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In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C

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In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post Updated on: 02 May 2016, 04:40
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  95% (hard)

Question Stats:

33% (02:49) correct 67% (02:37) wrong based on 157 sessions

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In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C are the vertices of the triangle and a\(^{\circ}\)and b\(^{\circ}\) denote the angles shown. Is the length of AB greater than that of AC?

(1) a – b = 30

(2) b = 70

Attachment:
100215.jpg
100215.jpg [ 9.91 KiB | Viewed 3316 times ]

Originally posted by jyotibrata on 12 Mar 2016, 11:03.
Last edited by ENGRTOMBA2018 on 02 May 2016, 04:40, edited 2 times in total.
Edited the question.
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 12 Mar 2016, 11:40
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3
jyotibrata wrote:
In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C are the vertices of the triangle and ao and bo denote the angles shown. Is the length of AB greater than that of AC?

(1) a – b = 30

(2) b = 70

Attachment:
The attachment 100215.jpg is no longer available


We can clearly see that in order for getting an answer for is AB>AC we need to find the relation between the angles opposite to this sides as in any triangle the side opposite to a greater angle is greater.

Also, from the property of quadrilaterals, sum of all the angles of a quad = 360 and when used in conjunction with the fact that sum of angles on a triangle = 180 --->

\(\angle {ACB} = a-90\) (refer to the attached picture to see the calculations).

Attachment:
2016-03-12_13-35-52.jpg
2016-03-12_13-35-52.jpg [ 12.77 KiB | Viewed 2706 times ]


Per statement 1, a-b=30 ---> a=30+b ---> c = a-90=30+b-90 = b-60 ---> c<b and as sides opposite to greater angles are longer ---> AC>AB

Per statement 2, b=70. Clearly not sufficient.

A is thus the correct answer.

Hope this helps.
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 01 May 2016, 01:21
Engr2012 wrote:
jyotibrata wrote:
In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C are the vertices of the triangle and ao and bo denote the angles shown. Is the length of AB greater than that of AC?

(1) a – b = 30

(2) b = 70

Attachment:
100215.jpg


We can clearly see that in order for getting an answer for is AB>AC we need to find the relation between the angles opposite to this sides as in any triangle the side opposite to a greater angle is greater.

Also, from the property of quadrilaterals, sum of all the angles of a quad = 360 and when used in conjunction with the fact that sum of angles on a triangle = 180 --->

\(\angle {ACB} = a-90\) (refer to the attached picture to see the calculations).

Attachment:
2016-03-12_13-35-52.jpg


Per statement 1, a-b=30 ---> a=30+b ---> c = a-90=30+b-90 = b-60 ---> c<b and as sides opposite to greater angles are longer ---> AC>AB

Per statement 2, b=70. Clearly not sufficient.

A is thus the correct answer.

Hope this helps.



Why are you assuming the angle as 90 degree in the triangle you have shown in your figure.
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 01 May 2016, 01:33
Bunuel, can you please help.
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 01 May 2016, 04:08
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sudhirmadaan wrote:
Bunuel, can you please help.


It's not courteous to post another message without letting the person reply. Do give the OP sufficient time in replying to your question.

I did not assume anything. The question says that the triangle ABC is drawn on the coordinate plane and as such the 2 lines can only be the coordinate axes. Hence, they are perpendicular, making that angle 90 degree

Posted from my mobile device
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 01 May 2016, 05:09
Engr2012 wrote:
sudhirmadaan wrote:
Bunuel, can you please help.


It's not courteous to post another message without letting the person reply. Do give the OP sufficient time in replying to your question.

I did not assume anything. The question says that the triangle ABC is drawn on the coordinate plane and as such the 2 lines can only be the coordinate axes. Hence, they are perpendicular, making that angle 90 degree

Posted from my mobile device



I apologies , I did not mean that way. I came across few posts from experts where it is clearly written that don't be decisive in DS question with coordinate geometer figures. Thanks for explanation I got your point.
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 01 May 2016, 05:16
sudhirmadaan wrote:
Engr2012 wrote:
sudhirmadaan wrote:
Bunuel, can you please help.


It's not courteous to post another message without letting the person reply. Do give the OP sufficient time in replying to your question.

I did not assume anything. The question says that the triangle ABC is drawn on the coordinate plane and as such the 2 lines can only be the coordinate axes. Hence, they are perpendicular, making that angle 90 degree

Posted from my mobile device



I apologies , I did not mean that way. I came across few posts from experts where it is clearly written that don't be decisive in DS question with coordinate geometer figures. Thanks for explanation I got your point.


You do raise a very valid question, something GMAT question will not do. All GMAT questions are unambiguous (or 99.9% of them) and I'm sure that if this would've been an official question, the question stem would've stated that the vertical and the horizontal lines that make the 90 degrees are the coordinate axes to remove any ambiguity.

Hope this helps.
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C  [#permalink]

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New post 15 Jan 2018, 06:58
Sorry I don´t understand why this is not a D.

I think that if I only know the value of B i can Solve de problem.

(180-a) +90 + (180-b) + (180-a) = 360

...
...

2a + b = 270


2) b= 70

----> a= 100 and as a + b+ c = 180 then C= 10 so AC > AB

is that right?
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Re: In triangle ABC (figure shown) drawn on a coordinate plane, A, B and C &nbs [#permalink] 15 Jan 2018, 06:58
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