Bunuel wrote:

Is 3x − y + z greater than 2x − y + 2z?

Is \(3x-y+z>2x-y+2z\)? --> is \(x>z\)?

(1) x is positive. No info about \(z\). Not sufficient.

(2) x^2*z is negative --> \(x^2*z<0\) --> \(z\) is negative, but limited info about \(x\) (we only know that \(x\neq{0}\)). Not sufficient.

(1)+(2) From (1) \(x\) is positive and from (2) \(z\) is negative --> \(x>z\). Sufficient.

Answer: C.

How did you deduce z must be negative?

From exponent rule, \(b^(-n)\) is \(1/b^n\). This will always be positive if n is even, regardless of the base. Since \(n = 2z\), \(x^(2*z)\) will always be positive, which contradicts the original statement #2. Am I missing something here?