If abc > 0, such that a,b,c are integers then which of the following must be true?

If abc is positive, it can have two cases:

Case 1: when all three integers are postive

Case 2: when any two are negative and the third is positive (as the two negative will cancel while multiplying)

We need to find the option which must be true:

Option 1: $$\dfrac{a}{b} < 0$$

It is not necessary that one of a and b is negative and the other one is positive. It can be possible that but both a and b are negative and hence the fraction can be greater than 0. Therefore, this option is not necessarily true. 

Option 2: $$\dfrac{ab}{c} > 0$$

Here, if all the three integers are positive then the expression will definitely be greater than 0. On the other hand, if any two are negative the according to the expression, the negatives will cancel out and the expression will again be greater than 0. Hence, this option must be true. 

Option 3: $$bc < 0$$

Same as option 1, it is not necessary that one of  b and c is negative and the other one is positive for the expression to be true. There can also be the possibility when both are negative and the product can be greater than 0 in that case.

Option 4: $$a > bc$$

We don't know the numeric values so we can't say that a will be greater than the product of b and c necessarily.