Let's analyse the question statement
z & x are integers. And |z| & |x|>1. This means z & x are not equal to 0. Thus, z & x are positive or negative integers and not equal to 0.
Now, \(z^x\) <1 only in following cases:
a) z>0 and x<0: i.e. z=2 & x=-2. Which means \(z^x\)=\(2^-2\)=\(1/4\)<1
b) z<0 and x<0: i.e. z=-2 & x=-2. Which means \(z^x\)=\(-2^-2\)=\(1/4\)<1 or z=-2 & x=-1. Which means \(z^x\)=\(-2^-1\)=\(-1/2\)<1
c) z<0 and x is positive odd integer. Which means \(z^x\)=\(-2^1\)=\(-2\)<1
With these in mind, let's check statements.
1) x<0, this means that first two cases discussed above are applicable. Checking on those, we can understand that for any value of z (positive or negative), \(z^x\)<1, given x<0. This statement is sufficient
2) \(z^z\) < 1. Applying the three cases discussed above, we can sum up that either this condition holds true only if z is negative. But, for \(z^x\)<1, we need to know value of x. Thus, this statement is insufficient.
Hence, answer is A
_________________
Hit Kudos if you like my answer!