GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Feb 2019, 07:59

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     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.
  • Valentine's day SALE is on! 25% off.

     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!

In the figure above, BD = DC. If AD = 6, what is BD?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52910
In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 17 Jan 2019, 23:13
2
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (01:44) correct 41% (01:40) wrong based on 56 sessions

HideShow timer Statistics

Intern
Intern
User avatar
B
Joined: 17 Jan 2019
Posts: 5
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 18 Jan 2019, 12:06
could anybody explain it pls?

Posted from my mobile device
Intern
Intern
User avatar
B
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

New post Updated on: 19 Jan 2019, 12:32
1
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= 180-160-10=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
Intern
User avatar
B
Joined: 17 Jan 2019
Posts: 5
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 18 Jan 2019, 14:24
Excuse me but how <a can be 20 if <ADB=180-20=160?? then <ABD is 0???
<BAC = <BDC only if BA||BD

Posted from my mobile device
Manager
Manager
User avatar
G
Joined: 15 Feb 2018
Posts: 243
Premium Member
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 18 Jan 2019, 18:04
This should be changed from sub-600. I have no idea how to get the answer and don't understand Staphyk 's explanation
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 957
Location: India
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 18 Jan 2019, 19:04
1
Bunuel wrote:
Image
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
Intern
User avatar
B
Joined: 17 Jan 2019
Posts: 5
In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 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
Director
avatar
G
Joined: 09 Mar 2018
Posts: 957
Location: India
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 18 Jan 2019, 19:53
1
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
Intern
User avatar
B
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

New post 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=180-20=160?? then <ABD is 0???
<BAC = <BDC only if BA||BD

Posted from my mobile device
Manager
Manager
User avatar
G
Joined: 15 Feb 2018
Posts: 243
Premium Member
In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 18 Jan 2019, 23:05
1
How do you know that ∠ABC is 90º for ∠DBC and ∠DBA to be complimentary?
SVP
SVP
User avatar
G
Joined: 18 Aug 2017
Posts: 1775
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post Updated on: 19 Jan 2019, 04:09
1
Bunuel wrote:
Image
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 2019-01-18_1111.png is no longer available

Imo b

Posted from my mobile device
Attachments

IMG_20190119_173610277.jpg
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
Intern
avatar
B
Joined: 04 Jan 2018
Posts: 13
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 19 Jan 2019, 03:59
Archit3110 wrote:
Bunuel wrote:
Image
In the figure above, BD = DC. If AD = 6, what is BD?

A 4
B 6
C 8
D 10
E 12


Attachment:
2019-01-18_1111.png

Imo b

Posted from my mobile device



In your solution, triangle ABD has a sum of 200, which cannot the case.
SVP
SVP
User avatar
G
Joined: 18 Aug 2017
Posts: 1775
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 19 Jan 2019, 04:04
nehalkapadi123 wrote:
Archit3110 wrote:
Bunuel wrote:
Image
In the figure above, BD = DC. If AD = 6, what is BD?

A 4
B 6
C 8
D 10
E 12


Attachment:
2019-01-18_1111.png

Imo b

Posted from my mobile device



In 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
Director
avatar
P
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 19 Jan 2019, 17:34
1
Bunuel wrote:
Image
In the figure above, BD = DC. If AD = 6, what is BD?

A 4
B 6
C 8
D 10
E 12


Attachment:
2019-01-18_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
Intern
avatar
B
Joined: 10 May 2018
Posts: 7
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 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
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4382
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 20 Jan 2019, 06:52
1
Bunuel wrote:
Image
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 2019-01-18_1111.png is no longer available
Attachment:
2019-01-18_1111.png
2019-01-18_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
Manager
User avatar
G
Joined: 15 Feb 2018
Posts: 243
Premium Member
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 20 Jan 2019, 15:47
Abhishek009 wrote:
Bunuel wrote:
Image
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


How do you know that ∠ABC is 90º for ∠DBC and ∠DBA to be complimentary?
Manager
Manager
User avatar
S
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
CAT Tests
In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 20 Jan 2019, 22:24
Bunuel chetan2u VeritasKarishma AjiteshArun
Please explain how to find the other two angles to prove Triangle BAD is isosceles.
Senior PS Moderator
User avatar
D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 722
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: In the figure above, BD = DC. If AD = 6, what is BD?  [#permalink]

Show Tags

New post 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 10-10 ( 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)

GMAT Club Bot
Re: In the figure above, BD = DC. If AD = 6, what is BD?   [#permalink] 20 Jan 2019, 22:51
Display posts from previous: Sort by

In the figure above, BD = DC. If AD = 6, what is BD?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.