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# In triangle ABC above, what is the lenght of side BC? 1)

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In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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16 Jul 2007, 13:44
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Difficulty:

45% (medium)

Question Stats:

42% (00:59) correct 58% (00:35) wrong based on 41 sessions

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In triangle ABC above, what is the lenght of side BC?

1) line segment AD has lenght 6

2) x=36

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-triangle- ... 68281.html
[Reveal] Spoiler: OA

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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16 Jul 2007, 14:03
Where is the figure? Without the figure, it is kind of hard to picture where x is and where point D lies.

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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16 Jul 2007, 14:06
don't you see it?? i ve attached it with the post... ????

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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16 Jul 2007, 14:57
1
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Sorry, I did see it now.

We know from the figure that <BAC=x , <BDC=<BCD=2x
So BD=BC, since <BDC=<BAC+<ABD, this tells you <ABD=x as well.
Therefore, AD=BD, since we have already find out that BD=BC, so AD=BC. Statement 1 alone is sufficient.

Statement 2 tells you the value of X, but didn't tell you anything about the length of the segment, therefore is not sufficient.

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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23 Oct 2010, 15:12
Awesome
Just one simple explanation for how <BDC = <BAC+<ABD, exterior angle in a triangle is the sum of the opposite interior angles. It took me a while to figure it out, may be helpful.

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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08 Nov 2010, 06:06
+1 A
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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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22 Nov 2010, 09:17
I was going to pick A originally, but upon seeing that x=36 (I assumed that x should be 30), I felt no choice but to pick C.

Why is it unnecessary to know what x is?
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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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22 Nov 2010, 13:15
rockzom wrote:
I was going to pick A originally, but upon seeing that x=36 (I assumed that x should be 30), I felt no choice but to pick C.

Why is it unnecessary to know what x is?

Regardless of the actual value of x, we can show that triangle ADB is an isosceles triangle.

Within the bounds of the givens in this problem, changing x will only lead to changes in the length of side AB and DC.

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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22 Nov 2010, 13:36
(180 -2x) + x + ABD = 180

therefore x= abd

So, AB=BD=BC=6; Answer A is sufficient.

B is not sufficient since merely knowing angles does not reach upon length of AB.

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Re: In triangle ABC above, what is the lenght of side BC? 1) [#permalink]

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21 Aug 2017, 07:01

In triangle ABC above, what is the length of side BC?

Since <BDC = <BCD then the BD=BC. Also, since <ADB = 180 -2x (exterior angle) and the sum of the angles of a triangle is 180 degrees, then in triangle ADB we'll have: x + (180 - 2x) + <ABD = 180 --> <ABD = x. Now, we have that <ABD = x = <DAB so AD = BD --> AD = BD = BC.

Question: BC=?

(1) Line segment AD has length 6 --> AD = BD = BC = 6. Sufficient.

(2) x = 36 --> we know only angles which is insufficient to get the length of any line segment.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-triangle- ... 68281.html
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Re: In triangle ABC above, what is the lenght of side BC? 1)   [#permalink] 21 Aug 2017, 07:01
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