I recalled the leering drunken old man, the toil-worn face of the dead woman -- and I shivered a little at the remorselessness of time...
-- Hastings (chapter 6)

Importance: This quote shows the happenstance at which the first victim was picked. The word 'remorselessness' shows that time is cruel and that the happenstance of this murder is likewise, as cruel. Hastings is wondering about the luck of some people over others. Why this woman had to deal with a drunken ex-husband, and why she was picked to die.

My friend, we are in the peculiar position of not knowing what questions to ask. We are like little children playing cache-cache in the dark."
-- Poirot (chapter 6)

Importance: Poirot's underlying message in this line is that he feels like everything is out of his control. Like a child, Poirot is not in charge and cannot say what will happen next. He feels that there is nothing more to do...