:32
Easy one, <BAC = <2BDC because they subtend from the same Arc BC so <a is 10 now <ADB=160 Again <ADB+ <DAB + <DBA=180 <DBA= 18016010=10 ,we can now see that triangle BDA is an isosceles we two equal sides 10 .Therefore length must be equal AD=DB=6 Answer is B Or better still look at my alternate solution down below
Posted from my mobile device
Originally posted by Staphyk on 18 Jan 2019, 13:07.
Last edited by Staphyk on 19 Jan 2019, 12:32, edited 2 times in total.



Intern
Joined: 17 Jan 2019
Posts: 5

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 14:24
Excuse me but how <a can be 20 if <ADB=18020=160?? then <ABD is 0??? <BAC = <BDC only if BABD
Posted from my mobile device



Manager
Joined: 15 Feb 2018
Posts: 243

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 18:04
This should be changed from sub600. I have no idea how to get the answer and don't understand Staphyk 's explanation



Director
Joined: 09 Mar 2018
Posts: 957
Location: India

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 19:04
Bunuel wrote: In the figure above, BD = DC. If AD = 6, what is BD? A 4 B 6 C 8 D 10 E 12 Will just place an idea here, on how i got B( A long explanation, Nevertheless an easy question) If BD=DC, this implies triangle BDC is an isosceles triangle with < DBC = < BCD = 80 If one can prove triangle BDC ~ triangle ABC, we can use the ratio of sides to calculate the side BD I am able to find, < C which will be common for both triangles, side BC which will be common again Now do note i am missing out at one more factor to make it similar. Nevertheless, now when i say those two triangles are similar, there is a property of similar triangles that ratio of corresponding sides are equall I agree on the part that < ABD cant be zero, it will be 10( because < BDA = 160 and if you drop a perpendicular at AB < DAE = < DBE = 10. Now if you understood what i wrote here, so i will be taking the corresponding sides to the equal angles triangle BDC ~ triangle ABC Do look into the properties of similar triangles BD/BD = DC/AD Since DC = BD We can write BD = 6
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up.



Intern
Joined: 17 Jan 2019
Posts: 5

In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 19:42
My mind has just exploded))).. Perpendicular droped on AB is not necessarily devides <ADB/2, therefore we can not assume that <DAE=<DBE=10... Anyway sum of this two angles is 20 and answer should be close 6))
Posted from my mobile device



Director
Joined: 09 Mar 2018
Posts: 957
Location: India

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 19:53
Maikosh wrote: My mind has just exploded))).. Perpendicular droped on AB is not necessarily devides <ADB/2, therefore we can not assume that <DAE=<DBE=10... Anyway sum of this two angles is 20 and answer should be close 6))
Posted from my mobile device Good to know, that it somehow helped you in thinking how to solve the question. I agreeon that part that if i drop a perpendicular bisector, only the sides will be equal.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up.



Intern
Joined: 20 Mar 2018
Posts: 48
Location: Ghana
Concentration: Finance, Real Estate

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 22:59
Sorry you couldn’t get it Let’s me see wether I can still help Now we given that line DC=BD if that is the case then <DCB=<DBC = (say x) now let’s solve x+x+20=180 x=80 therefore <DCB=80 and <DBC=80 also <ADB=160 since it’s supplementary to <BDC =20 Now rotate the figure clockwise such that Line BA sits flat we get <CBD to be complementary to <DBA=10 now triangle DBA adds up to 180 and we know <ADB=160 and <DBA=10 then <DAB must be 10 showing that line DA=DB =6 Hope it helps Maikosh wrote: Excuse me but how <a can be 20 if <ADB=18020=160?? then <ABD is 0??? <BAC = <BDC only if BABD
Posted from my mobile device



Manager
Joined: 15 Feb 2018
Posts: 243

In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
18 Jan 2019, 23:05
How do you know that ∠ABC is 90º for ∠DBC and ∠DBA to be complimentary?



