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# What is the perimeter of isosceles triangle MNP?

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What is the perimeter of isosceles triangle MNP? [#permalink]

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14 Jun 2012, 03:13
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What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 20

Diagnostic Test
Question: 28
Page: 25
Difficulty: 550
[Reveal] Spoiler: OA

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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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14 Jun 2012, 03:14
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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.

Similar question to practice: what-is-the-perimeter-of-isosceles-triangle-mnp-134505.html#p1096591
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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14 Jun 2012, 04:16
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.

Regards,

Last edited by cyberjadugar on 14 Jun 2012, 04:40, edited 1 time in total.
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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14 Jun 2012, 04:30
Expert's post
Hi,

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.

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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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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14 Jun 2012, 04:38
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Bunuel wrote:
Hi,

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.

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?

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

Regards,
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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14 Jun 2012, 04:46
Expert's post
Bunuel wrote:
Hi,

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.

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?

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

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.

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

Hope it helps.
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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16 Jun 2012, 05:15
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
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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22 Jun 2012, 04:02
Expert's post
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.

Similar question to practice: what-is-the-perimeter-of-isosceles-triangle-mnp-134505.html#p1096591
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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23 Jul 2012, 07:47
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)
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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09 Jan 2014, 10:16
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 20

Diagnostic Test
Question: 28
Page: 25
Difficulty: 550

Sides of an isosceles triangle: a, a, b.. We don't know if a = 16 or if a = 20, so E
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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12 Dec 2014, 02:34
Bunuel wrote:
What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 20

Diagnostic Test
Question: 28
Page: 25
Difficulty: 550

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
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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12 Dec 2014, 06:45
Expert's post
christian1904 wrote:
Bunuel wrote:
What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 20

Diagnostic Test
Question: 28
Page: 25
Difficulty: 550

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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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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22 Dec 2014, 11:12
Bunuel wrote:
christian1904 wrote:
Bunuel wrote:
What is the perimeter of isosceles triangle MNP?

(1) MN = 16
(2) NP = 20

Diagnostic Test
Question: 28
Page: 25
Difficulty: 550

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.

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} ???
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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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Re: What is the perimeter of isosceles triangle MNP? [#permalink]

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27 Mar 2016, 19:45
Here is a visual that should help.
Attachments

Screen Shot 2016-03-27 at 7.44.30 PM.png [ 87.61 KiB | Viewed 816 times ]

Re: What is the perimeter of isosceles triangle MNP?   [#permalink] 27 Mar 2016, 19:45
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