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Is triangle ABC obtuse angled?  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 22% (01:26) correct 78% (01:22) wrong based on 449 sessions

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Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

Originally posted by Tornikea on 05 Aug 2015, 12:45.
Last edited by Bunuel on 16 Aug 2015, 11:36, edited 1 time in total.
Edited the question.
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Is triangle ABC obtuse angled?  [#permalink]

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2
Please see the sketch for clarity.

gmatcracker2018 wrote:
Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

hi

Can anybody please post any image that depicts the scenario perfectly ...? Edit: Clearer pic updated
Attachments IMG_20180411_095312.jpg [ 683.49 KiB | Viewed 4322 times ]

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GMAT 1: 710 Q50 V34 Re: Is triangle ABC obtuse angled?  [#permalink]

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Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

IMO : E

Given ABC is a triangle

Statement 1: $$a^2 + b^2 > c^2$$

Condition for a triangle to be an obtuse is
$$c^2 > a^2 + b^2$$ (with "c" largest side)
Since nothing is given about which is the largest side
Not suff

Statement 2 : The center of the circle circumscribing the triangle does not lie inside the triangle.

Circum-center lies on the triangle = Right angled triangle
Circum center lies outside the triangle = Obtuse Triangle
Hence two possible cases, not suff

Combined:
Still not suff
##### General Discussion
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Re: Is triangle ABC obtuse angled?  [#permalink]

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Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

SOLUTION:

Statement 1): a^2 + b^2 > c^2. This condition works in Right angled triangle and Obtuse angled triangle.

Hence , Insufficient.

Statement 2): The Center of the circle circumscribing the triangle does not lie inside the triangle.

Centre of the circle can lie on the triangle or outside the triangle.

Here, Apply relation between Central Angle and Inscribed angle.

if Central Angle makes 180 degrees with any two vertices of the triangle then it is a right angled triangle, in this case centre of the circle is not inside the triangle.

if Central angle makes more than 180 degrees with any two vertices of the triangle then , as per relation between Central angle and Inscribed Angle . the triangle has a angle more than 90 degrees, in this case centre of the circle is not inside the triangle.

Hence , Insufficient.

Both statements together also same results as above.

Hence, Insufficient.

ANS) E
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Re: Is triangle ABC obtuse angled?  [#permalink]

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Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

I believe statement 1 is sufficient; I think the correct answer choice is A. I think triangle ABC will always be an acute triangle if statement 1 is true. Can someone offer me a counterexample?

Also I find it hard to believe that this question is from the official guide since the variables: a,b, and c are vague. I think sides AB, BC, and AC should be mentioned or the question should be edited in a way that it is not ambiguous.
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Re: Is triangle ABC obtuse angled?  [#permalink]

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1
Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

I believe statement 1 is sufficient; I think the correct answer choice is A. I think triangle ABC will always be an acute triangle if statement 1 is true. Can someone offer me a counterexample?

Also I find it hard to believe that this question is from the official guide since the variables: a,b, and c are vague. I think sides AB, BC, and AC should be mentioned or the question should be edited in a way that it is not ambiguous.

Please remember that it is a waste of time to doubt official questions and/or OAs for them. Take them as they are.

ABC with sides 3,3,3 in this case, 3^2+3^2>3^2 ---> triangle is NOT an obtuse angled triangle.

But with ABC as 3,4,6 (6^2+4^2>3^2), the angles are 36°, 26°, 118°, you do get a yes for an obtuse angle. Without knowing what do a,b,c, stand for, you wont be able to answer the question.

The ambiguity you are talking about is what makes this statement not sufficient and E as the correct answer.
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Re: Is triangle ABC obtuse angled?  [#permalink]

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Engr2012 wrote:
Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

I believe statement 1 is sufficient; I think the correct answer choice is A. I think triangle ABC will always be an acute triangle if statement 1 is true. Can someone offer me a counterexample?

Also I find it hard to believe that this question is from the official guide since the variables: a,b, and c are vague. I think sides AB, BC, and AC should be mentioned or the question should be edited in a way that it is not ambiguous.

Please remember that it is a waste of time to doubt official questions and/or OAs for them. Take them as they are.

ABC with sides 3,3,3 in this case, 3^2+3^2>3^2 ---> triangle is NOT an obtuse angled triangle.

But with ABC as 3,4,6 (6^2+4^2>3^2), the angles are 36°, 26°, 118°, you do get a yes for an obtuse angle. Without knowing what do a,b,c, stand for, you wont be able to answer the question.

The ambiguity you are talking about is what makes this statement not sufficient and E as the correct answer.

