6983manish wrote:If sets S and T are united into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?
1. S and T are one-element sets
2. Neither set S nor set T contains negative numbers
(1) Let S = 2, T = 3, then combined set = {2, 3}; (2 + 3)/2 = 2.5 < 5; here mean of combined set is smaller than the sum of means of sets S and T.
Let S = -2, T = -3, then combined set = {-2, -3}; (-2 - 3)/2 = -2.5 > -5; here mean of combined set is greater than the sum of means of sets S and T.
No unique answer.
So, (1) is NOT SUFFICIENT.
(2) This statement only reflects that the elements of both the sets do not contain negative numbers, without stating the no. of elements in each set. So, clearly this info is NOT SUFFICIENT again.
Combining (1) and (2), If S = 2, T = 3, then combined set = {2, 3}; (2 + 3)/2 = 2.5 < 5; here mean of combined set is smaller than the sum of means of sets S and T.
If S = T = 0, then mean of combined set is equal to the sum of means of sets S and T.
No unique answer. So, combining is also NOT SUFFICIENT.
The correct answer is
E.
