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For isosceles triangle LMN, what is the measure of angle N?

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For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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17 Sep 2015, 00:15
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In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
(2) Side MN measures $$4*\sqrt 2$$ inches

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Last edited by Vyshak on 10 May 2016, 00:20, edited 1 time in total.
Updated OA
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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17 Sep 2015, 08:15

Neither of the statements give information about the dimentions of two equal sides. In case if two equal sides are 4 in length, the angle measures would be different from the angle measures if the the two equal sides are 4 \sqrt{2}.
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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17 Sep 2015, 08:41
In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
Insufficient info
(2) Side MN measures $$4*\sqrt 2$$ inches
Insufficient info

Combined we dont know if the LM side is one of the 2 options given in the statement. Insufficient

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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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17 Sep 2015, 11:26
Hi Bunuel,

I am a non native speaker. In my language it is usually given what sides are equal, or
if the question says that LMN isosceles triangle, we can conclude that LM=MN.

I am not sure what the standard is in GMAT. In that question which sides are equal, LM=MN ??? How would we interpret the sides if no shapes are given?

Thank you
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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17 Sep 2015, 11:57

You know that LN=4 and MN=4 sqrt(2). As the triangle is isosceles, LM must be equal to 4. You can apply the law of cosines to find out the angles, when you know the sides of the triangle (if you really needed to calculate it).
Even without knowing the law of cosines, the relationship 1:1:sqrt(2) must ring a bell, this is a right triangle, and the angle N must be equal to 45 deg.
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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17 Sep 2015, 17:54
1. Insufficient
2. Insufficient

1+2 Sufficient
The LMN triangle formed is right angled isosceles triangle right angled at L. This is so because the 45-45-90 triangle has values as 1-1-$$\sqrt{2}$$. This is pretty clear from the information about the two sides given as LN=4 and MN=4$$\sqrt{2}$$. So MN is the hypotenuse and sides ML=LN.

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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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19 Sep 2015, 10:25
Bunuel wrote:
In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
(2) Side MN measures $$4*\sqrt 2$$ inches

Kudos for a correct solution.

Statement 1:-
It doesn't specify which 2 sides are equal.
INSUFFICIENT

Statement 2:-
Again doesn't specify which 2 sides are equal.
INSUFFICIENT

On combining statement 1 and 2 , we get no new information.
INSUFFICIENT

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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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19 Sep 2015, 19:42
Consider 1) : Nothing can be conclusively said. We do not even know if it's the equal or the unequal side. Insufficient
2) Again, we know only one side. Nothing can be said about it.

1 and 2 put together:

We know two sides and the shorter one must be the equal side. So, the three sides are 4, 4, 4$$\sqrt{2}$$. This is of the form 1 : 1 : $$\sqrt{2}$$ ie., a 45-45-90 triangle. So, $$\angle$$L = 90 (since it's the angle opposite to the larger side). The other angles must be 45 each, making $$\angle$$N 45.
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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19 Sep 2015, 22:57
rajarams wrote:
Consider 1) : Nothing can be conclusively said. We do not even know if it's the equal or the unequal side. Insufficient
2) Again, we know only one side. Nothing can be said about it.

1 and 2 put together:

We know two sides and the shorter one must be the equal side. So, the three sides are 4, 4, 4$$\sqrt{2}$$. This is of the form 1 : 1 : $$\sqrt{2}$$ ie., a 45-45-90 triangle. So, $$\angle$$L = 90 (since it's the angle opposite to the larger side). The other angles must be 45 each, making $$\angle$$N 45.

Hi Raja,

"two sides and the shorter one must be the equal side. So, the three sides are 4, 4, 4$$\sqrt{2}$$"

Can you tell why is this so. Why can't the equal sides be 4\sqrt{2}.

Vijay.
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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20 Sep 2015, 00:02
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Bunuel wrote:
In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
(2) Side MN measures $$4*\sqrt 2$$ inches

Kudos for a correct solution.

Statement (1) and (2) individually insufficient for providing inadequate information about isosceles to measure angle of N

By combining two statements we can find two sets of side for isosceles : (4$$\sqrt{2}$$,4$$\sqrt{2}$$,4) and (4,4,4$$\sqrt{2}$$)

So the Correct Answer is E
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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16 Nov 2015, 01:43
Hi Bunuel:

Why is the answer not C??
One side 4 and other 4sqrt2, and the triangle given is iscosceles, is it not enough for the triangle to be 45-45-90 triangle??

Thanks
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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01 Mar 2016, 09:52
Bunuel wrote:
In isosceles triangle LMN, what is the measure of angle N?

(1) Side LN measures 4 inches
(2) Side MN measures $$4*\sqrt 2$$ inches

Kudos for a correct solution.

Details of which sides are equal are not mentioned, also it is not possible to figure out from the statements which 2 sides are equal.

St. I --> LN = 4, what about other sides, which sides are similar, not useful
St. II --> MN = $$4*\sqrt 2$$, the angles can be 90-45-45 or 30-60-90, not useful.

Combined, both I n II does not help identify which sides are equal and also what are the angles.

Can't conclude anything, E is the answer
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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10 Mar 2016, 23:37
For isosceles triangle LMN, what is the measure of angle N?
(1) The lengths of all three sides of triangle LMN are the same.
(2) Angle L measures 60 degrees.
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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11 Mar 2016, 01:17
St1: Indicates that the triangle is equilateral. So N should be equal to 60 --> Sufficient

St2: Suppose L is not isosceles and other two angles (M and N) are isosceles then angle of M or N = (180 - 60)/2 = 60. Indicates its an equilateral triangle.
Suppose L is isosceles with one more angle (say M) then the remaining angle must be 180 - 120 = 60. Again its an equilateral triangle.
So St2 is sufficient.

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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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09 May 2016, 22:30
Vyshak wrote:
St1: Indicates that the triangle is equilateral. So N should be equal to 60 --> Sufficient

St2: Suppose L is not isosceles and other two angles (M and N) are isosceles then angle of M or N = (180 - 60)/2 = 60. Indicates its an equilateral triangle.
Suppose L is isosceles with one more angle (say M) then the remaining angle must be 180 - 120 = 60. Again its an equilateral triangle.
So St2 is sufficient.

How were you able to deduce that the triangle is Equilateral from Statement 1?
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For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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10 May 2016, 00:11
winionhi wrote:
Vyshak wrote:
St1: Indicates that the triangle is equilateral. So N should be equal to 60 --> Sufficient

St2: Suppose L is not isosceles and other two angles (M and N) are isosceles then angle of M or N = (180 - 60)/2 = 60. Indicates its an equilateral triangle.
Suppose L is isosceles with one more angle (say M) then the remaining angle must be 180 - 120 = 60. Again its an equilateral triangle.
So St2 is sufficient.

How were you able to deduce that the triangle is Equilateral from Statement 1?

Hi,

The question I have answered is quite different from the merged topic.

Quote:
For isosceles triangle LMN, what is the measure of angle N?
(1) The lengths of all three sides of triangle LMN are the same.
(2) Angle L measures 60 degrees.

I think there is some confusion with the answer choice in the main question. I have updated the OA in the main question to E.
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Re: For isosceles triangle LMN, what is the measure of angle N? [#permalink]

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28 Nov 2017, 21:00
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Re: For isosceles triangle LMN, what is the measure of angle N?   [#permalink] 28 Nov 2017, 21:00
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