Data Sufficiency

Hello vjesus12.

Here we are asked if zc > zf? Let's see how can we respond this question.

(1) z^3*c > z^3*f

$$z^3\cdot c>z^3\cdot f\ \ \ \ \ \Leftrightarrow\ \ \ \ z^3\cdot c\ -\ z^3\cdot f\ >0$$ $$\Rightarrow\ \ \ z^2\left(zc\ -\ zf\ \right)>0$$ $$\Rightarrow\ \ \ zc\ -\ zf\ >0\ \ \ \text{since}\ \ z^2\ge0\ always$$ $$\Rightarrow\ \ \ zc\ >zf\ .\ \ \ \ SUFFICIENT$$ Hence, this statement is sufficient.

(2) z is less than 10

Here, we don't have information about "c" and "f". Therefore, this statement is NOT sufficient.

In conclusion, the correct answer for this DS question is the option A.

I hope it helps you.