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Is triangle ABC an isosceles?
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Ljchen121
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Is triangle ABC an isosceles? [#permalink] New post  Updated on: 14 Aug 2013, 01:39
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A
B
C
D
E

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75% (hard)

Question Stats:

46% (01:23) correct 54% (01:29) wrong based on 499 sessions

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Is triangle ABC an isosceles?

(1) AB/BC = 2

(2) x≠y
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Originally posted by Ljchen121 on 08 May 2012, 09:06.
Last edited by Bunuel on 14 Aug 2013, 01:39, edited 1 time in total.
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Bunuel
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Re: Is triangle ABC an isosceles? [#permalink] New post  09 May 2012, 01:32
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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?

The OG says it's E though. Please help.


Your reasoning is correct answer should be C, not E.

Is triangle ABC an isosceles?
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Screen Shot 2012-05-08 at 1.05.37 PM.png
Screen Shot 2012-05-08 at 1.05.37 PM.png [ 7.39 KiB | Viewed 17874 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.

Answer: C.
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Re: Is triangle ABC an isosceles? [#permalink] New post  08 May 2012, 09:11
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?

The OG says it's E though. Please help.
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Re: Is triangle ABC an isosceles? [#permalink] New post  16 May 2012, 04:27
Initially tricked upon thinking it is E. Thanks Bunuel for the explanation.
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Re: Is triangle ABC an isosceles? [#permalink] New post  21 May 2012, 01:35
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?

The OG says it's E though. Please help.


Answer should be E
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] New post  21 May 2012, 01:42
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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?

The OG says it's E though. Please help.


Answer should be E
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] New post  23 May 2012, 10:51
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] New post  13 Sep 2013, 11:54
can side AB=AC from 1st statement by making x=y?
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Re: Is triangle ABC an isosceles? [#permalink] New post  14 Sep 2013, 03:00
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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] New post  20 May 2017, 15:47
Hi,

Basis Statement 1 alone: Given ratio of two sides of a triangle AB:BC as 2:1 and Triangle Inequality, how is it possible to create an isoslece triangle?

Please advice.
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Re: Is triangle ABC an isosceles? [#permalink] New post  21 May 2017, 01:00
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Shobhit7 wrote:
Hi,

Basis Statement 1 alone: Given ratio of two sides of a triangle AB:BC as 2:1 and Triangle Inequality, how is it possible to create an isoslece triangle?

Please advice.



2 - 2 - 1
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Re: Is triangle ABC an isosceles? [#permalink] New post  08 Sep 2017, 00:17
Ljchen121 wrote:
Attachment:
Screen Shot 2012-05-08 at 1.05.37 PM.png
Note: Figure not drawn to scale.
Is triangle ABC an isosceles?

(1) AB/BC = 2

(2) x≠y


St 1

This statement just tells us that angle A = 2Y however we don't know for certain whether this is an isosceles because

2(50) + 50 + x =180
x =30

Or you could have an isosceles

2(45) + 45 +45 =180

But we can't make that decision unless we have more info

Insuff

St 2

Not necessarily

St 1 and St 2

If x cannot equal y then we cannot have an equilateral

C
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Is triangle ABC an isosceles? [#permalink] New post  21 Mar 2021, 13:12
Is this an OG question?

Can we reason this way?

Let's assume angle A is z.

St1. AB/BC = 2...this implies y = 2z...but insufficient b/c we don't know whether x = y
St2 x cannot equal y...insufficient b/c we don't know whether x = z

Combined:

3 angles - x, y, and z...each of which are distinct. Hence, ABC is NOT isosceles.

C.
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