Bunuel wrote:
A set of integers, S, contains more than one element. Is the range of S greater than its mean?
(1) S does not contain positive integers.
(2) The mean of S is negative.
Nice question!
Given: Set S, contains more than one element. Target question: Is the range of set S greater than its mean? Statement 1: S does not contain positive integers. Key property: 0 is neither negative nor positiveThere are many sets that satisfy statement 1. Here are two:
Case a: Set S = {0, 0}, in which case the range = 0, and the mean = 0. In this case, the answer to the target question is
NO, the range is not greater than the meanCase b: Set S = {-1, -1}, in which case the range = 0, and the mean = -1. In this case, the answer to the target question is
YES, the range is greater than the meanSince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The mean of S is negative.The range of any set of numbers is always greater than or equal to 0So, if the mean of set S is
negative, we can be certain that
the range is greater than the mean.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent