Solution for the inequality: $(x-1)(x-2)(x-3)>0$ Recently I came across an inequality like this:
$$(x-1)(x-2)(x-3)>0$$
The question was: Which solution for this in inequality is correct?


*

*$x>3$ or $x<1$ 

*$x>3$ or $1<x<2$ 

*$x<1$ or $2<x<3$ 

*There are no solutions


There was a timelimit of 3 minutes for solving this. I freaked out a  bit as I haven't worked that much with these kind of inequalities yet. I thought about multiplying out the terms on the left side, and then checking the solutions, but even after I tried that on paper, there is no way I could have done that in 3 minutes under pressure. 
What is the expected, fast way to solve this inequality? Or was it just expected to "see" it, based on the given solutions?

Draw an axle from left to right, and mark 1, 2, 3 on it. Put a point for x at 0. then move x from left to right. 
When x < 1, x is at the left of 1, 2, and 3, therefore (x-1), (x-2), and (x-3) are all negative. We know answer (1) and (3) is not right.
When x > 3, x is at the right of 1, 2, and 3, therefore (x-1), (x-2), and (x-3) are all positive. This is a solution, at least. Then We know answer (4) is not right.
