SOLUTION

What is the perimeter of isosceles triangle MNP?

(1) MN = 16. We only know the length of one side. Not sufficient.
(2) NP = 20. We only know the length of one side. Not sufficient.

(1)+(2) If MN=MP=16 and NP=20 then the perimeter would be 16+16+20=52 but if MN=16 and NP=MP=20 then the perimeter would be 16+20+20=56. Not sufficient.

Answer: E.

Similar question to practice: what-is-the-perimeter-of-isosceles-triangle-mnp-134505.html#p1096591
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Hi,

Difficulty level: close to 600. ('cause at first glance, I said, answer is (C). Then, when I actually solved, I got the right answer.)

Perimeter of isosceles triangle MNP?

Using (1),
MN = 16, no idea about NP & MP. Insufficient.

Using (2)
NP = 20, no idea about MN & MP. Insufficient.

Combining both the statements,
MN = 16 & NP = 20
for MNP to be isosceles, the third side MP can be 16 or 20. Insufficient.

Thus, Answer is (E).

Regards,

Just a bit harder question, based on OG#28:

What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 32

What would be the answer in this case?
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Hi,

Using (1) & (2) alone we can't get the answer (similar to the explanation above)

Combinig (1) & (2),
MN = 16 & NP = 32
Possible sides of triangle (16, 16, 32) & (16, 32, 32),
now we know a+b>c (sum of two sides greater than third side)
(16, 16, 32) doesn't fulfill this criteria
Thus only possible triangle is (16, 32, 32)
perimeter = 80

Thus, Answer is (C)

Regards,

Correct.

What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 32

MUST KNOW FOR THE GMAT: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

When we consider the two statements together we can see that the case of {16, 16, 32} is not possible since the sum of two sides (16 and 16) is not greater then the third side (32), so only the following case is possible: {16, 32, 32}, which gives the perimeter equal to 16+32+32=80.

Answer: C.

For more on Triangles check: math-triangles-87197.html (Theory, Formulas, Tricks, and Tips).

Hope it helps.
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Higher then 550 for sure. I think 600.

Unless we know the property "The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides", we can not answer the question easily.

Stmt 1: We can know the second side but don't know the length of third side.
Stmt 2: Same logic as given for stmt 1.

Together the third side can be 16 or it can be 20 also.

E

SOLUTION

What is the perimeter of isosceles triangle MNP?

(1) MN = 16. We only know the length of one side. Not sufficient.
(2) NP = 20. We only know the length of one side. Not sufficient.

(1)+(2) If MN=MP=16 and NP=20 then the perimeter would be 16+16+20=52 but if MN=16 and NP=MP=20 then the perimeter would be 16+20+20=56. Not sufficient.

Answer: E.

Similar question to practice: what-is-the-perimeter-of-isosceles-triangle-mnp-134505.html#p1096591
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What is the perimeter of isosceles triangle MNP?
PERIMETER=MN+NP+MP
Not given which sides are equal
(1) MN = 16
NP&MP unavailable so insufficient
(2) NP = 20
MN&MP unavailable so insufficient
from (i)&(ii)
Perimeter=MN+NP+MP=16+20+?, we don't know which two sides are equal;insufficient (E)

Sides of an isosceles triangle: a, a, b.. We don't know if a = 16 or if a = 20, so E

Hi all,

when reading "What is the perimeter of Isosceles Triangle MNP", how can I be sure that "MNP" stands for the vertices (as it is the case here) and not for the sides?
If M, N and P each were sides, the result to the question in my opinion would change to "C", as M*N and N*P would HAVE to account for 4*4 and 4*5 in this logic as we're dealing with an isosceles and the rule for the sum of two triangle sides doesn't allow any other solution.

How can I identify these variables to be representing vertices instead of sides?


Thanks
Christian

You are over-thinking this one. Capital letters refer to vertices.
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Would the angle rules of isosceles triangles not apply here? Since we know sides of 16, 20 - would the remaining side not have to be 16 in order to maintain 1:1:\sqrt{2} ???

Here is a visual that should help.

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Isosceles Triangle - > first glance I thought answer is C
but after solving got the correct answer
there are 2 answer with So answer should be E

Statement One Alone:

MN = 16

Since we don’t know anything about NP and MP, statement one alone is not sufficient.

Statement Two Alone:

NP = 20

Since we don’t know anything about MN and MP, statement two alone is not sufficient.

Statements One and Two Together:

With two statements together, we know that MN = 16 and NP = 20. Since triangle MNP is isosceles, MP could be 16 or it could be 20. If MP is 16, then the perimeter is 16 x 2 + 20 = 52. However, if MP is 20, then the perimeter is 20 x 2 + 16 = 56. Since we don’t have a unique number for the perimeter, the two statements together are still not sufficient to answer the question.

Answer: E
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