Data Sufficiency

[GMAT math practice question]

If the average (arithmetic mean) of 5 numbers is 21, what is their standard deviation?

1) The least of the 5 numbers is 21
2) The greatest of the 5 numbers is 21

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

If the maximum or minimum value of a data set is the same as its average, then all data points are equal and their standard deviation is 0.
Thus, each of the conditions is sufficient.

Therefore, D is the answer.
Answer: D

Recall the property that the SD is zero if the maximum value or the minimum value is the same as the average, as this implies that all data points are equal.
Questions related to the above property have appeared frequently on recent GMAT exams.