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Re: Set S consists of 5 consecutive integers, and set T consists [#permalink]
28 May 2013, 11:40
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Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?
Sets S and T are evenly spaced. In any evenly spaced set (aka arithmetic progression): (mean) = (median) = (the average of the first and the last terms) and (the sum of the elements) = (the mean) * (# of elements).
So the question asks whether (mean of S) = (mean of T)?
(1) The median of the numbers in Set S is 0 --> (mean of S) = 0, insufficient as we know nothing about the mean of T, which may or may not be zero.
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T --> 5*(mean of S) = 7* (mean of T) --> answer to the question will be YES in case (mean of S) = (mean of T) = 0 and will be NO in all other cases (for example (mean of S) =7 and (mean of T) = 5). Not sufficient.
(1)+(2) As from (1) (mean of S) = 0 then from (2) (5*(mean of S) = 7* (mean of T)) --> (mean of T) = 0. Sufficient.
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