Problem:
If x<0, then which of the following must be positive?
Answer Choices:
A. ∣x∣x
B. −x2
C. −2x
D. −x−1
E. 3x
Solution:
Choice (D) may be written as −x1. If x is negative, choice (D) is positive. To see that the other choices need not be positive, let x=−1 and then
(A) ∣−1∣−1=−1 (B) −(−1)2=−1 (C) −2−1=−21 (E) 3−1=−1
The problems on this page are the property of the MAA's American Mathematics Competitions