What is the value of z/x?

\(\frac{z}{x}\) =?

Statement 1:
2x - y + 3z = 5
If we try to find out the value of \(\frac{z}{x}\), it will always be in terms of y for the given equation.
Statement 1 is Not Sufficient.

Statement 2:
x + 2y - z = -10
Here also, if we try to find out the value of \(\frac{z}{x}\), it will always be in terms of y for the given equation.
Statement 2 is also Not Sufficient.

Statement 1 and Statement 2 combined:
2x - y + 3z = 5 and x + 2y - z = -10
Multiplying first equation by 2 and adding it to second equation, we get:
(4 + 1)x + (-2 + 2)y + (6 - 1)z = 10 - 10
=> 5x + 5z = 0
=> x + z = 0
=> z = -x
=> \(\frac{z}{x}\) = -1
But if either of x or z is 0, then \(\frac{z}{x}\) can be not defined or 0 respectively.
Statement 1 and Statement 2 together are Not Sufficient.

So, correct answer is option E.

No, we should not. For an answer to be C, it should be mentioned that \(xz \neq 0\). In current form the answer is E, because of x = z = 0, then z/x would be undefined and not -1.