SVP
Joined: 18 Aug 2017
Posts: 1775
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
Updated on: 19 Jan 2019, 04:09
Bunuel wrote: In the figure above, BD = DC. If AD = 6, what is BD? A 4 B 6 C 8 D 10 E 12 Attachment: The attachment 20190118_1111.png is no longer available Imo b Posted from my mobile device
Attachments
IMG_20190119_173610277.jpg [ 1.03 MiB  Viewed 486 times ]
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Originally posted by Archit3110 on 19 Jan 2019, 02:35.
Last edited by Archit3110 on 19 Jan 2019, 04:09, edited 2 times in total.



Intern
Joined: 04 Jan 2018
Posts: 13

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
19 Jan 2019, 03:59
Archit3110 wrote: Bunuel wrote: In the figure above, BD = DC. If AD = 6, what is BD? A 4 B 6 C 8 D 10 E 12 Attachment: 20190118_1111.png Imo b Posted from my mobile deviceIn your solution, triangle ABD has a sum of 200, which cannot the case.



SVP
Joined: 18 Aug 2017
Posts: 1775
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
19 Jan 2019, 04:04
nehalkapadi123 wrote: Archit3110 wrote: Bunuel wrote: In the figure above, BD = DC. If AD = 6, what is BD? A 4 B 6 C 8 D 10 E 12 Attachment: 20190118_1111.png Imo b Posted from my mobile deviceIn your solution, triangle ABD has a sum of 200, which cannot the case. it would be 10 ... not 20 ...
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
19 Jan 2019, 17:34
Bunuel wrote: In the figure above, BD = DC. If AD = 6, what is BD? A 4 B 6 C 8 D 10 E 12 Attachment: 20190118_1111.png I feel this question is missing something. From the given info we cannot determine BD.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Intern
Joined: 10 May 2018
Posts: 7

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
20 Jan 2019, 03:16
Staphyk Just want to clarify ,are we assuming a circumcircle .Then AC would become the diameter and the D would become the center and BD would also be the radius (also as isosceles triangle the angles would be 10 )



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4382
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
20 Jan 2019, 06:52
Bunuel wrote: In the figure above, BD = DC. If AD = 6, what is BD? A 4 B 6 C 8 D 10 E 12 Attachment: The attachment 20190118_1111.png is no longer available Attachment:
20190118_1111.png [ 7.7 KiB  Viewed 242 times ]
After finding the angles of the triangle you will get 2 Triangles ADB and BCD in which both the Triangles are Isosceles Triangles with a common vertex BD. Thus in this figure AD = BD = CD = 6 , Answer will be (B) 6
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Manager
Joined: 15 Feb 2018
Posts: 243

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
20 Jan 2019, 15:47
Abhishek009 wrote: Bunuel wrote: After finding the angles of the triangle you will get 2 Triangles ADB and BCD in which both the Triangles are Isosceles Triangles with a common vertex BD. Thus in this figure AD = BD = CD = 6 , Answer will be (B) 6How do you know that ∠ABC is 90º for ∠DBC and ∠DBA to be complimentary?



Manager
Joined: 28 Jun 2018
Posts: 130
Location: Bouvet Island
GMAT 1: 490 Q39 V18 GMAT 2: 640 Q47 V30 GMAT 3: 670 Q50 V31 GMAT 4: 700 Q49 V36
GPA: 4

In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
20 Jan 2019, 22:24
Bunuel chetan2u VeritasKarishma AjiteshArunPlease explain how to find the other two angles to prove Triangle BAD is isosceles.



Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 722

Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
Show Tags
20 Jan 2019, 22:51
Something is definitely missing in this question. Bunuel sir can you please check/ provide OE? Thanks. BDC = 20 only gives us the info that the sum of the other two small angles is 20. ( Remote interior angles of triangle are same as exterior angle) Also, just one of the two triangles is isoceles. So we cannot determine whether the split is 1010 ( in which case the answer will be 6) or something else. This is my take on it. Posted from my mobile device
_________________
Regards, Gladi
“Do. Or do not. There is no try.”  Yoda (The Empire Strikes Back)




Re: In the figure above, BD = DC. If AD = 6, what is BD?
[#permalink]
20 Jan 2019, 22:51






