|x| > 1

|z| > 1

is z^x <1

(1) x < 0

If x = -2 ,

z=2 then z^x = 2^(-2)= 1/(2^2) = 1/4 <1

z=-2 then z^x = (-2)^(-2)=1/(-2^2)=1/4 < 1

if x=-3 ,

z=3 then z^x= 3^(-3) = 1/(3^3) = 1/27 <1

z=-3 then z^x = (-3)^(-3) = 1/(-3^3) = -1/27<1

Sufficient

(2) z^z < 1

=> z is negative , z^x <1 will depend on x .

if z=-2 , then z^z = (-2)^(-2) = 1/(-2^2)= 1/4 <1

if z=-3 , then z^z=(-3)^(-3) = 1/(-3^3) = -1/27<1

However , we have no information about x .

Not sufficient

Answer A

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