old PSAT math question... CB answer incorrect?

<p>the question:</p>

<p>Which of the following lists of numbers must the average (mean) of the numbers be 20 percent of the sum of the numbers?</p>

<p>I. v and w
II. v, w, x, and y
III. v, w, x, y, and z</p>

<p>a. none
b. I
c. II
d. III
e. II and III</p>

<p>The answers from the CB say the correct choice is D (set III). However, upon closer examination, if the sum of the numbers of set III is 0 (e.g. {-2,-1,0,1,2}) then the arithmetic mean is the same number, 0, not 20% of the number, making A correct (or at least so I thought).</p>

<p>.2*0 = 0 (anything times 0 is 0).</p>

<p>And I over-analyze things too much... derp</p>