LulaBrazilia wrote:S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements cannot be true?
A) The mean of S is equal to the mean of T.
B) The median of S is equal to the median of T.
C) The range of S is equal to the range of T.
D) The mean of S is greater than the mean of T.
E) The range of S is less than the range of T.
Let T = [1, 2, 3, 4, 5, 6, 7, 8}.
Let x = the value added to T to form S.
Try to prove that one of the answer choices CANNOT be true.
Answer choices C and E compare the range of S to the range of T.
Range = biggest - smallest.
The range of T = 8-1 = 7.
If 1<x<8, then S and T will have SAME RANGE, as in the following cases:
If x=1.5, then S = {1, 1.5, 2, 3, 4, 5, 6, 7, 8}, in which case the range of S = 8-1 = 7.
If x=7.5, then S = {1, 2, 3, 4, 5, 6, 7, 7.5, 8}, in which case the range of S = 8-1 = 7.
Since S and T can have the same range, eliminate C.
If x<1 or x>8, then S will have a GREATER range than T, as in the following cases:
If x=0, then S = {0, 1, 2, 3, 4, 5, 6, 7, 8}, in which case the range of S = 8-0 = 8.
If x=9, then S = {1, 2, 3, 4, 5, 6, 7, 8, 9}, in which case the range of S = 9-1 = 8.
The cases above illustrate that there is no way for S to have a smaller range than T.
Thus, answer choice
E cannot be true.
The correct answer is
E.
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