Hi Engr2012,

The problem I had with the question was that no where in the question stem does it mention that variables a,b, and c represent the lengths of triangle ABC. So I thought that If I had to assume that a,b,c represent the lengths of a triangle, then I can also assume that length c of triangle of ABC was the biggest as it is when describing the Pythagorean theorem. I agree that the official answer is E because we don't know whether C represents the largest side of the triangle or not.
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Is triangle ABC obtuse angled?  [#permalink]

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Hi Engr2012,

The problem I had with the question was that no where in the question stem does it mention that variables a,b, and c represent the lengths of triangle ABC. So I thought that If I had to assume that a,b,c represent the lengths of a triangle, then I can also assume that length c of triangle of ABC was the biggest as it is when describing the Pythagorean theorem. I agree that the official answer is E because we don't know whether C represents the largest side of the triangle or not.

If you know c is the largest side, then statement will become sufficient.

Hope this helps.

Originally posted by ENGRTOMBA2018 on 21 Oct 2015, 17:53.
Last edited by ENGRTOMBA2018 on 21 Oct 2015, 18:36, edited 1 time in total.
Corrected the solution
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Re: Is triangle ABC obtuse angled?  [#permalink]

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Engr2012 wrote:

Hi Engr2012,

The problem I had with the question was that no where in the question stem does it mention that variables a,b, and c represent the lengths of triangle ABC. So I thought that If I had to assume that a,b,c represent the lengths of a triangle, then I can also assume that length c of triangle of ABC was the biggest as it is when describing the Pythagorean theorem. I agree that the official answer is E because we don't know whether C represents the largest side of the triangle or not.

Your interpretation is partially correct. Even if you know c is the largest side, I gave you 2 cases above that make statement 1 as not sufficient.

So in order to answer this particular question, the knowledge of whether side c is the largest is not important.

Hope this helps.

In your example, the sides of the triangle were 3,4, and 6. If we were to assume that side c was the largest side of the triangle, then your example doesn't satisfy statement 1.
Let's say a=3, b=4, and c=6 then $$a^2 +b^2 <c^2$$
I would expect it to be obtuse triangle.

According to GMAT expert, Mike Mcgarry of Magoosh, the following properties are true if c is the largest side:
If $$a^2+b^2 < c^2$$, the triangle is obtuse.
If $$a^2+b^2 > c^2$$, the triangle is acute.
If $$a^2+b^2 =c^2$$, the triangle is right.

Here is a link to the article: http://magoosh.com/gmat/2012/re-thinkin ... le-obtuse/
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Is triangle ABC obtuse angled?  [#permalink]

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Engr2012 wrote:

Hi Engr2012,

The problem I had with the question was that no where in the question stem does it mention that variables a,b, and c represent the lengths of triangle ABC. So I thought that If I had to assume that a,b,c represent the lengths of a triangle, then I can also assume that length c of triangle of ABC was the biggest as it is when describing the Pythagorean theorem. I agree that the official answer is E because we don't know whether C represents the largest side of the triangle or not.

Your interpretation is partially correct. Even if you know c is the largest side, I gave you 2 cases above that make statement 1 as not sufficient.

So in order to answer this particular question, the knowledge of whether side c is the largest is not important.

Hope this helps.

In your example, the sides of the triangle were 3,4, and 6. If we were to assume that side c was the largest side of the triangle, then your example doesn't satisfy statement 1.
Let's say a=3, b=4, and c=6 then $$a^2 +b^2 <c^2$$
I would expect it to be obtuse triangle.

According to GMAT expert, Mike Mcgarry of Magoosh, the following properties are true if c is the largest side:
If $$a^2+b^2 < c^2$$, the triangle is obtuse.
If $$a^2+b^2 > c^2$$, the triangle is acute.
If $$a^2+b^2 =c^2$$, the triangle is right.

Here is a link to the article: http://magoosh.com/gmat/2012/re-thinkin ... le-obtuse/

I dont think I made myself clear. What I wanted to say with my example above, with sides 3,4,6, until the question tells me that c=largest side, I can play around with the sides to prove that a statement may or may not work. A "sufficient" statement MUST work for ALL different cases possible within scope of the question and the given statement(s).

(3,4,6) does work as an example case for statement 1. You are given a^2+b^2>c^2. No one knows whether c is the greatest side. I can take c=3 or 4 or 6 in this case to prove my point. This ambiguity is what is making this statement not sufficient.

Isnt 6^2+4^2>3^2? Yes. Can you have a triangle with sides 3,4,6 ? Yes.

As per the definition, yes a^2+b^2>c^2 will give you an acute angled triangle only if you know that c is the greatest side. You can not apply this in this question because of the inherent ambiguity.

Hope this clears the confusion.

