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Is MNP isosceles? (1) Exactly two of the angles, M and N, have the

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Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   14 Nov 2018, 09:39
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Is ΔMNP isosceles?

(1) Exactly two of the angles, ∠M and ∠N, have the same measure
(2) ∠N and ∠P do not have the same measure.
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Re: Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   14 Nov 2018, 09:48
Stmt 1: States that 2 angles are equal, hence the triangle is isosceles. Sufficient.

Stmt 2: States that 2 angles are not equal, does not tell us if the other remaining angle is equal to any of these two. Not Sufficient.

Hence Option A
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Re: Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   14 Nov 2018, 10:17
S1 : Angle M=Angle N => MP=NP
Now, if MP=NP=MN, it's an equilateral triangle.
But, if MP/NP!=MN, it's an isoceles triangle.
Hence, NS.

S2 : Angle N!= Angle P => MN!=MP.
No info about 3rd side.
It could be an Isoceles Triangle or an Acute or an Obtuse Triangle.
Hence, NS.

Both S1 & S2 together => SUFFICIENT.
Since 2 sides MP and NP are equal and third side MN is not equal.

Ans = C

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Re: Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   14 Nov 2018, 10:25
shibanis01 wrote:
S1 : Angle M=Angle N => MP=NP
Now, if MP=NP=MN, it's an equilateral triangle.
But, if MP/NP!=MN, it's an isoceles triangle.
Hence, NS.

S2 : Angle N!= Angle P => MN!=MP.
No info about 3rd side.
It could be an Isoceles Triangle or an Acute or an Obtuse Triangle.
Hence, NS.

Both S1 & S2 together => SUFFICIENT.
Since 2 sides MP and NP are equal and third side MN is not equal.

Ans = C

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shibanis01 I believe, every equilateral triangle is isosceles, but not every isosceles triangle is equilateral. Here's a link that might help clarify: https://www.sparknotes.com/math/geometr ... /section3/
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Re: Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   06 Sep 2019, 03:31
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nkin wrote:
shibanis01 wrote:
S1 : Angle M=Angle N => MP=NP
Now, if MP=NP=MN, it's an equilateral triangle.
But, if MP/NP!=MN, it's an isoceles triangle.
Hence, NS.

S2 : Angle N!= Angle P => MN!=MP.
No info about 3rd side.
It could be an Isoceles Triangle or an Acute or an Obtuse Triangle.
Hence, NS.

Both S1 & S2 together => SUFFICIENT.
Since 2 sides MP and NP are equal and third side MN is not equal.

Ans = C

Posted from my mobile device


shibanis01 I believe, every equilateral triangle is isosceles, but not every isosceles triangle is equilateral. Here's a link that might help clarify: https://www.sparknotes.com/math/geometr ... /section3/


(1) Exactly two of the angles, M and N, have the same measure.
"Exactly two" means that the triangle cannot be an equilateral, since ONLY 2 angles can be the same.
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Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   14 Feb 2020, 08:09
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GMATBusters wrote:
Is triangle MNP isosceles?

(1) Exactly two of the angles, M and N, have the same measure.
(2)Angles N and P do not have the same measure.

Target question: Is triangle MNP isosceles?

Statement 1: Exactly two of the angles, M and N, have the same measure.
Perfect. This is the precise definition of an isosceles triangle
The answer to the target question is YES, triangle MNP is isosceles
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Angles N and P do not have the same measure
Here are two conflicting scenarios that satisfied statement 2
Case a: ∠N = 50°, ∠P = 80°, and ∠M = 50°. In this case, the answer to the target question is YES, triangle MNP is isosceles
Case b: ∠N = 50°, ∠P = 70°, and ∠M = 60°. In this case, the answer to the target question is NO, triangle MNP is not isosceles
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent­
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Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   17 Feb 2022, 10:54
GMATBusters wrote:
Is triangle MNP isosceles?


(1) Exactly two of the angles, M and N, have the same measure.

(2)Angles N and P do not have the same measure.

(1) Exactly two angles have the same measure. Sufficient.

(2) Two angles not having the same measure gives us no information about the third angle. Insufficient.

Hence, A.­
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Re: Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink] New post   02 Apr 2024, 21:33
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Re: Is MNP isosceles? (1) Exactly two of the angles, M and N, have the [#permalink]
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