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18 Apr 2019, 00:25
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Difficulty:
65%
(hard)
Question Stats:
56% (02:31) correct
44%
(02:17)
wrong
based on 45
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Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
18 Apr 2019, 07:42
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Since the central angles form a A.P , whose sum will be 360 ( sum of all central angles of a circle)
Number of central angles/sectors = 12 = n
common difference = d
So, 360 = n/2 { 2a + (n-1)d}
substitutingn = 12
360 = 6{ 2a + 11d }
60 - 2a = 11d
substituting option values ( trial method)
option C , a = 8 then 60 - 16 = 11d , d = 44/11 = 4
d has to be a integer and only option C satisfy that condition.
Number of central angles/sectors = 12 = n
common difference = d
So, 360 = n/2 { 2a + (n-1)d}
substitutingn = 12
360 = 6{ 2a + 11d }
60 - 2a = 11d
substituting option values ( trial method)
option C , a = 8 then 60 - 16 = 11d , d = 44/11 = 4
d has to be a integer and only option C satisfy that condition.
20 Apr 2019, 12:19
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Is there another explanation? I don't understand the question.
