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it says difficult geometry (tricky)

by Night reader » Mon Nov 22, 2010 4:31 pm
In the Â…figure (attached below), if triangle ABC and triangle ADC are isosceles
triangles, what is the value of x?
(1) y = 140
(2) Angle DCA is one half the measure of Angle BCA.
Image
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by karanrulz4ever » Mon Nov 22, 2010 11:10 pm
IMO C
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by Night reader » Mon Nov 22, 2010 11:35 pm
karanrulz4ever wrote:IMO C
it's not C ):
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by rishab1988 » Tue Nov 23, 2010 1:09 am
It should be E

Here is why:

we are given that tri ABC and ADC are isosceles.

1) y=140.Since we know ADC is isosceles,at least 2 angles must have same measure.We also know sum of the angles of a tria=180.Therefore 140 is not the common angles ,because if two angles measure 140 ,sum >280. So the other 2 angles must be 20 each.

But we can't infer the measure of angles x from this.because its measure depends on measure of angles BAD and BCD.If angles BAD=BCD=30 x= 180-(100)=80;but if BAD=BCD=40 x=180-(120)=60.

Not sufficient

2) We are told angle DCA =1/2 BCA or angle DCA= BCD.

Lets assume DCA=BCD=50.Therefore BCA=100;Since ABC must be isosceles x=40.However if DCA=BCD=40 which means BCA=80.x could be either 20 or 80.

Insufficient.

Combining 1 and 2.

From 1 we know ADC=20 and from 2 we know BCA =40.

Now,since tri ABC is isoceles either angle x= angle BAC= 140/2=70 or angle x= angle BCA= 40.

Again Insufficient.

Hence E.

What is the OA?


Remember we are told ABC is isosceles,but not which sides are equal.
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by Night reader » Tue Nov 23, 2010 1:29 am
Rishab, you are correct. Initially, I selected answer C.
OA is E. I re-read the problem; it doesn't specify which are the baseline angles in triangle ABC. So x may or may not baseline angle. Statements 1&2 are not sufficient.
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by frank1 » Tue Nov 23, 2010 3:03 am
I think the problem here is
we cannot determine which sides are equal in larger Isoceles triangle and even in smaller triangle
so we cannot determine triangle.
The it specified AB=BC and so on i think there would have been possibility solve it
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by goyalsau » Tue Nov 23, 2010 3:14 am
rishab1988 wrote:It should be E

Here is why:

we are given that tri ABC and ADC are isosceles.

1) y=140.Since we know ADC is isosceles,at least 2 angles must have same measure.We also know sum of the angles of a tria=180.Therefore 140 is not the common angles ,because if two angles measure 140 ,sum >280. So the other 2 angles must be 20 each.

But we can't infer the measure of angles x from this.because its measure depends on measure of angles BAD and BCD.If angles BAD=BCD=30 x= 180-(100)=80;but if BAD=BCD=40 x=180-(120)=60.

Not sufficient

2) We are told angle DCA =1/2 BCA or angle DCA= BCD.

Lets assume DCA=BCD=50.Therefore BCA=100;Since ABC must be isosceles x=40.However if DCA=BCD=40 which means BCA=80.x could be either 20 or 80.

Insufficient.

Combining 1 and 2.

From 1 we know ADC=20 and from 2 we know BCA =40. ADC=20 I think it should be DCA

Now,since tri ABC is isoceles either angle x= angle BAC= 140/2=70 or angle x= angle BCA= 40.

Again Insufficient.

Hence E.

What is the OA?


Remember we are told ABC is isosceles,but not which sides are equal.
Great Explanation, I just want to know one thing,
Is there any theorem as well, Where there is any relation Between Angle x and angle y ,
I am not pretty sure , If there is any Please share that ...
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by Night reader » Tue Nov 23, 2010 5:36 am
goyalsau wrote: Great Explanation, I just want to know one thing,
Is there any theorem as well, Where there is any relation Between Angle x and angle y ,
I am not pretty sure , If there is any Please share that ...
Qoyalsau, to answer your question we need to understand angle itself. What forms an angle? Two lines sharing a common point. What is line, then? The word 'line' denotes a straight line (ray) that extends both directions toward infinity. Line is different from 'line segment'. The 'line segment' has endpoints. The 'line segment' does not extend in either direction beyond its endpoints.

Two (or more) angles may be related directly if they are formed by at least one common line, e.g. supplementary, vertical, complimentary angles.

To answer your question - No the angles x and y are not related directly. They may be related indirectly, which is not the point in DS. For DS we must ascertain the exact facts.
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by diebeatsthegmat » Wed Nov 24, 2010 12:02 am
rishab1988 wrote:It should be E

Here is why:

we are given that tri ABC and ADC are isosceles.

1) y=140.Since we know ADC is isosceles,at least 2 angles must have same measure.We also know sum of the angles of a tria=180.Therefore 140 is not the common angles ,because if two angles measure 140 ,sum >280. So the other 2 angles must be 20 each.

But we can't infer the measure of angles x from this.because its measure depends on measure of angles BAD and BCD.If angles BAD=BCD=30 x= 180-(100)=80;but if BAD=BCD=40 x=180-(120)=60.

Not sufficient

2) We are told angle DCA =1/2 BCA or angle DCA= BCD.

