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DS Question - properties of Triangles

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DS Question - properties of Triangles

by bazzle23 » Fri Oct 29, 2010 8:36 am
Below is a pretty basic questions that I came across on the GMAT prep book diagnostic test. Wanted to verify the answer here

What is the perimeter of isosceles triangle MNP ?

1) MN = 16
2) NP = 20

The answer per the OG is E. But would "C" not be a possibility as well since if you took into consideration the property of a triangle - "where the sum of the smaller 2 sides should be greater than the larger side"

In this case since we are told that MNP is an isosceles triangle the smaller sides would be 16's. if we were to choose 20 to be the equal sides it would violate this rule!

not sure why we cant accomadate this logic. Would much appreciate an explanation.

thanks!
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by Rahul@gurome » Fri Oct 29, 2010 9:22 am
bazzle23 wrote:Below is a pretty basic questions that I came across on the GMAT prep book diagnostic test. Wanted to verify the answer here

What is the perimeter of isosceles triangle MNP ?

1) MN = 16
2) NP = 20

The answer per the OG is E. But would "C" not be a possibility as well since if you took into consideration the property of a triangle - "where the sum of the smaller 2 sides should be greater than the larger side"

In this case since we are told that MNP is an isosceles triangle the smaller sides would be 16's. if we were to choose 20 to be the equal sides it would violate this rule!

not sure why we cant accomadate this logic. Would much appreciate an explanation.

thanks!
There is no such property of a triangle.
May be you've confused (or misunderstood) with the property : The sum of lengths of any two sides of a triangle is always greater than the length of the third side.

Now for this question, it is obvious that the statements are individually insufficient. Taking both of them together says MN = 16 and NP = 20. But we don't know whether MN is one of the equal sides or NP. There is two possibilities:
(1) MN is one of the equal sides. Perimeter = 2*MN + NP = 52
(2) NP is one of the equal sides. Perimeter = 2*NP + MN = 56

Not sufficient.

The correct answer is E.
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by bazzle23 » Fri Oct 29, 2010 9:38 am
Rahul thank you for the explanation I understand the reasoning more clearly now.

I think I may have misunderstood the rule - that I indicated on my original post below (took the rule off Page 53 on the OG diagnostic test for the explanation of the solution to problem #19)

Quote per the OG as "In a triangle, the sum of the smaller two sides must be larger than the largest side"

this most probably might be a typo.

thanks again for your help.
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by Rahul@gurome » Fri Oct 29, 2010 9:53 am
bazzle23 wrote:Rahul thank you for the explanation I understand the reasoning more clearly now.

I think I may have misunderstood the rule - that I indicated on my original post below (took the rule off Page 53 on the OG diagnostic test for the explanation of the solution to problem #19)

Quote per the OG as "In a triangle, the sum of the smaller two sides must be larger than the largest side"

this most probably might be a typo.

thanks again for your help.
No, this is not a typo. This is true indeed.
But this is certainly not a property of triangle.
This is a corollary, just a specific case of the actual property I mentioned. :)

Now, you may ask the question why this is mentioned so specially?
Well, in any case, (larger + medium) is always greater than the smaller. But (smaller + medium) is not always greater than the larger. But for triangle, this happens. And thus, it is special! :)
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by Ian Stewart » Fri Oct 29, 2010 11:09 am
Rahul@gurome wrote:
No, this is not a typo. This is true indeed.
But this is certainly not a property of triangle.
This is a corollary, just a specific case of the actual property I mentioned. :)
I think this thread has become confusing. It certainly *is* a property of a triangle that the sum of the two shortest sides is greater than the longest side, and I don't understand why you are insisting it is not; that's just an equivalent way of saying that the sum of any two sides is longer than the third side. bazzle23 was clever to think about this property here, since it can very easily be used to trap test takers on similar questions. For example, in a question like the following:

What is the perimeter of isosceles triangle ABC?
1. The length of AB is 17
2. The length of BC is 8

then using both statements, the lengths can only be 17, 17 and 8, and the answer is C. The sides cannot be 8, 8 and 17, since then the sum of the two shorter sides is not greater than 17.

This trap does not show up in the OG question quoted in the original post above, however, since the triangle can be both a 16, 16, 20 triangle or a 16, 20, 20 triangle. So the numbers matter; given the lengths of two unequal sides of an isosceles triangle, sometimes you can make two different triangles, and sometimes you can make only one triangle.

If you do see a question similar to these on the GMAT, it is crucial that you consider whether the triangles you are considering in your answer can actually exist - that is, you must verify that the sum of any two sides exceeds the third side. If not, you'll end up picking the wrong answer quite often (though, as the OG question illustrates, not always).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by [email protected] » Sun Feb 18, 2018 8:16 pm
Hi All,

We're told that triangle MNP is ISOSCELES. We're asked for the PERIMETER of that triangle.

1) MN = 16

Fact 1 tells us that either 1 of the sides or 2 of the sides = 16 (depending on which two sides are equal. We don't have enough information to determine the perimeter of the triangle though.
Fact 1 is INSUFFICIENT

2) NP = 20

Fact 2 tells us that either 1 of the sides or 2 of the sides = 20 (depending on which two sides are equal. We don't have enough information to determine the perimeter of the triangle though.
Fact 2 is INSUFFICIENT

Combined, we know:
At least one side = 16
At least one side = 20
Since the triangle is ISOSCELES, it's perimeter is either 16+16+20 = 52 OR 16+20+20 = 56. We don't know which one though.
Combined, INSUFFICIENT

Final Answer: E

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by Jeff@TargetTestPrep » Fri May 18, 2018 10:39 am

What is the perimeter of isosceles triangle MNP ?

1) MN = 16
2) NP = 20
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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Re: DS Question - properties of Triangles

by Brent@GMATPrepNow » Wed Jan 15, 2020 2:23 pm
bazzle23 wrote: ↑
Fri Oct 29, 2010 8:36 am
 What is the perimeter of isosceles triangle MNP ?

1) MN = 16
2) NP = 20
Target question: What is the perimeter of isosceles triangle MNP?

Statement 1: MN = 16
No idea about the other 2 sides
Statement 1 is NOT SUFFICIENT

Statement 2: NP = 20
No idea about the other 2 sides
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since we have an ISOSCELES triangle, we know that two sides have the same length, but which two sides?
There are two possible cases:
Case a: The side lengths are 16, 16, 20. In this case, the answer to the target question is the perimeter = 16+16+20=52
Case b: The side lengths are 16, 20, 20. In this case, the answer to the target question is the perimeter = 16+20+20=56
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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