RACHVIK 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 Set A are positive.
(2) The mean of the new set is smaller than R.
Answer after soem discussion...
Is there an easy systematic approach??
I received a PM asking me to comment.
Let A = {L,H}. L = lowest value, H = highest value.
R = H-L = value to be added to the set.
If L and H are negative, then the inclusion of R (which is positive, since the range of a set is by definition positive) will increase the range.
If L and H are positive, then in order for the range to increase when R is added, it must be true that R < L.
Thus, for the range to increase:
H-L < L
H < 2L.
So, given two positive numbers in A, the question can be rewritten:
Is H < 2L?
Statement 1: All the numbers in set A are positive.
No way to determine whether H < 2L.
Insufficient.
Statement 2: The mean of the new set is smaller than R.
Let M = mean of new set.
M = (H + L + (H-L))/3 = 2H/3.
If all the numbers are negative, then M = 2H/3 will be negative no matter what values are chosen. As noted above, if L and H are negative, then the inclusion of R (which is positive) will increase the range.
If all the numbers are positive, since M < R, we get:
2H/3 < H-L
2H < 3H - 3L
H > 3L.
If all the numbers are positive and H > 3L, then it is not true that H < 2L, so the inclusion of R will not increase the range.
Insufficient.
Statements 1 and 2 together:
If all the numbers are positive and H > 3L, then it is not true that H < 2L, so the inclusion of R will not increase the range.
Sufficient.
The correct answer is
C.
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