The Official SAT Question of the Day™

Read the following SAT test question, then click on a button to select your answer.

A list of 100 integers has the property that the average (arithmetic mean), a, of the integers is greater than the median, m, of the integers. Which of the following must be true?

I. More of these integers are greater than a than are less than a.
II. More of these integers are greater than m than are less than m.
III. More of these integers are less than m than are greater than m.

A. None
B. I only
C. II only
D. I and II
E. I and III

Correct Answer: A

Here's Why:

If the 100 integers are ordered from least to greatest, the median, m, is found by taking the average of the 50th and 51st numbers in the ordered list. Suppose the list of integers is -1 (98 Zeros) 101. Then the average, a, of the integers is -1+101/100 = 1 , and the median, m, is equal to 0. So a > m, and the list satisfies the conditions given in the question. For this list, 1 term is greater than a, and 99 terms are less than a, so statement I is not true. Also, 1 term is greater than m, and 1 term is less than m, so neither statement II nor statement III is true. Thus, for this list, none of the given statements is true. Therefore, the correct answer is choice (A), none of the statements must be true.


Difficulty: Hard
Question Type: Standard Multiple Choice

(Mathematics)