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M24-08

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M24-08 [#permalink]

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New post 16 Sep 2014, 01:20
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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

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Re M24-08 [#permalink]

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New post 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
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Re: M24-08 [#permalink]

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New post 17 Apr 2016, 12:53
To make the explanation visual, did someone solve this question graphically? thank you.
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Re: M24-08 [#permalink]

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New post 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!
>> !!!

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Re: M24-08 [#permalink]

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New post 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...
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Re: M24-08 [#permalink]

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New post 07 Dec 2016, 21:45
Hi Bunnel,


Can you please elaborate more on solution .. i got this question wrong.
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Re: M24-08 [#permalink]

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New post 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
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Re: M24-08 [#permalink]

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New post 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.
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Re: M24-08 [#permalink]

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New post 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 => \(\angle BAD + \angle ADC=180\)

\(\angle ADC=180-80=100\)

Am I right here?
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Re: M24-08 [#permalink]

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New post 11 May 2017, 02:23
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Here is the image for visual view
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Re: M24-08 [#permalink]

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New post 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 => \(\angle BAD + \angle ADC=180\)

\(\angle ADC=180-80=100\)

Am I right here?


Yes, consecutive angles in a parallelogram are supplementary, add to 180°, so yes you are right.
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Collection of Questions:
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Re: M24-08 [#permalink]

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New post 17 Apr 2018, 06:00
+1 for option D. The angle is 100.
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Re: M24-08 [#permalink]

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New post 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?
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Re: M24-08 [#permalink]

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New post 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 Solving
Figures: 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.
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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: M24-08   [#permalink] 17 Apr 2018, 22:39
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