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In isoceles triangle MNP, MN=MP and NP=6. Which of the following could

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In isoceles triangle MNP, MN=MP and NP=6. Which of the following could [#permalink]

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In isoceles triangle MNP, MN=MP and NP=6. Which of the following could be the length of side MN?

I. 2
II. 6
III. 12

A) II only
B) III only
C) I and II only
D) II and III only
E) I,II, and III

I have marked answer as 'B' considering we have to check the triangle rules for Isosceles. But the OA is 'D', Isn't II true for an equilateral triangle or should I say doesn't II make the isosceles triangle an equilateral? Do we have to even test this?
[Reveal] Spoiler: OA

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Re: In isoceles triangle MNP, MN=MP and NP=6. Which of the following could [#permalink]

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New post 23 Feb 2015, 21:13
Hi Pretz,

While this might seem like a 'nitpick' issue, an Isosceles triangle has 2 (or more) equal sides, so a triangle with sides of 6, 6 and 6 DOES fall under the technical definition of Isosceles. You're not likely to see an Official GMAT question worded the way this prompt is written though. It would likely state:

"In triangle MNP, MN=MP and NP=6....."

In this phrasing, you know that 2 of the sides are equal, but the third side MIGHT also equal the other two. While the GMAT is designed to test the thoroughness of your thinking, it's NOT designed to try to trick you.

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Re: In isoceles triangle MNP, MN=MP and NP=6. Which of the following could [#permalink]

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New post 24 Feb 2015, 00:39
Pretz wrote:
In isoceles triangle MNP, MN=MP and NP=6. Which of the following could be the length of side MN?

I. 2
II. 6
III. 12

A) II only
B) III only
C) I and II only
D) II and III only
E) I,II, and III

I have marked answer as 'B' considering we have to check the triangle rules for Isosceles. But the OA is 'D', Isn't II true for an equilateral triangle or should I say doesn't II make the isosceles triangle an equilateral? Do we have to even test this?


hi pretz

an equilateral triangle is a type of an isosceles triangle in the similar way as a square is a type of rectangle..
so you will require to consider equilateral triangle also as an isosceles triangle
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Re: In isoceles triangle MNP, MN=MP and NP=6. Which of the following could [#permalink]

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New post 06 Jan 2018, 10:37
Why can it not be 2 also??? You can make the base as long or short as you want by in/decreasing the angle of the two equal sides right?

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Re: In isoceles triangle MNP, MN=MP and NP=6. Which of the following could [#permalink]

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New post 06 Jan 2018, 10:48
Hermes wrote:
Why can it not be 2 also??? You can make the base as long or short as you want by in/decreasing the angle of the two equal sides right?


Hi Hermes

if side MN=2 then MP=2 as it is an isosceles triangle. in this case sum of two sides will not be greater than third side i.e. 2+2<6 which is not possible.

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Re: In isoceles triangle MNP, MN=MP and NP=6. Which of the following could   [#permalink] 06 Jan 2018, 10:48
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