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

Question

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.

nkin · Answer

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

shibsz · Answer

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

nkin · Answer

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/

exc4libur · Answer

(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.

BrentGMATPrepNow · Answer

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

kungfury42 · Answer

(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.

Juhitha · Answer

1)two angles equal doesnt mean the third angle cant be equal to the two 
according to statement one it can be an isoceles triangle or equilateral triangle 
2)only statement two doesnt say much 
so option c

Legend2k23 · Answer

Since the question specifically said exactly two of the angles had the same measure, we can eliminate the possibility of the third being the same as well. This makes the first statement sufficient. Had the word "exactly" been ommitted then this assessment would be correct and would make S1 insufficient.

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

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