Official Solution:If \(x\) is an integer such that \(x ≠ 1\) and \(x ≠ 0\), what is the value of \(\frac{|x| - 1}{x - 1}\)? (1) \(x^x < 0\)
Notice that \(x\) cannot be positive because \(positive^{positive}=positive\).
Also, notice that \(x\) cannot be negative even integer because \(negative^{even}=positive\)
So, above works for negative odd integers only: -1, -3, -5, ... Each of which give different value for \(\frac{|x| - 1}{x - 1}\). Not sufficient.
(2) \(\frac{|x|}{x}=-1\)
\(|x|=x\). This implies that \(x\) is negative. Different negative values give different values for \(\frac{|x| - 1}{x - 1}\). Not sufficient.
(1)+(2) The second statement adds no additional info to what we already knew from the first one, so even taken together the statements are not sufficient.
Answer: E