Set S contains exactly four distinct positive integers. Is the mean of S equal to the median of S?
(1) The smallest term in S is equal to the sum of the two middle terms minus the largest term in S.
(2) When the range of S is added to the sum of all the terms in S, the resulting sum is equal to the
smallest term in S plus three times the largest term in S.
Let the 4 distinct integers be w,x,y and z, where these are arranged in ascending order.
Mean of S=(w+x+y+z)/4
Median of S= (x+y)/2
The question is asking whether (w+x+y+z)/4=(x+y)/2? or is (w+x+y+z)=2x +2y or Is \(w+z=x+y?\)
\(w=x+y-z\) or \(w+z=x+y\).
When this range is added to sum of all the terms in S, then the resulting sum is equal to the smallest term in S plus three times the largest term in S.
The above can be rewritten as (x+y+2z)=w+3z or \(x+y=w+z\).
This is what statement 1 is saying.
IMO the answer has to be D and not C.
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