Oct 22 08:00 AM PDT  09:00 AM PDT Join to learn strategies for tackling the longest, wordiest examples of Counting, Sets, & Series GMAT questions Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58411

Question Stats:
68% (01:39) correct 32% (01:53) wrong based on 167 sessions
HideShow timer Statistics
In quadrilateral \(ABCD\), \(AB = CD\) and \(BC = AD\). If \(\angle CBD = 30\) degrees and \(\angle BAD = 80\) degrees, what is the value of \(\angle ADC\)? A. 30 degrees B. 50 degrees C. 70 degrees D. 100 degrees E. 120 degrees
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58411

Re M2408
[#permalink]
Show Tags
16 Sep 2014, 01:20
Official Solution:In quadrilateral \(ABCD\), \(AB = CD\) and \(BC = AD\). If \(\angle CBD = 30\) degrees and \(\angle BAD = 80\) degrees, what is the value of \(\angle ADC\)? A. 30 degrees B. 50 degrees C. 70 degrees D. 100 degrees E. 120 degrees Because \(AB = CD\) and \(BC = AD\), \(ABCD\) is a parallelogram. \(\angle ADC = \angle BDA + \angle BDC = \angle CBD + \angle ABD = \angle CBD + (180  \angle BAD  \angle BDA) =\) \(= 30 + (180  80  30) = 100\). Answer: D
_________________



Current Student
Joined: 12 Nov 2015
Posts: 55
Location: Uruguay
Concentration: General Management
GMAT 1: 610 Q41 V32 GMAT 2: 620 Q45 V31 GMAT 3: 640 Q46 V32
GPA: 3.97

Re: M2408
[#permalink]
Show Tags
17 Apr 2016, 12:53
To make the explanation visual, did someone solve this question graphically? thank you.



Intern
Joined: 27 Mar 2014
Posts: 9

Re: M2408
[#permalink]
Show Tags
16 Aug 2016, 18:52
Hi Bunuel, Thanks for all that you do. Your explanations have made the study grind a lot more manageable. I was under the impression that when you write out an angle expression (ex. ∠ABC), it means the angle is formed by the intersection of line AB with line BC (see attached illustration) Is this the case? If so, I'm having trouble visualizing how you could form the parallelogram above using the given information. Thanks in advance!
>> !!!
You do not have the required permissions to view the files attached to this post.



Current Student
Joined: 26 Jan 2016
Posts: 98
Location: United States
GPA: 3.37

Re: M2408
[#permalink]
Show Tags
27 Nov 2016, 19:32
Can someone explain how B can be the vertex of angle CBD if the prompt states AB=CD and AD=BC? I can't figure out how to draw this...



Intern
Joined: 12 Jul 2013
Posts: 7

Re: M2408
[#permalink]
Show Tags
07 Dec 2016, 21:45
Hi Bunnel,
Can you please elaborate more on solution .. i got this question wrong.



Manager
Joined: 03 Jan 2016
Posts: 57
Location: India
WE: Engineering (Energy and Utilities)

Re: M2408
[#permalink]
Show Tags
05 Apr 2017, 01:55
Question didn't mentioned that Opposite sides are parallel !!!!
can we still assume that given quadrilateral is Parallelogram?
Requesting expert analysis on this !!!
Thanks in advance
Narayana Raju



Math Expert
Joined: 02 Sep 2009
Posts: 58411

Re: M2408
[#permalink]
Show Tags
05 Apr 2017, 02:08
gvvsnraju@1 wrote: Question didn't mentioned that Opposite sides are parallel !!!!
can we still assume that given quadrilateral is Parallelogram?
Requesting expert analysis on this !!!
Thanks in advance
Narayana Raju This is explained in the solution: Because \(AB = CD\) and \(BC = AD\), \(ABCD\) is a parallelogram. If two pairs of opposite sides of a quadrilateral are equal in length then the quadrilateral is a parallelogram.
_________________



Current Student
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 126
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 660 Q47 V34 GMAT 2: 700 Q48 V38
GPA: 3.1
WE: General Management (Entertainment and Sports)

