If n ≠ 0, which of the following could be true?
I. 2n < n2 T>
II. 2n < n
III. n2
A. None.
B. I only.
C. I and II only.
D. I and III only.
E. I, II, and III.
Take control -- put in your own numbers. This is a COULD question, so you will want to try several different numbers to attempt to make I, II, and III true.
The exponents might have tipped you off that a negative fraction would be a good choice. Putting in –1/2 for n we find:
I. 2n = 2(–1/2) = –1 < n2 =(–1/2)2 = 1/4. TRUE
II. 2n = 2(–1/2) = –1 < n = –1/2. TRUE
III. n2 = (–1/2)2 = 1/4 < –n = –(–1/2) = 1/2. TRUE
Thus, I, II, and III COULD be true.