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# Is triangle ABC an isosceles?

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Is triangle ABC an isosceles? [#permalink]

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08 May 2012, 10:06
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Question Stats:

39% (01:56) correct 61% (00:55) wrong based on 258 sessions

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Screen Shot 2012-05-08 at 1.05.37 PM.png [ 7.39 KiB | Viewed 5758 times ]
Note: Figure not drawn to scale.
Is triangle ABC an isosceles?

(1) AB/BC = 2

(2) x≠y
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Aug 2013, 02:39, edited 1 time in total.
Edited the OA.
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Re: Is triangle ABC an isosceles? [#permalink]

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08 May 2012, 10:11
I thought it was C, because the only way for the triangle to be isosceles given both conditions is for BC = AC , and that's not possible because side AC + BC (assuming they are the same length) would equal AB. And the third side of the triangle must be greater than the sum of the other two sides or less than the difference of the other two sides. So given both conditions, should we be able to say for sure that the triangle is not isosceles?

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Re: Is triangle ABC an isosceles? [#permalink]

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09 May 2012, 02:32
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Ljchen121 wrote:
I thought it was C, because the only way for the triangle to be isosceles given both conditions is for BC = AC , and that's not possible because side AC + BC (assuming they are the same length) would equal AB. And the third side of the triangle must be greater than the sum of the other two sides or less than the difference of the other two sides. So given both conditions, should we be able to say for sure that the triangle is not isosceles?

Is triangle ABC an isosceles?
Attachment:

Screen Shot 2012-05-08 at 1.05.37 PM.png [ 7.39 KiB | Viewed 5682 times ]

(1) AB/BC = 2 --> $$AB\neq{BC}$$. Not sufficient on its own.
(2) x≠y --> $$AB\neq{AC}$$. Not sufficient on its own.

(1)+(2) Since $$AB\neq{BC}$$ and $$AB\neq{AC}$$, then the only way ABC to be isosceles is when $$AC=BC$$. But in this case as given that AB=2BC then AB=BC+BC=BC+AC which is not possible because the length of any side of a triangle must be smaller than the sum of the other two sides. So, $$AC\neq{BC}$$, which means that ABC is not isosceles. Sufficient.

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Re: Is triangle ABC an isosceles? [#permalink]

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09 May 2012, 21:45
E

Both statements give you an impossible triangle
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Re: Is triangle ABC an isosceles? [#permalink]

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16 May 2012, 05:27
Initially tricked upon thinking it is E. Thanks Bunuel for the explanation.
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Re: Is triangle ABC an isosceles? [#permalink]

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21 May 2012, 02:35
Ljchen121 wrote:
I thought it was C, because the only way for the triangle to be isosceles given both conditions is for BC = AC , and that's not possible because side AC + BC (assuming they are the same length) would equal AB. And the third side of the triangle must be greater than the sum of the other two sides or less than the difference of the other two sides. So given both conditions, should we be able to say for sure that the triangle is not isosceles?

even if we cosider both 1) & 2) consider the below examples:

Case 1--> x= 30, y=100 & third angle= 50
Case 2--> x=45, y=90 & third angle =45

here both 1) & 2) are satisfied but there is contradiction in result, i.e. in one case traingle is issoceles, in other it is not, for the same conditions. Hence E
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Re: Is triangle ABC an isosceles? [#permalink]

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21 May 2012, 02:42
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narangvaibhav wrote:
Ljchen121 wrote:
I thought it was C, because the only way for the triangle to be isosceles given both conditions is for BC = AC , and that's not possible because side AC + BC (assuming they are the same length) would equal AB. And the third side of the triangle must be greater than the sum of the other two sides or less than the difference of the other two sides. So given both conditions, should we be able to say for sure that the triangle is not isosceles?

even if we cosider both 1) & 2) consider the below examples:

Case 1--> x= 30, y=100 & third angle= 50
Case 2--> x=45, y=90 & third angle =45

here both 1) & 2) are satisfied but there is contradiction in result, i.e. in one case traingle is issoceles, in other it is not, for the same conditions. Hence E

When considering the statements together the red scenario is not possible. If x=z then it would mean that AC=BC. But in this case as given that AB=2BC then AB=BC+BC=BC+AC which is not possible because the length of any side of a triangle must be smaller than the sum of the other two sides.
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Re: Is triangle ABC an isosceles? [#permalink]

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23 May 2012, 11:51
intense reasoning guys! I picked E and didnt test the problem from the length of sides perspective. looked only at the angles.
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Re: Is triangle ABC an isosceles? [#permalink]

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14 Aug 2013, 02:40
Expert's post
Bumping for review and further discussion.
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Re: Is triangle ABC an isosceles? [#permalink]

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13 Sep 2013, 12:54
can side AB=AC from 1st statement by making x=y?
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Re: Is triangle ABC an isosceles? [#permalink]

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14 Sep 2013, 04:00
Expert's post
saggii27 wrote:
can side AB=AC from 1st statement by making x=y?

Yes, for (1) it's possible that AB=AC as well as it's possible that AB#AC, so the first statement is not sufficient.
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Re: Is triangle ABC an isosceles? [#permalink]

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17 Mar 2016, 11:44
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Re: Is triangle ABC an isosceles?   [#permalink] 17 Mar 2016, 11:44
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