Re: M2408
[#permalink]
Show Tags
10 May 2017, 22:53
Bunuel wrote: In quadrilateral \(ABCD\), \(AB = CD\) and \(BC = AD\). If \(\angle CBD = 30\) degrees and \(\angle BAD = 80\) degrees, what is the value of \(\angle ADC\)?
A. 30 degrees B. 50 degrees C. 70 degrees D. 100 degrees E. 120 degrees Consecutive angles are supplementary => \(\angle BAD + \angle ADC=180\) \(\angle ADC=18080=100\) Am I right here?
_________________
Yours, Siva Rama Krishna Meka



Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1331
Location: Viet Nam

Re: M2408
[#permalink]
Show Tags
11 May 2017, 02:23
Here is the image for visual view Attachment: Capture.PNG
>> !!!
You do not have the required permissions to view the files attached to this post.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58411

Re: M2408
[#permalink]
Show Tags
11 May 2017, 02:42
Sirakri wrote: Bunuel wrote: In quadrilateral \(ABCD\), \(AB = CD\) and \(BC = AD\). If \(\angle CBD = 30\) degrees and \(\angle BAD = 80\) degrees, what is the value of \(\angle ADC\)?
A. 30 degrees B. 50 degrees C. 70 degrees D. 100 degrees E. 120 degrees Consecutive angles are supplementary => \(\angle BAD + \angle ADC=180\) \(\angle ADC=18080=100\) Am I right here? Yes, consecutive angles in a parallelogram are supplementary, add to 180°, so yes you are right.
_________________



Senior Manager
Joined: 08 Jun 2015
Posts: 420
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38
GPA: 3.33

Re: M2408
[#permalink]
Show Tags
17 Apr 2018, 06:00
+1 for option D. The angle is 100.
_________________
" The few , the fearless "



Manager
Joined: 14 Aug 2012
Posts: 78
Location: United States
GMAT 1: 620 Q43 V33 GMAT 2: 690 Q47 V38

Re: M2408
[#permalink]
Show Tags
17 Apr 2018, 17:16
Does the position of A, B , C and D matter for these types of problems? If we wanted to draw it, what is the correct placement?



Math Expert
Joined: 02 Sep 2009
Posts: 58411

Re: M2408
[#permalink]
Show Tags
17 Apr 2018, 22:39
bpdulog wrote: Does the position of A, B , C and D matter for these types of problems? If we wanted to draw it, what is the correct placement? OFFICIAL GUIDE:Problem SolvingFigures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.Data Sufficiency:Figures:• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). • Lines shown as straight are straight, and lines that appear jagged are also straight. • The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.• All figures lie in a plane unless otherwise indicated.
_________________



Intern
Joined: 02 Feb 2018
Posts: 31

Re: M2408
[#permalink]
Show Tags
12 Nov 2018, 07:16
Because you know that its a parallelogram, you don't need the information that CBD is 30 degrees. Opposite angles in parallelogram are the same and quadrilateral has 360 degrees in total > ADC = [360(2*80)]/2



Intern
Joined: 11 Mar 2017
Posts: 11

Re: M2408
[#permalink]
Show Tags
06 Dec 2018, 22:19
Hi, I solved by simply deducting angle(BAD) from 180 degrees to find the supplementary angel of BAD, which will be equal to angle ADC since AB and DC are parallel. Is this approach correct? Bunuel wrote: Official Solution:
In quadrilateral \(ABCD\), \(AB = CD\) and \(BC = AD\). If \(\angle CBD = 30\) degrees and \(\angle BAD = 80\) degrees, what is the value of \(\angle ADC\)?
A. 30 degrees B. 50 degrees C. 70 degrees D. 100 degrees E. 120 degrees
Because \(AB = CD\) and \(BC = AD\), \(ABCD\) is a parallelogram. \(\angle ADC = \angle BDA + \angle BDC = \angle CBD + \angle ABD = \angle CBD + (180  \angle BAD  \angle BDA) =\) \(= 30 + (180  80  30) = 100\).
Answer: D










