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17 Nov 2018, 10:21
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
16% (02:41) correct
84%
(02:51)
wrong
based on 50
sessions
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Not Attempted Yet
In a triangle ABC, BC is produced to D and bisectors of angle ABC and angle ACD meet at E. Is Angle BEC <30 deg?
1) Angle BAC = 60 deg
2) Angle BCA = 40 deg
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
Data Sufficiency Forum
17 Nov 2018, 10:32
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Let ABE = EBC = x, and ACE = ECD = y
Stmt 1: BAC = 60, 2x + 60 = 2y using exterior angle property or x + 30 = y which gives, Angle BEC = 30 deg. Hence answer is always NO. Hence Sufficient!
Stmt 2: BCA = 40, so ACD = 140 = 2y which gives y = 70, Also, EBC + 40 + ACE + BEC = 180, hence, x + 40 + 70 + BEC = 180, or BEC = 180 - 110 - x = 70 - x.
Now, y = 70, so, BEC = y - x, cannot proceed further on this without more details. Hence, Insufficient.
Hence Option A
Stmt 1: BAC = 60, 2x + 60 = 2y using exterior angle property or x + 30 = y which gives, Angle BEC = 30 deg. Hence answer is always NO. Hence Sufficient!
Stmt 2: BCA = 40, so ACD = 140 = 2y which gives y = 70, Also, EBC + 40 + ACE + BEC = 180, hence, x + 40 + 70 + BEC = 180, or BEC = 180 - 110 - x = 70 - x.
Now, y = 70, so, BEC = y - x, cannot proceed further on this without more details. Hence, Insufficient.
Hence Option A
17 Nov 2018, 11:19
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A) Does not give any information on any other angle. Not sufficient
B)If angle BCA=40, then angle ACD=140
angle ACE=70
So, angle BCE=110
Angle ABC+ Angle BAC= angle ACD=140
But, angle BEC can be greater or lesser than 30. Not sufficient
combine:
angle BCE=110
Angle ABC=140-60=80
Angle EBC=40
So, Angle BEC=180-(110+40)
Sufficient
IMO:OPTION C
B)If angle BCA=40, then angle ACD=140
angle ACE=70
So, angle BCE=110
Angle ABC+ Angle BAC= angle ACD=140
But, angle BEC can be greater or lesser than 30. Not sufficient
combine:
angle BCE=110
Angle ABC=140-60=80
Angle EBC=40
So, Angle BEC=180-(110+40)
Sufficient
IMO:OPTION C
