vanidhar 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
my question : what if the extra number is zero ?? ???
S has 9 different numbers. T has 8 of these different numbers in it.
Which of the following cannot be true?
A. The mean of S is equal to the mean of T
This is possible. Let's say the mean of set S is a number 20 and one of the numbers in S is 20. If T has all numbers in it except 20, its mean will still be 20.
B. The median of S is equal to the median of T
This is possible. Let's say the median of set S is the middle number 20 and set T does not have 20 but has 19 and 21 in the middle. The median of T will still be 20.
C. The range of S is equal to the range of T
When we read range, think of numbers arranged from lowest to highest. Range is highest - lowest. T could include both the lowest number and the highest number and hence its range will be same as the range of S.
D. The mean of S is greater than the mean of T
Mean of T could be less than or higher than that of S. Again, arrange all elements of S in ascending order. If you pick just the greatest 8 numbers to have in T, mean of T will be more than that of S. If you pick the smallest 8 elements, mean of T will be less than mean of S.
E. The range of S is less than the range of T
Can the range of T be greater than that of S? Arrange all numbers of S in ascending order. Which 8 numbers will you pick to have a higher range? For maximum range, you can pick the smallest and greatest number of S. But that will give just the same range as that of S. T cannot have a range greater than the range of S.
Answer (E)
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