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# M23-18

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:19
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Difficulty:

45% (medium)

Question Stats:

59% (01:16) correct 41% (01:30) wrong based on 149 sessions

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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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Joined: 02 Sep 2009
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16 Sep 2014, 01:19
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".

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14 Sep 2015, 17:23
Bunuel wrote:
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".

It would be really helpful if it is explained how many possible scenarios possible for which Statement 2 alone is insufficient.
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Joined: 17 Oct 2015
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02 Mar 2016, 18:08
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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03 Mar 2016, 07:34
3
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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08 Jul 2016, 11:19
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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08 Jul 2016, 12:43
1
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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11 Sep 2016, 04:35
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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10 Mar 2018, 07:33
+1 for option C.
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23 Mar 2019, 13:25
1
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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24 Mar 2019, 02:02
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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21 May 2019, 03:38
Hi,

I think it would be possible to determine the answer through each statement. Can anyone explain why that is not possible?
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24 Jun 2019, 11:49
I think B is alone sufficient to answer the question

As for the basic principle for a polygon to be a triangle is that sum of 2 sides is greater than the third side and difference of the 2 sides is always less than the 3 rd side.
So if angle B=80
This puts a limit on the other two angle(supposed x and y) to be between the range of 11-89 degrees.
Hence all the angles would be less than 90 degrees.

Kindly explain if this doesn't makes sense
Re: M23-18   [#permalink] 24 Jun 2019, 11:49
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