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# Is MNO a right triangle?

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