Bunuel wrote:
GMAT CLUB TESTS' FRESH QUESTION
Is the standard deviation of numbers x, y, and z, positive?
(1) The average (arithmetic mean) of x, y, and z, is less than x
(2) The median of x, y, and z, is greater than z
The SD will always be Greater Than or Equal to 0. It can never be Negative.{
Background Information:Case 1: SD=0
This means that all the elements of the set are the same.
Case 2: SD>0
This means that the all the elements of the set are not equal.}
Getting back to the Question:
Statement 1:(1) The average (arithmetic mean) of x, y, and z, is less than x
This means that atleast 1 element of the 3 is different than the rest 2.
Therefore, the SD >0.
Statement 2: The median of x, y, and z, is greater than z
This means that at least z is different than x or y
This implies that atleast on e element is different in the set.
Therefore, SD >0.
Hence,
the answer is D.
Please Note that the probability of GMAT asking test takers to calculate the value of SD is very low. However, it does asks questions on the basics of SD.
This is a very good question testing the basics of GMAT.
_________________
~R.
If my post was of any help to you, You can thank me in the form of
Kudos!!
Applying to ISB ? Check out the
ISB Application Kit.