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05 Mar 2019, 05:13
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:11) correct
16%
(00:51)
wrong
based on 96
sessions
History
Date
Time
Result
Not Attempted Yet
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 4676 times ]
Chethan92
Joined: 18 Jul 2018
Last visit: 21 Apr 2022
Posts: 899
Own Kudos:
Given Kudos: 95
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy)
Products:
05 Mar 2019, 10:21
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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?
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?
05 Mar 2019, 10:30
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Bunuel
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
