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06 Sep 2022, 01:36
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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:
55%
(hard)
Question Stats:
50% (01:36) correct
50%
(01:42)
wrong
based on 56
sessions
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Not Attempted Yet
Within the circle with center O, how many degrees is angle MNO?
(1) Angle ONP = 31°
(2) Angle NPM = 48°
Attachment:
222.png [ 5.97 KiB | Viewed 1703 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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07 Sep 2022, 08:56
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Condition 1: Insufficient
ONP makes angle 31 but ONP can still be stretched to any point on the circle.
Condition 2: Sufficient
Angle at center: 2*48 and equal angles for equal radii ON and OM.
ONP makes angle 31 but ONP can still be stretched to any point on the circle.
Condition 2: Sufficient
Angle at center: 2*48 and equal angles for equal radii ON and OM.
08 Sep 2022, 00:00
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Bunuel
Solution:
Pre-Analysis:
If we look at triangle ONM, we will notice that it is an isosceles triangle with ON = OM because both are the radius of the circle.
Let us assume \(\angle ONM=\angle OMN=x\) and \(\angle NOM=180-2x\)
And \(\angle NPM=\frac{\angle NOM}{2}=\frac{180-2x}{2}=90-x\)
Attachment:
circle4.png [ 18.13 KiB | Viewed 2172 times ]
We need the value of x
Statement 1: Angle ONP = 31°
This will not help us get the value of x
Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: Angle NPM = 48°
According to this statement, \(90-x=48\)
We can very easily get the value of x from here
thus, statement 2 alone is sufficient
Hence the right answer is Option B
