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range of set

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range of set

by ri2007 » Sat Nov 17, 2007 1:01 pm
The range of set A is R. A number having a value equal to R, is added to set A. Will the range of set A increase?

(1) All numbers in the set are positive

(2) The mean of the new set is smaller than R

interesting q for practice
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Source: — Data Sufficiency |
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Re: range of set

by jayhawk2001 » Sat Nov 17, 2007 1:42 pm
ri2007 wrote:The range of set A is R. A number having a value equal to R, is added to set A. Will the range of set A increase?

(1) All numbers in the set are positive

(2) The mean of the new set is smaller than R

interesting q for practice
Is it C?

1 - insufficient.
Take {100, 101}, range increases
Take {1,2,3}, range remains the same

2 - insufficient.
Take {0,3}, range = 3, new set = {0,3,3} where mean = 2,
range does not change
Take {-1,1}, range = 2, new set = {-1,1,2}, mean = 2/3,
range changes

Taking 1 and 2 together - sufficient.
Set S = {A} U R.

If all numbers in A are positive and mean(S) < R,
then R < greatest element of A.

Similarly, if mean(S) <R> smallest element in A

So, adding R to the set will not change the range. Hence
sufficient.
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