CAMANISHPARMAR wrote:
Set X consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Y consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Z consists of all of the members of both set X and set Y.
Which of the following statements must be true?
I. The standard deviation of set Z is not equal to the standard deviation of set X.
II. The standard deviation of set Z is equal to the standard deviation of set Y.
III. The average (arithmetic mean) of set Z is 37.
A) I only
B) II only
C) III only
D) I and III
E) II and III
Not a precise definition of SD, but close enough for the GMAT:
SD = average distance from the mean.
The prompt indicates that X and Y are each composed of consecutive odd integers.
They have the SAME MEAN but could have the SAME NUMBER of terms or a DIFFERENT NUMBER of terms.
Consider an easy case in which X and Y have the same mean and the SAME number of terms:
X = 1, 3, 5
Y = 1, 3, 5
Z = 1, 1, 3, 3, 5, 5
In this case, the average distance from the mean in Z is equal to the average distance from the mean in X, implying that the two sets have the same SD.
The case above illustrates the following:
If X and Y have the same number of terms, then Z and X will have the same SD.
Since Statement I does not have to be true, eliminate A and D.
Consider an easy case in which X and Y have the same mean but a DIFFERENT number of terms:
X = 1, 3, 5, 7, 9
Y = 3, 5, 7
Z = 1, 3, 3, 5, 5, 7, 7, 9
In this case, the values in Z deviate more from the mean than do the values in Y, implying that the two sets do NOT have the same SD.
The case above illustrates the following:
If X and Y have a DIFFERENT number of terms, then Z and Y will NOT have the same SD.
Since Statement II does not have to be true, eliminate B and E.