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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] New post 14 Jun 2012, 02:13
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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


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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 14 Jun 2012, 02:14
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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.

Answer: E.

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] New post 14 Jun 2012, 03:16
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.

Thus, Answer is (E).

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Last edited by cyberjadugar on 14 Jun 2012, 03:40, edited 1 time in total.
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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 14 Jun 2012, 03:30
Expert's post
cyberjadugar 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.

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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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 14 Jun 2012, 03:38
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This post received
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Bunuel wrote:
cyberjadugar 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.

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?

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,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 14 Jun 2012, 03:46
Expert's post
cyberjadugar wrote:
Bunuel wrote:
cyberjadugar 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.

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?

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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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 16 Jun 2012, 04:15
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.

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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 22 Jun 2012, 03:02
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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.

Answer: E.

Similar question to practice: what-is-the-perimeter-of-isosceles-triangle-mnp-134505.html#p1096591
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: What is the perimeter of isosceles triangle MNP? [#permalink] New post 23 Jul 2012, 06:47
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] New post 09 Jan 2014, 09:16
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
Re: What is the perimeter of isosceles triangle MNP?   [#permalink] 09 Jan 2014, 09:16
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