The range of a set A is R. A number having a value of R is added to set A. Will the range of set A increase?
1) All numbers in set A are positive.
2) The mean of the new set is smaller than R.
I think the above posts confirm that the answer is either C or E, so I won't bother looking at the statements individually. Let's look at both statements together.
When we add R to set A, the range will only increase if R is either the largest element in the new set, or the smallest element in the new set. We want to know if R could be the largest or the smallest element in the new set.
Let's assume A contains at least two elements, and call the largest g, and the smallest s. So set A is {s, other stuff, g}. Then R = g - s. From this, because g and s are positive, R must be less than g. So R can't be the largest element in the new set.
The only question is whether R might be the smallest; that is, we want to know if it's possible that R < s. This would make R smaller than everything else in the set, since s was the smallest element of the old set. But if R is the smallest element of the new set, there's no way statement 2 could be true; the mean of a set cannot be smaller than its smallest element. So R can neither be the smallest nor the largest element in the set, and the range of the new set must be equal to the range of the old set. Sufficient. C.
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