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Data Suff: Sides of a Triangle. CAT Exam #2

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afvatcha
 Post subject: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Wed Dec 23, 2009 9:35 pm 
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Course Students


Posts: 34
I posted the entire problem below. I felt that either answer should be sufficient. If you have a large triangle and within that triangle you know for a fact that one of the two smaller triangles in a 30-60-90, why can't you assume the other smaller triangle is a 30-60-90?

The correct answer was C.

If AD is 6, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12
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afvatcha
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Mon Dec 28, 2009 8:34 pm 
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Posts: 34
I have attached a pic via link below.

http://www.postimage.org/image.php?v=gx1cJ7ui
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jchong8250
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Wed Dec 30, 2009 5:14 pm 
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Posts: 4
I think the main thing to take away here is that although the drawing makes it seem like the triangle can be an isosceles, you can't assume that. In (A), you can figure out the length of BD using the 30-60-90 triangle properties, but you can't assume the same properties for triangle ADC. For (B), you can figure out the length of DC using the Pythagorean Theorem. So, you'd need both (A) and (B) to figure out the area of triangle ABC.
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afvatcha
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Wed Dec 30, 2009 9:14 pm 
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Posts: 34
Thanks. I knew that if there are two 30-60-90 triangles within a larger triangle then you know the larger triangle is an equaliteral triange. But you cannot assume that if one of the smaller triangles is a 30-60-90 then the other has to be a 30-60-90. Thanks again.
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Ben Ku
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Tue Feb 16, 2010 8:55 pm 
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ManhattanGMAT Staff


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jchong8250: good points.

Key takeaway is that pictures can be deceiving. Solve problems only with information that has been explicitly stated.

_________________
Ben Ku
Instructor
ManhattanGMAT
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ganeshraj
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Thu Feb 18, 2010 7:31 am 
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Posts: 6
Cannot we solve the problem with (A) alone,

In triangle ABD , we know : AD=6 ,and B=60 dg.

tan x = opp/adj (x = B )
=> tan 60 = 6/BD.
=> sqrt 3 = 6 /BD.
=> BD = 2 sqrt 3.

Area of the triangle ABD = 1/2 .6. 2 sqrt 3 =>6 sqrt 3.
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ganeshraj
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Thu Feb 18, 2010 7:42 am 
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Sorry , got the question wrong; its area of triangle ABC ,not ABD.

Thanks.
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RonPurewal
 Post subject: Re: Data Suff: Sides of a Triangle. CAT Exam #2
 Post Posted: Fri Feb 19, 2010 8:53 am 
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ManhattanGMAT Staff


Posts: 6765
ganeshraj wrote:
Cannot we solve the problem with (A) alone,

In triangle ABD , we know : AD=6 ,and B=60 dg.

tan x = opp/adj (x = B )
=> tan 60 = 6/BD.
=> sqrt 3 = 6 /BD.
=> BD = 2 sqrt 3.

Area of the triangle ABD = 1/2 .6. 2 sqrt 3 =>6 sqrt 3.


fyi, you should make sure that you have the skill set to solve 30°-60°-90° triangles without trigonometry. i.e., you should just memorize the ratio of the sides (1:√3:2), so that you don't have to waste precious time setting up trig functions.

...especially since trigonometry is not required on this test!

the only right triangles for which you'll have to determine side lengths are 30-60-90, 45-45-90, and/or triangles for which the pythagorean theorem is all you need.
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