Lets assume DCA=BCD=50.Therefore BCA=100;Since ABC must be isosceles x=40.However if DCA=BCD=40 which means BCA=80.x could be either 20 or 80.

Insufficient.

Combining 1 and 2.

From 1 we know ADC=20 and from 2 we know BCA =40.

Now,since tri ABC is isoceles either angle x= angle BAC= 140/2=70 or angle x= angle BCA= 40.

Again Insufficient.

Hence E.

What is the OA?


Remember we are told ABC is isosceles,but not which sides are equal.
excuse men, i dont really understand your solution.
obviously, from the question we know that triangle ABC and ADC are isoscesles.
so AB=BC and AD=DC and ^BAC=^BCA and DAC^=DCA^ ( right?)
statement 1 and 2 both are insufficient ( agreed)
1+2/ since DCA^=20 => DAC^20
DAC=1/2BCA so BCA^=40
is it not right that we will find the angle x? since ^BCA=BAC=40 so the other angle x=100?
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by beat_gmat_09 » Wed Nov 24, 2010 1:12 am
diebeatsthegmat wrote: obviously, from the question we know that triangle ABC and ADC are isoscesles.
so AB=BC and AD=DC
You haven't been told that AB=BC and AD=DC
The information just says that the two triangles are isosceles.
You can also count AC=BC or AB=AC in triangle ABC, same goes for the other triangle.
This is the trick in the question. It coaxes to think AB=BC
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by tomada » Wed Nov 24, 2010 4:08 pm
What is the source of this question?

Night reader wrote:In the Â…figure (attached below), if triangle ABC and triangle ADC are isosceles
triangles, what is the value of x?
(1) y = 140
(2) Angle DCA is one half the measure of Angle BCA.
Image
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by tomada » Wed Nov 24, 2010 4:21 pm
Leave it to me to go against the grain here, but...

I understand what everyone has been saying, namely that we're told that the triangles are isosceles, but not which sides of each triangle are equal to each other.

We're given that angle Y = 140. We know triangle ADC is isosceles. The only way this is possible is if angles DCA and DAC each = 20.

Then we're told that angle BCA = 2*DCA = 40. Thus, angle C = 20+40 = 60.
We're told that ABC is isosceles so, since C=60, either X or A must = 60.

If we say X=60, then A must = 60 for the total angles in the larger triangle to equal 180.
If we say A=60, then X must = 60 for the same reason.

Either way, X=60, so the answer should be C.

Night reader wrote:In the Â…figure (attached below), if triangle ABC and triangle ADC are isosceles
triangles, what is the value of x?
(1) y = 140
(2) Angle DCA is one half the measure of Angle BCA.
Image
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by Night reader » Wed Nov 24, 2010 5:56 pm
tomada wrote:Leave it to me to go against the grain here, but...
...
Either way, X=60, so the answer should be C.

I agree with you!


Statement (1) is insufficient. It allows us to determine that Angle DAC = Angle DCA = 20, but that doesn't give us any information about Triangle ABC.

Statement (2) is also insufficient: it may prove helpful, but in order to solve this problem, we need some number to start with.
Taken together, the statements are still insufficient. Since Angle DCA = 20, Angle BCA = 40. Since Triangle ABC is isosceles, two of the angles in the triangle are equal, but we don't know which ones. It may be that Angle BCA = Angle BAC, in
which case x = 180 - 40 - 40 = 100. However, it could also be the case that Angle BAC = Angle ABC, in which case 180 = 40 + x + x, so x = 70.

Choice (E) is correct.

The above is an explanation by Jeff Sackman, an author of the original question placed with 'Total GMAT Math' book, Geometry section.

Problem text>>>>
In the Â…figure (attached below), if triangle ABC and triangle ADC are isosceles triangles, what is the value of x?
(1) y = 140
(2) Angle DCA is one half the measure of Angle BCA.
<<<

p.s. I first made myself to e-mail this problem to author, but then, may be because I switched to other problems, this came out as a big discussion here. So, TOMADA you are absolutely right; the answer here is C!
Attachments
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by diebeatsthegmat » Wed Nov 24, 2010 7:17 pm
beat_gmat_09 wrote:
diebeatsthegmat wrote: obviously, from the question we know that triangle ABC and ADC are isoscesles.
so AB=BC and AD=DC
You haven't been told that AB=BC and AD=DC
The information just says that the two triangles are isosceles.
You can also count AC=BC or AB=AC in triangle ABC, same goes for the other triangle.
This is the trick in the question. It coaxes to think AB=BC
you meant the two traingle ABC and ADC are just told to be issoscessles but we are not known which point two equal sides of these isoscesles are intersected at, thus we cant find which sides are equal, right?
man, its tricky!
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by rishab1988 » Mon Nov 29, 2010 3:45 am
Not that I'm bragging.But I have got q51 two times in GMAT quant,so I'm kind of used to such tricks in the question.Doing MGMAT quant and LSAT CR can improve your score a lot because they improve your critical thinking skills.Infer only what you can infer.DO NOT ASSUME ANYTHING

This way you are not so easily tricked by the question...

The answer obviously cannot be C,as explained by nightreader and by me,in my previous post.

If you guys carefully read my explanation you'll know why the answer is NOT C.
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