nalinnair wrote:

A certain list consists of 400 different numbers. Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?

(1) Of the numbers in the list, 280 are less than the average.

(2) Of the numbers in the list, 30 percent are greater than or equal to the average.

We need to determine whether the average (A) of the 400 numbers in the list is greater than the median (M). Note that since there are 400 numbers in the list, the median is the average of the numbers in the 200th and 201st spots when the numbers are listed in increasing order.

Statement One Alone:

Of the numbers in the list, 280 are less than the average.

Since 280 of the 400 numbers are less than the average, the numbers in the 200th and 201st spots are both less than A. Therefore, the median M is less than the average A. Statement one alone is sufficient to answer the question.

Statement Two Alone:

Of the numbers in the list, 30 percent are greater than or equal to the average.

Since there are 400 numbers in the list, this statement is actually saying (0.3)400 = 120 numbers are greater than or equal to the average, which is equivalent to saying 400 - 120 = 280 numbers are less than the average. By our analysis of statement one, we already know that this information is enough to answer the question. Statement two alone is sufficient to answer the question.

Answer: D

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