<< This Month's Problem
On the number line above, if c = –a, which of the following cannot be positive?
In figures without numbers or distance labels, don’t make assumptions about relative distances. In this figure, you can trust that a < b < c < d, but you cannot assume anything about how much greater b is than a or how much greater c is than b, etc. The text indicates that c = –a, which means those points have opposite signs. Since a < c, it must be that a is negative and c is positive (this would also imply that d is positive). Thus, zero is between a and c, and equidistant from both. Don’t assume that b is negative because it might appear to be closer to a than to c; zero might be on either side of b, since the figure is not necessarily drawn to scale.
So, a is definitely negative, c and d are definitely positive, but b could be either positive or negative.
(A) abd = (negative)(positive or negative)(positive) = negative or positive
(B) acd = (negative)(positive)(positive) = negative
(C) b2d = (positive or negative)2(positive) = (positive)(positive) = positive
(D) bcd = (positive or negative)(positive)(positive) = positive or negative
(E) cd2 = (positive)(positive)2 = positive
The correct answer is B.