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555-605 (Medium)|   Geometry|      
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Xin Cho
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Is angle M = 90? 18 Aug 2019, 08:38
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

66% (00:38) correct 34% (00:59) wrong based on 53 sessions

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Is angle M = 90?

(1) The length of arc LMN is half the circumference of the circle.
(2) LN is the diameter of the circle.




Source: Princeton Review, Cracking the GMAT Premium 2020
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D
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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Is angle M = 90? 18 Aug 2019, 08:40
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Xin Cho
Attachment:
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Is angle M = 90?

(1) The length of arc LMN is half the circumference of the circle.
(2) LN is the diameter of the circle.




Source: Princeton Review, Cracking the GMAT Premium 2020
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Is angle M = 90?

(1) The length of arc LMN is half the circumference of the circle.
If length of arc LMN is half the circumference of the circle then LN is the diameter of the circle
Diameter of a circle extends 90 on the circumference of the circle
M = 90
SUFFICIENT

(2) LN is the diameter of the circle.
Diameter of a circle extends 90 on the circumference of the circle
M = 90
SUFFICIENT

IMO D
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Is angle M = 90? 18 Aug 2019, 08:43
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Kinshook can I possibly ask you how we know from (1) that LN is the diameter?
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Is angle M = 90? 18 Aug 2019, 17:43
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Kinshook can I possibly ask you how we know from (1) that LN is the diameter?
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Only a diameter divides a circle into 2 equal halves. If an arc is half the circumference then circle is divided in to 2 equal parts by a diameter.

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Is angle M = 90? 18 Aug 2019, 19:05
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The question here can be simplified to whether LN is the diameter or not. If LN is the diameter then any point M on the circle will make triangle LNM a right triangle (this is called Thale's theorem, feel free to wiki!)

(1) The arc covers exactly half the circle, then LN must be the diameter. Sufficient.
(2) Sufficient.

Answer: D
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Is angle M = 90? 19 Aug 2019, 10:41
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Kinshook, thank you very much. I realized that I mistook the LMN for LNM - it all makes sense now.
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