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Chembeti
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Bunuel
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?

Welcome to GMAT Club.

I think you misunderstood the statement: it's \((x^2)*z<0\) not \(x^{(2z)}<0\): 2 is an exponent and z is a multiple and not that 2z is an exponent.

Hope it's clear.
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Ahhh! Thanks for the clarification! This changes everything! :)
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Bunuel
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.


If X was a +ve fraction?
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Sri07
Bunuel
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.


If X was a +ve fraction?

What exactly do you mean? From (1)+(2) we get that x > z, no matter whether x is a fraction or not.
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