The range of a set is the difference between the largest and smallest elements of a set.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.

The arithmetic mean (average) of a set equals the sum of all of the elements in a set divided by the number of elements in that set.

Consider the set A to be {-3, -2, -1, 0, 1, 2, 3} --> \(mean=median=0\) and \(range=3-(-3)=6\).

A. The range of A = range of B --> remove 0 from set A, then the range of B still would be 6 --> could be true;

B. The mean of A > the mean of B --> remove 3, then the mean of B would be negative -0.5 so less than 0 --> could be true;

C. The range of A < the range of B --> the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set --> NEVER TRUE.

D. The mean of A = the mean of B --> remove 0 from set A, then the mean of B still would be 0 --> could be true;

E. The median of A = the median of B --> again remove 0 from set A, then the median of B still would be 0 --> could be true;

Answer: C.

Hope it's clear.
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hi,

only C is not possible:

let say set A has : a== b== c== d== e== f== g==>these are 7 elements in ascending order(just think they are on the number line starting from left)
range =g-a(distance from a to g)
now for B we have select 6 elements from A...and have to leave 1 element.
Now for making B YOU HAVE TO remove any one....no wyou can clearly see if you remove any of the one b/c/d/e/f===>range is g-a==>same as set A's range.
if you remove g==>range is f-a==>clearly distance is less than g-a
if you remove a ==>range is g-b==>clearly distance is less than g-a

hence you can see range of set B is always less than or equal to range of set A

hope i made my point clear
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Distilling the problem down to set notation, you can see that Set B = {n1,n2,n3,n4,n5,n6}

Set A contains everything in Set B, but with an additional number. In essence, Set A = {n1,n2,n3,n4,n5,n6,N}

The additional number, N, is the only thing that can be manipulated in this problem, so that is what you should naturally focus on. The problem then asks you to find out which of the statements given CANNOT be true. Turning this around from the viewpoint of the Testmaker, your job is then to try to discover a condition where each statement IS true.










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