\vec{E}=-(\frac{\partial V}{\partial x}\hat{i}+\frac{\partial V}{\partial y}\hat{j}+\frac{\partial V}{\partial z}\hat{k})
in the question, it is given as\left|\frac{\partial V}{\partial x} \right|=10
i think i made a mistake in #2, thinking that derivatives are zero at co-ordinates 0,
i think this is the correct explanation
so, |E|=10 wherever \frac{\partial V}{\partial y}=\frac{\partial V}{\partial z}=0
since we have no information about the other derivatives, the statement is false