danzig wrote:
S is a set containing 8 different positive odd numbers. T is a set containing 7 di¤erent numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The range of T is even.
(B) The mean of S is even.
(C) The mean of T is even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T.
Option C.
Given: S is a set containing 8 different positive odd numbers
Easily inferred: T is a set containing 7 different
odd numbers
(A) The range of T is even. - Always even, since it is a difference of two odd numbers
(B) The mean of S is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of T is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of S is equal to the range of T.
(E) The median of T is equal to the mean of T
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