Additionally, I have updated my post above.
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Re: Is triangle ABC obtuse angled?  [#permalink]

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I completely understand what you are saying. The confusion arose when you originally said,
Engr2012 wrote:
Your interpretation is partially correct. Even if you know c is the largest side, I gave you 2 cases above that make statement 1 as not sufficient.

So in order to answer this particular question, the knowledge of whether side c is the largest is not important.

We both agree that if you know c is the largest side, then statement will become sufficient. Just to clarify, I completely understand that this statement is insufficient without knowing whether c is the largest side or not. But the knowledge of the magnitude of c would certainly be important in determining sufficiency. As we both agree that without knowing whether c is the largest side or not, makes this statement is insufficient.

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Re: Is triangle ABC obtuse angled?  [#permalink]

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Hi

If $$a^2+b^2 < c^2$$, it means the angle between side a & b is obtuse, the triangle is obtuse.
If $$a^2+b^2 > c^2$$, it means the angle between a & b is acute, but since other angle can be obtuse, the triangle cant be taken as acute.
If $$a^2+b^2 =c^2$$, it means the angle between a & b is 90 deg, hence the triangle is right.

I hope it helps.

ENGRTOMBA2018 wrote:

Hi Engr2012,

The problem I had with the question was that no where in the question stem does it mention that variables a,b, and c represent the lengths of triangle ABC. So I thought that If I had to assume that a,b,c represent the lengths of a triangle, then I can also assume that length c of triangle of ABC was the biggest as it is when describing the Pythagorean theorem. I agree that the official answer is E because we don't know whether C represents the largest side of the triangle or not.

Your interpretation is partially correct. Even if you know c is the largest side, I gave you 2 cases above that make statement 1 as not sufficient.

So in order to answer this particular question, the knowledge of whether side c is the largest is not important.

Hope this helps.[/quote]

In your example, the sides of the triangle were 3,4, and 6. If we were to assume that side c was the largest side of the triangle, then your example doesn't satisfy statement 1.
Let's say a=3, b=4, and c=6 then $$a^2 +b^2 <c^2$$
I would expect it to be obtuse triangle.

According to GMAT expert, Mike Mcgarry of Magoosh, the following properties are true if c is the largest side:
If $$a^2+b^2 < c^2$$, the triangle is obtuse.
If $$a^2+b^2 > c^2$$, the triangle is acute.
If $$a^2+b^2 =c^2$$, the triangle is right.

Here is a link to the article: http://magoosh.com/gmat/2012/re-thinkin ... le-obtuse/[/quote]

I dont think I made myself clear. What I wanted to say with my example above, with sides 3,4,6, until the question tells me that c=largest side, I can play around with the sides to prove that a statement may or may not work. A "sufficient" statement MUST work for ALL different cases possible within scope of the question and the given statement(s).

(3,4,6) does work as an example case for statement 1. You are given a^2+b^2>c^2. No one knows whether c is the greatest side. I can take c=3 or 4 or 6 in this case to prove my point. This ambiguity is what is making this statement not sufficient.

Isnt 6^2+4^2>3^2? Yes. Can you have a triangle with sides 3,4,6 ? Yes.

As per the definition, yes a^2+b^2>c^2 will give you an acute angled triangle only if you know that c is the greatest side. You can not apply this in this question because of the inherent ambiguity.

Hope this clears the confusion.

Additionally, I have updated my post above.[/quote]
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Re: Is triangle ABC obtuse angled?  [#permalink]

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Tornikea wrote:
Is triangle ABC obtuse angled?

(1) a^2 + b^2 > c^2

(2) The center of the circle circumscribing the triangle does not lie inside the triangle.

hi

Can anybody please post any image that depicts the scenario perfectly ...? Manager  S
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Is triangle ABC obtuse angled?  [#permalink]

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If any angle in triangle is grater 90, then that triangle is obtuse.
The question asks whether triangle ABC is obtuse, not whether angle C is greater than 90.
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Originally posted by Blackishmamba on 13 Aug 2018, 02:45.
Last edited by Blackishmamba on 23 Aug 2018, 07:40, edited 1 time in total.
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Re: Is triangle ABC obtuse angled?  [#permalink]

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Blackishmamba wrote:
I disagree with OA
If any angle in triangle is grater 90, then that triangle is obtuse.
The question asks whether triangle ABC is obtuse, not whether angle C is greater than 90.
Correct answer choice would be A.

The question is from Official Guide. You can 1 000 times disagree, but it won't help you on GMAT. I'm more than sure that several Math PhD had reviewed this question before GMAT released it. Chanhe your mind and approach OA in official questions as a must. Peace.
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