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