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# Is MNO a right triangle?

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Is MNO a right triangle?  [#permalink]

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05 Mar 2019, 05:13
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Difficulty:

15% (low)

Question Stats:

85% (01:12) correct 15% (00:54) wrong based on 53 sessions

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Is MNO a right triangle?

(1) $$MN = 2\sqrt{2}$$

(2) ∠MNO = ∠MON = 1/2*∠OMN

Attachment:

2019-03-05_1611.png [ 30.64 KiB | Viewed 576 times ]

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Re: Is MNO a right triangle?  [#permalink]

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05 Mar 2019, 10:21
From S1:

Only MN is given. No extra info.
Hence Insufficient.

From S2:

Angle N = Angle O = 1/2*Angle M
Let N = x
then O = x and M = 2x
4x = 180
x = 45
N = O = 45
M = 90

Triangle NMO is a right angle triangle.
Bunuel sir, as the question is asking whether MNO is a right-angled triangle, then angle N should be 90 degrees as per the question.
Here I'm getting M as 90 degrees. Both aren't same, right?
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Re: Is MNO a right triangle?  [#permalink]

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05 Mar 2019, 10:30
Bunuel wrote:

Is MNO a right triangle?

(1) $$MN = 2\sqrt{2}$$

(2) ∠MNO = ∠MON = 1/2*∠OMN

Attachment:
2019-03-05_1611.png

(1) mn = 2 ROOT 2. We can draw two such triangles with MN = 2root 2. Suppose MO=ON = 2root2, then we have a equilateral triangle with all angles = 60 degrees and the answer is NO Suppose OM=ON = 2, then we have a 45-45-90 degree right triangle and the answer is YES

Since we get a Yes and a No given the constraint, we mark NS

(2) <MNO = <MON = 1/2 OMN. Let MNO = MON = x, and OMN = x/2, then we have 2 1/2 x = 180. Solving gives 5/2 x =180 and x =72. Thus we have a 72-72-36 degree triangle, which is certainly not a right triangle, giving us a clear NO Sufficient.

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Re: Is MNO a right triangle?  [#permalink]

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05 Mar 2019, 10:33
1
Bunuel wrote:

Is MNO a right triangle?

(1) $$MN = 2\sqrt{2}$$

(2) ∠MNO = ∠MON = 1/2*∠OMN

Attachment:
2019-03-05_1611.png

#1
not suffieint
#2

∠MNO = ∠MON = 1/2*∠OMN
let
∠MON=x
so
∠MNO=x and ∠OMN= 2x
so x+x+2x=180
4x=180
x= 45= ∠MNO = ∠MON
and
∠OMN= 90*

so angle MNO is not right angled but ∠OMN is right angled ; sufficient
IMO B
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Joined: 02 Sep 2009
Posts: 58453
Re: Is MNO a right triangle?  [#permalink]

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05 Mar 2019, 11:22
Chethan92 wrote:
From S1:

Only MN is given. No extra info.
Hence Insufficient.

From S2:

Angle N = Angle O = 1/2*Angle M
Let N = x
then O = x and M = 2x
4x = 180
x = 45
N = O = 45
M = 90

Triangle NMO is a right angle triangle.
Bunuel sir, as the question is asking whether MNO is a right-angled triangle, then angle N should be 90 degrees as per the question.
Here I'm getting M as 90 degrees. Both aren't same, right?

The question asks whether triangle MNO is a right triangle, not whether angle MNO is a right angle. MNO could be right-angled if any of the three angles is right, not only angle MNO. So, here if you get from (2) that M = 90 degrees, then you still have an YES answer to the question: YES, triangle MNO is a right triangle.

Even if the question were "is angle MNO a right angle" and from one of the statement you get that angle NMO is right, then the statement is still sufficient because you got a definite NO to the question: NO, angle MNO is NOT a right angle (NMO is).
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Posts: 58453
Re: Is MNO a right triangle?  [#permalink]

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05 Mar 2019, 11:27
Bunuel wrote:
Chethan92 wrote:
From S1:

Only MN is given. No extra info.
Hence Insufficient.

From S2:

Angle N = Angle O = 1/2*Angle M
Let N = x
then O = x and M = 2x
4x = 180
x = 45
N = O = 45
M = 90

Triangle NMO is a right angle triangle.
Bunuel sir, as the question is asking whether MNO is a right-angled triangle, then angle N should be 90 degrees as per the question.
Here I'm getting M as 90 degrees. Both aren't same, right?

The question asks whether triangle MNO is a right triangle, not whether angle MNO is a right angle. MNO could be right-angled if any of the three angles is right, not only angle MNO. So, here if you get from (2) that M = 90 degrees, then you still have an YES answer to the question: YES, triangle MNO is a right triangle.

Even if the question were "is angle MNO a right angle" and from one of the statement you get that angle NMO is right, then the statement is still sufficient because you got a definite NO to the question: NO, angle MNO is NOT a right angle (NMO is).

To add more: there are two types of data sufficiency questions:

1. YES/NO DS Questions:

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

2. VALUE DS QUESTIONS:

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Strategies and Tactics for DS Section

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: Is MNO a right triangle?   [#permalink] 05 Mar 2019, 11:27
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