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M23-18
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Bunuel
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M23-18 [#permalink] New post  16 Sep 2014, 00:19
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Are all the angles of triangle \(ABC\) smaller than 90 degrees?


(1) \(AB \lt BC \lt AC\)

(2) \(\angle ABC = 80\) degrees
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Bunuel
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Re M23-18 [#permalink] New post  16 Sep 2014, 00:19
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Official Solution:


Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are sufficient. S1 and S2 gives that \(\angle ABC\) is the largest angle. Thus, the other two angles are smaller than 80 degrees and the answer to the question is "yes".


Answer: C
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Re M23-18 [#permalink] New post  02 Mar 2016, 17:08
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I did not get why abc is the largest degree..
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Bunuel
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Re: M23-18 [#permalink] New post  03 Mar 2016, 06:34
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mestrec wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I did not get why abc is the largest degree..


Since AB<BC<AC, then AC is the largest side. The largest angle in a triangle is opposite the largest side.
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Re: M23-18 [#permalink] New post  08 Jul 2016, 10:19
Hi Bunnel ,
As per statement 2 angle ABC = 80 so it is clear that NOT ALL angles of triangle ABC is <90 as other to angles can be (0,100). Therefore statement 2 is sufficient . Am I right ?
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Bunuel
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Re: M23-18 [#permalink] New post  08 Jul 2016, 11:43
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mahawarchirag wrote:
Hi Bunnel ,
As per statement 2 angle ABC = 80 so it is clear that NOT ALL angles of triangle ABC is <90 as other to angles can be (0,100). Therefore statement 2 is sufficient . Am I right ?


Since the answer is C and not B, then obviously you are not right:
{80, 80, 20} ALL the angles are less than 90 degrees
{80, 95, 5} NOT ALL the angles are less than 90 degrees
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Re: M23-18 [#permalink] New post  11 Sep 2016, 03:35
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From option 1 ac is the largest side that implies angle ABC to be the largest angle which equals 80 hence any other angle will be less than 80 degrees.
Which implies all the angles of triangle ABCABC smaller than 90 degrees.

Awesome question :)
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Re: M23-18 [#permalink] New post  23 Mar 2019, 12:25
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Bunuel wrote:
mahawarchirag wrote:
Hi Bunnel ,
As per statement 2 angle ABC = 80 so it is clear that NOT ALL angles of triangle ABC is <90 as other to angles can be (0,100). Therefore statement 2 is sufficient . Am I right ?


Since the answer is C and not B, then obviously you are not right:
{80, 80, 20} ALL the angles are less than 90 degrees
{80, 95, 5} NOT ALL the angles are less than 90 degrees


Hi Bunuel, could you please explain how the example {80, 95, 5} works? Isn't there a property for triangles where the third side has to be greater than the difference of the other two sides?

95-80=15 so the third side has to be greater than 15. I would think B is the correct answer in this question.
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Re: M23-18 [#permalink] New post  24 Mar 2019, 01:02
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rodri102 wrote:
Bunuel wrote:
mahawarchirag wrote:
Hi Bunnel ,
As per statement 2 angle ABC = 80 so it is clear that NOT ALL angles of triangle ABC is <90 as other to angles can be (0,100). Therefore statement 2 is sufficient . Am I right ?


Since the answer is C and not B, then obviously you are not right:
{80, 80, 20} ALL the angles are less than 90 degrees
{80, 95, 5} NOT ALL the angles are less than 90 degrees


Hi Bunuel, could you please explain how the example {80, 95, 5} works? Isn't there a property for triangles where the third side has to be greater than the difference of the other two sides?

95-80=15 so the third side has to be greater than 15. I would think B is the correct answer in this question.


Those are degree measure not side lengths.
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Re M23-18 [#permalink] New post  03 Feb 2020, 12:29
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I didnt understood what the second statment means
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Bunuel
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Re: M23-18 [#permalink] New post  03 Feb 2020, 12:36
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Rcand92 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I didnt understood what the second statment means


You can find more solutions here: https://gmatclub.com/forum/are-all-the- ... fl=similar
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Re M23-18 [#permalink] New post  12 Mar 2021, 22:11
If you know comparison between sides and also one angle, you can find out if that angle is the largest

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