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.

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