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The range of a set A is R. A number having a value equal to [#permalink]

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19 Oct 2005, 21:51

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The range of a set A is R. A number having a value equal to R, is included in this set A. Will the range of set A increase?
1) All numbers in set A are positive
2) Mean of the new set is smaller than R _________________

Stmt 1 indicates all numbers are +ve and range = max - min. Hence R (range) lies between min and max and do not increase (Sufficient)

Stmt 2 indicates the mean of new set is less than R. This indicates, that R was less than the mean of old set. However old mean should be greater than min and less than max. Hence R lies between old min and old max. (Sufficient)

i have a question on A!
Consider 2 sets {0,...,10} and {11,...,21} both the cases the range is 10.
If I add R=10 to each of these sets,
1. Adding 10 doesn't increase range in {0,...,10}
2. Adding 10 increases the range in {11,...,21}
Is A not insuffient?

Using (1), The set could be {1,5,10} and the range is 9. By adding 9 to the set, the range won't increase. Trying out another set {5,10,15}, the range is 10 and adding 10 won't increase the set either. For positive numbers, the set will never increase as the number added will be smaller than the biggest number.

For (2),

Set {1,5,10}: Mean = 16/3, Range = 9. Add in 9, set becomes {1,5,9,10} with mean 9/4 which is smaller than R, but range does not increase.

Set {-5,0,10}, Mean = 2.5, Range = 15. Add in 15, set becomes {-5,0,10,15}, the range increases to 20, mean = 5 <-- not feasible

Set {-6,-2, -1}, mean = -3, Range = 5. Add in 5, the set becomes {-6,-2,-1,5}, the range is now 11, mean = -1. <-- again not feasible.

It seems once the set invovles a negative number, then the range and mean will increase after adding R.

i have a question on A! Consider 2 sets {0,...,10} and {11,...,21} both the cases the range is 10. If I add R=10 to each of these sets, 1. Adding 10 doesn't increase range in {0,...,10} 2. Adding 10 increases the range in {11,...,21} Is A not insuffient?

You're right !! I did not manage to think of this set.

The range of a set A is R. A number having a value equal to R, is included in this set A. Will the range of set A increase? 1) All numbers in set A are positive 2) Mean of the new set is smaller than R

1) R=max-min
If R<max and R>min then range would not change.
Since min>0 we know R<max
But we don't know if R>min as gsr showed

2) (n*mean+R)/(n+1)<R
=> R> mean
Therefore R>min
But we don't know if R <max
eg. {1,2,3,4} mean=2.5 R=3 range doesn't change
{-1,0,1) mean =0 R=2 Range does change after adding 2 into the set.

Combined, from 1) we know R<max, from 2) we know R>min. Therefore we can determine that range would not change. Therefore C. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

i have a question on A! Consider 2 sets {0,...,10} and {11,...,21} both the cases the range is 10. If I add R=10 to each of these sets, 1. Adding 10 doesn't increase range in {0,...,10} 2. Adding 10 increases the range in {11,...,21} Is A not insuffient?

Please note that you can not use 0, from A you know that only +ive number are ok

if you have {5,6} the range will be 1 so including 1 in the new set will increase the range
if you consider {2,3,4,5} the range will be 3 so including 3 in the new set will not increase the range