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Is MNO a right triangle?

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Is MNO a right triangle?  [#permalink]

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New post 05 Mar 2019, 05:13
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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
2019-03-05_1611.png [ 30.64 KiB | Viewed 375 times ]

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

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New post 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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New post 05 Mar 2019, 10:30
Bunuel wrote:
Image
Is MNO a right triangle?


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

(2) ∠MNO = ∠MON = 1/2*∠OMN


Attachment:
2019-03-05_1611.png


IF YOU FIND MY SOLUTION HELPFUL, PLEASE GIVE ME KUDOS

(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.

The answer is B
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Re: Is MNO a right triangle?  [#permalink]

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New post 05 Mar 2019, 10:33
1
Bunuel wrote:
Image
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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Re: Is MNO a right triangle?  [#permalink]

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New post 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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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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 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.
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
GMAT Club Bot
Re: Is MNO a right triangle?   [#permalink] 05 Mar 2019, 11:27
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