BrentGMATPrepNow wrote:
Is the standard deviation of set X greater than the standard deviation of set Y?
(1) Set Y consists of 3 different negative integers.
(2) The range of set X is 0.
Since no one has answered this question yet, here's my solution....
Target question: Is the standard deviation of set X greater than the standard deviation of set Y? Key property #1: If all of the numbers in a set are the same, the standard deviation of that set is zero
Key property #2: If the numbers in a set are NOT all the same, the standard deviation of that set is greater than zero Statement 1: Set Y consists of 3 different negative integers. Since the three numbers are different, we know (from
property #2) about the standard deviation of set Y is greater than zero.
Since we have no information about set X, it's impossible to determine whether
the standard deviation of set X is greater than the standard deviation of set YSince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The range of set X is 0If the range is zero, then all of the values in set X must be the same.
So, (from
property #1), we know that
the standard deviation of set X must be zero. Important: Even though we have no information about set Y, we can still answer the
target question with certainty. Here's why:
Since all standard deviations are greater than or equal to 0, we know that the standard deviation of set Y is EITHER zero OR greater than zero. Let's examine both cases:
- If the standard deviation of set Y is 0, then the answer to the target question is
NO, the standard deviation of set X is NOT greater than the standard deviation of set Y- If the standard deviation of set Y is greater than 0, then the answer to the target question is
NO, the standard deviation of set X is NOT greater than the standard deviation of set YSince both cases yield the SAME answer to the target question, we know that we can answer the
target question with certainty.
So, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent