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22 Sep 2009, 19:55
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Set C is a set of positive integers where 4 is least. If the average (arithmetic mean) of C equals its range, then how many positive integers does set C have?
(1) The elements in C are consecutive integers.
(2) The average (arithmetic mean) of C is 8.
(1) The elements in C are consecutive integers.
(2) The average (arithmetic mean) of C is 8.
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23 Sep 2009, 03:30
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Set C is a set of positive integers where 4 is least. If the average (arithmetic mean) of C equals its range, then how many positive integers does set C have?
(1) The elements in C are consecutive integers means that set is A.P. Average of set of consecutive elements = (2x1+n-1)/2 where x1 is the first term(x1=4) and n is number of elements in the set. The range of set of consecutive elements =n-1
We have "the average (arithmetic mean) of C equals its range" --> (8+n-1)/2=n-1 --> n=9
Sufficient
(2) The average (arithmetic mean) of C is 8 --> (x1+x2+...+xn)/n=8=The range of set=xn-x1=8
Not sufficient
Answer A.
(1) The elements in C are consecutive integers means that set is A.P. Average of set of consecutive elements = (2x1+n-1)/2 where x1 is the first term(x1=4) and n is number of elements in the set. The range of set of consecutive elements =n-1
We have "the average (arithmetic mean) of C equals its range" --> (8+n-1)/2=n-1 --> n=9
Sufficient
(2) The average (arithmetic mean) of C is 8 --> (x1+x2+...+xn)/n=8=The range of set=xn-x1=8
Not sufficient
Answer A.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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