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tough geo. problem

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by criszerriny » Thu May 14, 2009 3:03 pm
Need help guys...I posted the picture for this problem...I can't figure this out at all, any help is much appreciated........

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

(1) Line segment AD has length 6
(2) x=36

Thanks everyone
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Source: — Data Sufficiency |
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by Jose Ferreira » Thu May 14, 2009 4:36 pm
This is a great question, and one with a very common GMAT strategy that I espouse to all my students: just start filling in variables for all possible angles, and see what happens.

(I'm going to refer to angles just as the three letters.)

So, for example, is BDC=2x, then we know that BDA=180-2x.

Now, we take that information and apply it to what we know in the triangle to the left:

ADB + DBA + BAD = 180.
(180-2x) + DBA + x = 180
DBA = 180 - x - (180-2x) = x
If DBA= x, and BAD=x, then triangle BAD is isosceles.

Statement one says that segment AD is 6. With our knowledge of isosceles triangles, we then know that BD is also 6. And since the right- hand triangle is isosceles based on the information given, then segment BC must also be 6.

Statement one is sufficient.

Statement two just talks about angles, and gives no information about side lengths.
Last edited by Jose Ferreira on Mon May 18, 2009 9:57 am, edited 1 time in total.
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Excellent Questions.

by farooq » Fri May 15, 2009 1:27 am
Excellent problem with brilliant explanation. I can say GMAC always design questions on basic math's rules..the only trick is "how we can recognize it" :)

Regards,
Farooq
Regards,
Farooq Farooqui.
London. UK

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by PAB2706 » Fri May 15, 2009 3:22 am
here is another simpler way to solve within seconds....

you have to remember one property of triangles.... i guess it is called exterior angle property or something

in our case angle BDC= angle DAB + angle DBA

thus we have 2x=x + angle DBA

we get angle DBA =x

so triangle ADB is isosceles.

A is sufficient
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by Brent@GMATPrepNow » Mon Feb 11, 2019 9:17 am
criszerriny wrote:Need help guys...I posted the picture for this problem...I can't figure this out at all, any help is much appreciated........

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

(1) Line segment AD has length 6
(2) x=36

Thanks everyone
Target question: What is the length of side BC?

Statement 1: Line segment AD has length 6.
BEFORE we deal with statement 1, let's see what information we can add to the diagram.

For example, since ∆BDC has 2 equal angles (of 2x°), we know that side BD = side BC:
Image

Next, since angles on a line add to 180°, and since ∠BDC = 2x°, we know that ∠ADB = (180 - 2x)°
Image


Now focus on ∆BAD
Since angles in a triangle add to 180°, we know that ∠ABD = x°
ASIDE: Notice that x° + x° + (180 - 2x)° = 180°
Image


Now that we know ∆BAD has two equal angles (x° and x°), we know that side AD = side BD
Image
This means AD = BD = BC

Statement 1 tells us that AD = 6, which means BC = 6
The answer to the target question is side BC has length 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 36
Notice that our diagram doesn't any lengths.
We can SHRINK or ENLARGE the diagram and the angles remain the same.
However the length of side BC changes.

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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