vtran wrote:
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
Alternatively, you can use the concept of deviation from mean to solve it.
Median is average of middle two terms = (-4 + 4)/2 = 0
So mean = 0 too.
Now notice the terms on either side of mean.
-4 is 4 less than 0 but 4 is 4 more so they balance out.
-5 is 5 less but 6 is 6 more so there is an extra positive 1.
-8 and 9 have an extra positive 1 too.
To get a mean of 0, x should have negative 2 more than y i.e. x = -12, y = 10 or x = -13, y = 11 etc.
In any case, |x|-|y| = 2
Check this post for more on this method: http://www.veritasprep.com/blog/2012/05 ... eviations/