Does a positive or negative charge attract a neutral object? 
Three objects are brought close to each other, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude that:
  (a) objects A and C possess charges of the same sign. 
  (b) objects A and C possess charges of opposite sign. 
  (c) all three of the objects possess charges of the same sign. 
  (d) one of the objects is neutral. 
  (e) we need to perform additional experiments to determine information about the charges on the objects.

From this question, I thought we can create two scenarios:
scenario 1: A: + 
B: - 
C: - 
scenario 2:A: - 
B: + 
C: + 
A and B attract, so I thought they have to be opposite signs.  B and C repel, so they must be the same sign.  I was surprised when I saw solutions, the selected answer was just (e).

Answer: (e). In the first experiment, objects A and B may have charges with opposite signs, or one of the objects may be neutral. The second experiment shows that B and C have charges with the same signs, so that B must be charged. But we still do not know if A is charged or neutral.

I thought a neutral charged object would have no affect.  Since when does a neutral charge and charged object attract?  Is this implying that two objects with a neutral charge and an object that is positive or negative will attract?  And is this attractive referring to induction?
A: This is the phenomenon of electrostatic induction.
Since "neutral" objects are made out of many positive and negative charges in equal measure, some of which can move, the presence of an electric field from a charged object will move these charges, and result in a region of opposite (to the object creating the field) charge where the neutral object is nearest to the charged object, and this will indeed result in an attraction between the formerly neutral object and the charged object.
Therefore, you cannot conclude from the attraction of two conducting objects that they must have the opposite charge - one of them may well be uncharged.
