killerdrummer 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
Target question:
Is the mean of the new set less than the sum of means of sets S and T?
Statement 1: S and T are one-element sets
There are several sets that meet this condition. Here are two:
Case a: S = {2}, T = {3} and new set = {2,3}, in which case
the mean of the new set is less than the sum of means of set S and set T
Case b: S = {0}, T = {0} and new set = {0,0}, in which case
the mean of the new set is not less than the sum of means of set S and set T
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Neither set S nor set T contains negative numbers
There are several sets that meet this condition. Here are two:
Case a: S = {2}, T = {3} and new set = {2,3}, in which case
the mean of the new set is less than the sum of means of set S and set T
Case b: S = {0}, T = {0} and new set = {0,0}, in which case
the mean of the new set is not less than the sum of means of set S and set T
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
There are several sets that meet both conditions. Here are two:
Case a: S = {2}, T = {3} and new set = {2,3}, in which case
the mean of the new set is less than the sum of means of set S and set T
Case b: S = {0}, T = {0} and new set = {0,0}, in which case
the mean of the new set is not less than the sum of means of set S and set T
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
