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Math Expert V
Joined: 02 Sep 2009
Posts: 57297
In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 58% (02:39) correct 42% (02:55) wrong based on 129 sessions

### HideShow timer Statistics In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

(2) AD = BD

Kudos for a correct solution.

Attachment: gdrtq_img4.png [ 8.74 KiB | Viewed 62493 times ]

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Director  Joined: 07 Aug 2011
Posts: 510
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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1
Bunuel wrote: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

(2) AD = BD

Kudos for a correct solution.

Attachment:
The attachment gdrtq_img4.png is no longer available

Answer D .
Attachments gmatclub.jpg [ 43.18 KiB | Viewed 44210 times ]

Manager  Joined: 05 Feb 2015
Posts: 50
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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I'll go with C.

Given : AC=AB
this implies angle ABC=angle ACB
Let angle DAB=x=angle DBC

Condition 1: angle BDC=2*angle DAB=2x
So, angle BCD=180-(x+2x)=180-3x
This could not help any further.

Condition 2: AD=BD
This gives angle DAB=angle DBA=x
This also is insufficient.

Both 1+2
As angle ABC=angle ACB
angle DBA+angle DBC=angle ACB
x+x=180-3x
2x=180-3x
5x=180
x=36
So, angle BCD=180-3x=180-3*36=180-108=72
Director  Joined: 07 Aug 2011
Posts: 510
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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1
Naina1 wrote:
I'll go with C.

Given : AC=AB
this implies angle ABC=angle ACB
Let angle DAB=x=angle DBC

Condition 1: angle BDC=2*angle DAB=2x
So, angle BCD=180-(x+2x)=180-3x
This could not help any further.

Condition 2: AD=BD
This gives angle DAB=angle DBA=x
This also is insufficient.

Both 1+2
As angle ABC=angle ACB
angle DBA+angle DBC=angle ACB
x+x=180-3x
2x=180-3x
5x=180
x=36
So, angle BCD=180-3x=180-3*36=180-108=72

please see attached for option A. you can do the same for option B.
Attachments gmatclub.jpg [ 34.23 KiB | Viewed 44141 times ]

Manager  Joined: 05 Feb 2015
Posts: 50
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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my bad..
yes each statement alone is sufficient.
Math Expert V
Joined: 02 Sep 2009
Posts: 57297
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Bunuel wrote: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

(2) AD = BD

Kudos for a correct solution.

Attachment:
gdrtq_img4.png

VERITAS PREP OFFICIAL SOLUTION:

From the prompt, we know that triangle ABC is isosceles, with AB = AC and angle ABC = angle DCB. Because angle DAB = angle DBC, and they share the angle at C, we know triangle BCD is similar to triangle ABC; therefore, triangle BCD must also be isosceles, with BC = BD and angle BDC = angle BCD. For simplicity, let’s say that

x = angle DAB = angle DBC

y = angle ABC = angle DCB = angle BDC

We know that (x + 2y) = 180°, and the prompt is asking for the value of y.

Statement #1: angle BDC = 2*(angle DAB)

In other words, y = 2x. Then

x + 2y = x + 4x = 5x = 180°

This means x = 36° and y = 72°. This statement leads directly to the numerical value sought in the prompt. This statement, alone and by itself, is sufficient.

Statement #2: AD = BD

This tell us that triangle ABD is also isosceles. This means that angle DAB = angle ABD. Think about angle ABD. That angle is the “leftover” between two angles we have already discussed:

angle ABD = (angle ABC) – (angle CBD) = y – x

Well, angle DAB = x, so if these two are equal, this means:

y – x = x

y = 2x

This turns out to be the exact same information that was given in statement #1, which we already know is full sufficient.

Answer = (D)

(BTW, more than you need to know for the GMAT, but these are Golden Triangles, because the ratio AB/BC equals the Golden Ratio! )
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Magoosh GMAT Instructor G
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In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Attachment: isosceles triangle.JPG [ 16.07 KiB | Viewed 43963 times ]

In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?
Statement #1: angle BDC = 2*(angle DAB)
Statement #2: AD = BD

For a collection of 12 challenging DS practice questions, and the OE for this particular question, see:
http://magoosh.com/gmat/2015/gmat-data- ... uestion-2/

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Manager  Joined: 15 May 2014
Posts: 62
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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given $$\triangle ABC$$ is an isosceles triangle
$$AB = AC$$
$$\angle ABC = \angle ACB$$ $$= ?$$
Let's assume $$\angle ABC = \angle ACB = x; \angle CAB = \angle DBC = y$$

from the question stem:
$$2x + y = 180$$ -----------------> (i)

Statement 1:
$$\angle BDC = 2*\angle DAB = 2*\angle DBC$$
From $$\triangle DBC x + 3y = 180$$ --------- (ii)
Solving (i) and (ii)
$$x = 72; y = 36; \angle ACB = 72$$
Sufficient

Statement 2:
AD = BD, $$\triangle ABD is isosceles, \angle ABD = \angle DAB =y$$
So $$\angle ABC = 2y$$
$$x + 3y = 180$$ ---------------------> (iii); same as (ii)
Solving (i) and (iii)
$$x = 72; y = 36; \angle ACB = 72$$
Sufficient

Answer D
Manager  B
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GMAT 1: 710 Q50 V34 Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Bunuel wrote: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

(2) AD = BD

Kudos for a correct solution.

Attachment:
The attachment gdrtq_img4.png is no longer available

Attachment: Capture.JPG [ 31.76 KiB | Viewed 42535 times ]

St 1: BDC = 2 (180 -2x)
Sum of angles in triangle BDC = 180. On solving we get x =72

St 2: AD+BD .. angles opp to equal sides are equal.
180-2x= 3x-180
x=72
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Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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