If X'>'Y^2'>'Z^4, which of the following statements could be true:
I. X '>' Y '>' Z (easy)

II. Z '>' Y '>' X

III. X '>' Z '>' Y
A. I only

B. I and

II only

C. I and III only

D. II and III only

E. I, II and III


you can take 3 cases, 1. When X,Y,Z are positive integers in that case: I. X '>' Y'>' Z holds true
2. When X, Y, Z are fractions: Z '>' Y '>' X 1/2 '>' 1/3 '>' 1/4 X'>'Y^2'>'Z^4 1/4 '>' 1/9 '>' 1/16
3. X '>' Z '>' Y (Negative, positive) 20 '>' -3 '>' -4 X'>'Y^2'>'Z^4 20 '>' 16 '>' 9

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note that number plugging is NOT random. whenever you do number plugging in a number properties problem, you have to figure out what types of numbers will have different effects upon the problem. in this case, you're considering both even and odd powers, and you're comparing those powers. therefore, you must consider signs (because there are both even and odd powers) AND fractions (because power comparisons are reversed with fractions). plug numbers accordinglyTherefore answer is E.